bluuebunny/crossref_metadata_2025 huggingface dataset:
The effect of typhoon on particulate organic carbon flux in the southern East China Sea
Authors: Hung C.-C. , Gong G.-C. , Chou W.-C. , Chung C.-C. , Lee M.-A. , Chang Y. , Chen H.-Y. , Huang S.-J. , Yang Y. , Yang W.-R. , Chung W.-C. , Li S.-L. , Laws E.
Published: May 2010

Abstract. Severe tropical storms play an important role in triggering phytoplankton blooms, but the extent to which such storms influence carbon flux from the euphotic zone is unclear. In 2008, typhoon Fengwong provided a unique opportunity to study the in situ biological responses including phytoplankton blooms and particulate organic carbon fluxes associated with a severe storm in the southern East China Sea (SECS). After passage of the typhoon, the sea surface temperature (SST) in the SECS was markedly cooler (~25 to 26 °C) than before typhoon passage (~28 to 29 °C). The POC flux 5 days after passage of the typhoon was 265 ± 14 mg-C m−2 d−1, which was ~1.7-fold that (140–180 mg-C m−2 d−1) recorded during a period (June–August, 2007) when no typhoons occurred. A somewhat smaller but nevertheless significant increase in POC flux (224–265 mg-C m−2 d−1) was detected following typhoon Sinlaku which occurred approximately 1 month after typhoon Fengwong, indicating that typhoon events can increase biogenic carbon flux efficiency in the SECS. Remarkably, phytoplankton uptake accounted for only about 5% of the nitrate injected into the euphotic zone by typhoon Fengwong and it is likely that phytoplankton population growth was presumably constrained by a combination of light limitation and grazing pressure. Modeled estimates of new/export production were remarkably consistent with the average of new and export production following typhoon Fengwong. The same model suggested that during non-typhoon conditions approximately half of the export of organic carbon occurs via convective mixing of dissolved organic carbon, a conclusion consistent with earlier work at comparable latitudes in the open ocean.
Altered response to nitrogen supply of mixed grassland communities in a future climate: a controlled environment microcosm study
Authors: Van den Berge J. , Naudts K. , Zavalloni C. , Janssens I. A. , Ceulemans R. , Nijs I.
Published: May 2010

Abstract. Few studies have investigated whether responses to nutrient supply of mixed plant communities change under combined elevated CO2 and climate warming. In this study we analyzed the response of constructed temperate grassland communities to five levels of nitrogen (N) supply, ranging from 0 to 150 kg N ha−1, under two climate scenarios. Biomass of the plant communities responded positively to N supply in the current climate, but was insensitive to N supply in the future climate. This altered response was not the result of a changing response from a single species, but all species seemed to contribute to it. The weaker response in the future climate was caused by changes in N uptake rather than by changes in nitrogen use efficiency, as community N stocks showed the same response pattern as community biomass. Climate change apparently modified the relation between fertilizer N addition and plant available N.
B
lack,
F
ischer
Authors: Mehrling Perry
Published: May 2010

The central focus of the career of Fischer Black (1938–1995) was on teasing out the implications of the capital asset pricing model (CAPM) for the changing institutional framework of financial markets of his day. He became famous for the Black–Scholes options formula, an achievement that is now widely recognized as having opened the door to modern quantitative finance and financial engineering.
S
harpe,
W
illiam
F
.
Authors: Boyle Phelim
Published: May 2010

This is a brief summary of two of the major contributions of William F. Sharpe to modern financial economics. Sharpe developed the Capital Asset Pricing Model (CAPM) which is an equilibrium relationship between the expected return on a security and the expected return on the market portfolio. The CAPM is a cornerstone of modern finance. Sharpe also introduced the Sharpe ratio which is an elegant and compact risk‐adjusted measure of portfolio performance. The Sharpe ratio plays an important theoretical role in modern continuous‐time finance.
Markowitz, Harry
Authors: Mehta Nina
Published: May 2010

Harry Markowitz, whose now‐famous “Portfolio Selection” paper appeared in the March 1952 issue of the
Journal of Finance
, went on to win the Nobel Prize in Economic Sciences in 1990 for providing the cornerstone to what came to be known as
modern portfolio theory
. He shared the Nobel Prize with Merton H. Miller and William F. Sharpe. Markowitz's imaginative leap was to look at risk as the variance of the portfolio's returns, and to understand that a diversified portfolio lowers risk without forsaking returns. He came up with what was eventually known as the
efficient frontier
to describe the set of portfolios that provides the least risk for a given level of expected return or the highest expected return for a given level of risk. Markowitz's portfolio theory revolutionized the way investors looked at the trade‐off between risk and reward. It also transformed the investment business by enabling investment managers to construct diversified portfolios and to rigorously measure the performance of those portfolios. Two other areas where Markowitz has made significant contributions are in sparse matrices and a simulation language called
SIMSCRIPT
.
Arbitrage: Historical Perspectives
Authors: Poitras Geoffrey
Published: May 2010

This article discusses the history of arbitrage from ancient times until the beginning of the twentieth century. Opportunities for arbitrage trading in ancient times were related to the movement of goods over long distances. The key role of the bill of exchange in arbitrage trading during the Middle Ages is identified and the connection to “arbitration of exchange” is discussed. A seventeenth‐century arbitrage involving the gold and bill of exchange markets is detailed. As reflected in merchant manuals of that period, the connection between riskless arbitrage trading and the method of conducting arbitration of exchange in the eighteenth and nineteenth centuries is detailed. An overview of nineteenth century arbitrage trading in securities and commodities is also provided. The article concludes with an examination of the etymology and historical usage of the word “arbitrage” and the associated “arbitration of exchange”.
Itô, Kiyosi (1915–2008)
Authors: Stroock Daniel W.
Published: May 2010

This is a brief account of Itô's mathematical carrier by someone who was fortunate enough to know him.
Thorp, Edward
Authors: Boyle Phelim
Published: May 2010

This article reviews the contributions of Edward Thorp to games of chance and investment science. Thorp invented original methods for playing blackjack and also made seminal contributions to the pricing and hedging of derivatives, hedging of warrants, and other areas of mathematical finance.
Efficient Markets Theory: Historical Perspectives
Authors: Jovanovic Franck
Published: May 2010

Efficient market hypothesis (EMH) has been crucial in the creation of financial economics as a proper subfield of economics. What we know today as the EMH was formulated in the period from 1959 to 1976 to give a theoretical explanation to the random character of stock market prices, a feature that had been noted as early as 1863. But the main characteristic of the EMH lies in linking three elements that originally existed independently of each other: (i) the mathematical model of stochastic process; (ii) the concept of economic equilibrium; (iii) the statistical results about the unpredictability of stock market prices. Although debate continues about the interpretation and characterization of the EMH, the link between these three elements allowed the creation of financial economics.
Econophysics
Authors: Daniel Gilles , Sornette Didier
Published: May 2010

Econophysicsdesignates the modeling of economic systems as complex, self‐organized systems using tools from physics. This brief historical survey emphasizes thateconophysicshas many historical precursors and is, in fact, rooted in a continuous cross‐fertilization between economics and physics that has been active in the last centuries.
Treynor, Lawrence Jack
Authors: Namvar Ethan
Published: May 2010

Jack L. Treynor, a pioneer in the use of quantitative methods in finance, helped establish the foundation of academic research in the field of finance and promoted notions such as random walks, efficient markets, risk/return trade‐off and betas that others in the field actively avoided. Treynor is renowned not only for pushing the envelope with new ideas, but also for encouraging others to do the same as well. His articles have also received widespread acclaim in the finance and business communities. In 2008, the International Association of Financial Engineers (IAFE) named him as the 2007 IAFE/SunGard Financial Engineer of the Year.
Fractional Brownian Motion
Authors: Marquardt Tina M.
Published: May 2010

A fractional Brownian motion (fBm) is a self‐similar Gaussian process characterized by its Hurst parameterH ∈ (0, 1). In particular, it is a process with stationary increments which are long‐range dependent forH > 0.5. Unless,H = 0.5 (when fBm is a Brownian motion), it is not a semimartingale, and hence, integrals with respect to fBm cannot be definedviaItô calculus. Models based on fBm have been used in various fields of application such as economics, finance, turbulence, and telecommunications.
Lévy Processes
Authors: Kyprianou Andreas E.
Published: May 2010

We give a brief introduction to the class of stochastic processes known asLévy processes, concentrating principally on their relation with infinitely divisible distributions and the Lévy–Itô decomposition.
Wiener–Hopf Decomposition
Authors: Kyprianou Andreas E.
Published: May 2010

We give a description of Wiener–Hopf factorization from the point of view of excursion theory, first for random walks and then in the case of Lévy processes. The exposition relies primarily on the ideas of Greenwood and Pitman.
Poisson Process
Authors: Jeanblanc Monique
Published: May 2010

We present the main properties of standard Poisson processes, and the notion of stochastic integral with respect to a Poisson process. Some particular martingales are studied and a representation theorem is given. We extend our presentation to compound Poison processes.
Point Processes
Authors: Jeanblanc Monique
Published: May 2010

We present marked point processes, which are an extension of compound Poisson processes. A representation theorem is given, which allows to write any martingale in the filtration of a marked point process as an integral with respect to the compensated martingale. We briefly present general point processes.
Compensators
Authors: Jeanblanc Monique
Published: May 2010

We present the notion of compensator of a random time and give applications related to reduced form approach of credit risk modeling. We also study compensated random measures.
Filtrations
Authors: Coculescu Delia , Nikeghbali Ashkan
Published: May 2010

In this article, we define the notion of a filtration and the related notion of the usual hypotheses. We then explain the problem of enlargements of filtrations: how are (semi)martingales affected under a change of filtrations? We state the main theorems in the classical frameworks of initial and progressive enlargements of filtrations. In the case of initial enlargements of filtrations, we state the well known Jacod's condition and in the framework of progressive enlargements of filtrations, we give the decomposition of a local martingale in the larger filtration. We finally specialize to the case of immersed filtrations, which is very widely used in credit risk modeling, and study the effect of a combination of changes of filtration and probability measure in this situation.
Local Times
Authors: Eisenbaum Nathalie
Published: May 2010

Local time is defined for real Brownian motion, semimartingales, and Markov processes. Some basic properties are given.
Stochastic Integrals
Authors: Çetin Umut
Published: May 2010

Stochastic integrals are first defined with respect to Brownian motion for left‐continuous integrands and then extended to semimartingale integrators and predictable integrands. The conditions under which stochastic integration preserves the martingale property are discussed. Further general properties of stochastic integrals as well as Itô's formula are given.
Doob–Meyer Decomposition
Authors: Kallsen Jan
Published: May 2010

Submartingales are processes that grow on average. Subject to some condition of uniform integrability, they can be written uniquely as the sum of a martingale and a predictable increasing process. This result is known as the
Doob–Meyer decomposition
.
Forward–Backward Stochastic Differential Equations (
SDEs
)
Authors: Zhang Jianfeng
Published: May 2010

In this article, we introduce the basic theory of forward–backward stochastic differential equations (FBSDEs), including both decoupled and coupled ones. In the Markovian case, FBSDEs are closely associated with parabolic partial differential equations (PDEs),
via
the so‐called nonlinear Feynman–Kac formula. We also introduce several typical applications of FBSDEs, most notably in option pricing theory and in stochastic control.
Martingale Representation Theorem
Authors: Ma Jin
Published: May 2010

This note gives a brief history of the “martingale representation theorem”, one of the most powerful and fundamental theorems in stochastic calculus. Various forms of the theorem are presented so that a broad picture of the theorem can be seen from different perspectives. Some new extensions of the theorem, especially those connected to mathematical finance theory, are provided at different levels of depth as pointers for future study.
Backward Stochastic Differential Equations
Authors: Quenez Marie‐Claire
Published: May 2010

Backward stochastic differential equations (BSDEs) are stochastic differential equations where the terminal condition is a given random variable. We give the main properties of BSDEs and some classical applications to the pricing and hedging of European derivatives, risk measures, and recursive utilities. We also present reflected BSDEs and their application to the pricing of American options.
Stochastic Exponential
Authors: Rheinländer Thorsten
Published: May 2010

Let
X
be a semimartingale with
X
0
 = 0. Then there exists a unique semimartingale
Z
that satisfies

urn:x-wiley:9780470061602:media:eqf02022:xm1

It is called the
stochastic exponential
of
X
and is denoted by ℰ(
X
).
Semimartingale
Authors: Podolskij Mark
Published: May 2010

In this article, we present the basic notions of the semimartingale theory. We start with two equivalent definitions and state some simple examples. We proceed with the definition of the quadratic variation, which is one of the most important objects in the semimartingale theory. Semimartingales turn out to be invariant under some transformations: under change of measure (Girsanov's Theorem), under certain changes of filtration (Stricker's Theorem, Jacod's Countable Expansion), and under
C
2
‐transformation (Itô's Formula).
Capital Asset Pricing Model
Authors: Gatfaoui Hayette
Published: May 2010

Financial markets build regulated structures whose role is to provide market participants with continuous liquidity among others. By nature, they are composed of dependent elements, which have to conform to the prevailing regulation for stability prospects. Therefore, the financial flows resulting from such markets are mutually dependent to some extent. Here is the cornerstone underlying the seminal theory proposed by William Sharpe (1963, 1964) with the capital asset pricing model (CAPM). A nonnegligible portion of financial asset prices results then from the broad market trend, namely, the propensity of security prices to move together and at the same time. The complementary part or residual part of financial asset prices depends consequently on the specific features peculiar to each financial asset or, at least, to each financial asset class a security can belong to. Of course, the residual part of asset prices is totally different and independent from the broad market trend. This setting yields William Sharpe to propose a model pricing the expected asset return as a function of the risk‐free rate, the expected market risk premium, and the strength of the link prevailing between the asset return and the broad market return as represented by the market portfolio.
Stochastic Discount Factors
Authors: Kardaras Constantinos
Published: May 2010

The valuation process that economic agents undergo for investments with uncertain payoff typically depends on their statistical views regarding possible future outcomes, their attitudes toward risk, and, of course, the payoff structure itself. Yields vary across different investment opportunities and their interrelations are difficult to explain. For the same agent, a different discounting factor has to be used for every separate valuation occasion. If, however, one is ready to accept discounting that varies randomly with the possible outcomes, and therefore accepts the concept of a stochastic discount factor, then an economically consistent theory can be developed. Asset valuation becomes a matter of randomly discounting payoffs under different states of nature and weighing them according to the agent's probability structure. The advantages of this approach are obvious, since a single discounting mechanism suffices to describe how any asset is priced by the agent.
Utility Function
Authors: Marinacci Massimo
Published: May 2010

This article introduces the reader to modern utility theory.
Recursive Preferences
Authors: Schroder Mark
Published: May 2010

This article reviews the continuous‐time optimal portfolio and consumption problem for an agent with recursive utility in a financial market with information generated by Brownian motion. We allow trading constraints, nontradeable income, and nonlinear wealth dynamics. We present the general solution approach and first‐order conditions, as well as specializations to the scale‐invariant (homothetic) and translation‐invariant classes of preferences.
Risk Aversion
Authors: Montesano Aldo
Published: May 2010

The decision‐making situation under risk is defined and the certainty equivalent of a lottery with unidimensional outcomes is introduced. An agent is globally risk averse if the risk premium (defined as the difference between the expected value and the certainty equivalent) of every lottery is nonnegative. This definition is used to show some characteristics of the certainty equivalent function that are associated with risk aversion. Risk aversion is equivalent to concavity of utility function if the expected utility theory holds. The comparison of risk aversion across agents is also examined. The notion of local risk aversion is introduced in general and with respect to the expected utility case, where again it is equivalent to concavity of utility function. A measure of risk aversion, if expected utility theory holds, is provided by the de Finetti–Arrow–Pratt index. Aversion toward increases in risk, that is, preference for less risky lotteries, is then examined with respect to two ways that increase risk: mean preserving spreads and probability mixtures. The equivalence of the former with second‐order stochastic dominance is examined. Finally, risk aversion and aversion to increasing risk with reference to the rank‐dependent expected utility model are examined mainly to show a kind of risk aversion (first‐order risk aversion) that is stronger than the risk aversion permitted by the expected utility theory (second‐order risk aversion).
Risk Premia
Authors: Verdelhan Adrien
Published: May 2010

Risk premia are, by definition, expected excess returns that compensate investors for aggregate risk. There is now a wealth of empirical evidence on risk premia. Expected excess returns in equity, bond, and currency markets appear sizable and time‐varying. However, few models reproduce these findings. Only three classes of models can currently account for such risk premia: habit preferences, long‐run risk, and disaster risk models.
Predictability of Asset Prices
Authors: Xu Yexiao
Published: May 2010

A large literature has been devoted to address the issue whether security markets are predictable. This is an enormously important question from both practitioners' perspective in exploring investment opportunities and academia to understand whether capital markets are informationally efficient and how asset allocation decisions will be affected. In this article, some of the important theories either for or against the case of predictability are reviewed. From the existing evidence, it is believed that the US equity markets as a whole are predictable to some extent.
Real Options
Authors: Ruffino Doriana
Published: May 2010

Real options theory consists of identifying and valuing firm investments under uncertainty. The techniques derived from financial options pricing have been precious tools for modeling the managerial operating flexibility ignored by conventional quantitative approaches. By explicitly incorporating management flexibility into the analysis, real options have improved the valuation of corporate resources and capital budgeting. For this reason, the theory has gained significant importance among management practitioners. Moreover, over the last 20 years, advances in both computational power and understanding of the options techniques have made it feasible to apply real options thinking to strategic decision making. The evidence that firms taking into account real options considerations outperform firms that do not, has made real options the most important growth area in the theory and practice of finance.
Hedging
Authors: Rheinländer Thorsten
Published: May 2010

In incomplete markets, not all claims are attainable, and there are different possible hedging criteria. We focus here on mean–variance hedging under the martingale measure, and relate it to utility‐indifference hedging.
Complete Markets
Authors: Rutkowski Marek
Published: May 2010

A market model is said to be complete if any financial derivative admits a replicating strategy. The completeness of a market model ensures that any derivative security can be priced by arbitrage and hedged through dynamic trading in primary traded assets. In a complete market model, not only call and put options but also any exotic option can be replicated by dynamic trading in the primary securities. The Cox, Ross, and Rubinstein binomial model of the stock price is complete. The classic Black and Scholes options pricing model enjoys the property of completeness under suitable technical assumptions
Second Fundamental Theorem of Asset Pricing
Authors: Biagini Francesca
Published: May 2010

The second fundamental theorem of asset pricing concerns the mathematical characterization of the economic concept of
market completeness
for liquid and frictionless markets. The theorem establishes the mathematical necessary and sufficient conditions in order to guarantee that every contingent claim on the market can be duplicated with a portfolio of primitive assets. For finite asset economies, completeness (i.e.,
perfect replication
of every claim on the market by admissible self‐financing strategies) is equivalent to uniqueness of the equivalent martingale measure. This result can be extended to market models with an infinite number of assets by defining completeness in terms of
approximate replication
of claims by attainable ones.
Change of Numeraire
Authors: Björk Tomas
Published: May 2010

We give an overview of the change of numeraire technique and in particular the concept ofT‐forward measure. For a general numeraire, we provide the Radon‐Nikodym derivative for the associated measure transformation and derive a general option pricing formula. A pricing formula for an exchange option is given as an example.
Utility Indifference Valuation
Authors: Becherer Dirk
Published: May 2010

Under market frictions like illiquidity or transaction costs, contingent claims can incorporate some inevitable intrinsic risk that cannot be completely hedged away but remains with the holder. In general, they cannot be synthesized by dynamical trading in liquid assets and hence cannot be priced by no‐arbitrage arguments alone. Still, an agent (she) can determine a valuation with respect to her preferences toward risk. The utility indifference value for a variation in the quantity of illiquid assets held by the agent is defined as the compensating variation of wealth, under which her maximal expected utility remains unchanged.
Arrow–Debreu Prices
Authors: Becherer Dirk , Davis Mark H.A.
Published: May 2010

Arrow–Debreu prices are the prices of atomic time and state‐contingent claims, which deliver one unit of a specific consumption good if a specific state realizes at a specific future date. Such claims were introduced by Arrow and Debreu in their work on general equilibrium theory under uncertainty to allow agents to exchange state and time contingent claims, reducing the equilibrium problem with uncertainty to a conventional one without uncertainty. In finite‐state models, Arrow–Debreu securities delivering one unit of the numeraire good can be viewed as atomic building blocks for all other state–time contingent financial claims. Their prices determine a unique arbitrage‐free price system.
Black–Scholes Formula
Authors: Davis Mark H.A.
Published: May 2010

This article describes and proves the Black–Scholes formula, the most famous formula in financial economics. Its relationship to partial differential equations is discussed, as well as the hedge parameters used in trading and an alternative form, the Black “forward” option pricing formula. Finally, the relationship of this theoretical formula to the practical world of option trading is discussed.
Exchange Options
Authors: Jamshidian Farshid
Published: May 2010

The exchange option contract is described and practical examples are given. The essential theoretical developments are chronologically described. The principles and techniques of hedging and unique pricing are illustrated for the two simplest nontrivial examples: the classical Black–Scholes/Merton/Margrabe exchange option model brought slightly up to date from its form three decades ago and a lesser exponential Poisson analog to illustrate jumps. Beyond these, a simplified Markovian stochastic differential equation (SDE)/ partial differential equation (PDE) line is sketched in an arbitrage‐free semimartingale setting. The focus is on the construction of a hedge using Itô’s formula and on unique pricing, now for general homogeneous payoff functions. The concrete cases of the multivariate log‐Gaussian and exponential‐Poisson cases are worked out.

Numéraire invariance is emphasized as the primary means to reduce dimensionality by one to the projective space, where the stochastic differential equation (SDE) dynamics are specified and the partial differential equations (PDEs) are solved (or expectations explicitly calculated). A predictable representation of a homogeneous payoff with deltas (hedge ratios) as partial derivatives or partial differences of the option price function is highlighted. Equivalent martingale measures are utilized to show unique pricing with bounded deltas (and in the nondegenerate case unique hedging) and to exhibit the PDE or closed‐form solutions as numéraire‐deflated conditional expectations in the usual way. Homogeneity, change of numéraire, and extension to dividends are discussed.
American Options
Authors: Chevalier Etienne
Published: May 2010

We present the main results concerning the American options theory. We give the characterization of the American option value process as the Snell envelope of the option pay‐off process. Consequently, we describe optimal exercise times and derive a hedging strategy for the option. We also explain how this is used for numerical methods based on dynamic programming equation. In the second section of the article, we study the analytic approach to American option valuation. Option prices are solutions of variational inequalities and can be approximated using finite difference methods. Finally, we quote some properties of the exercise region. In particular, we give the early exercise premium formula that links the American and European options prices and allows to obtain an integral equation for exercise boundaries.
Asian Options
Authors: Henderson Vicky
Published: May 2010

Asian options are exotic, path‐dependent options that have a payoff dependent on the average of the asset price and a strike that is fixed in advance. This article gives an overview of the no‐arbitrage pricing methods for such options. Typically, contracts involve the arithmetic average of prices, and in this case, since the distribution of the average is not lognormal, there is no closed‐form solution for the option price.
Foreign Exchange Markets
Authors: Braun Michael
Published: May 2010

The article provides overview on the FX Market and the conventions in option trading. The interbank market uses a special “language”. The “greeks”, which reflect the sensitivity of the product, are explained. The basics of the FX smile including the term structure are shown.
Foreign Exchange Symmetries
Authors: Wystup Uwe
Published: May 2010

The symmetries of the foreign exchange market are the key feature that distinguishes this market from all others. We discuss many relationships for pricing of options based on symmetry, apply them to exotic options, and outline the basic quotation conventions in the foreign exchange (FX) options market.
Foreign Exchange Smiles
Authors: Tompkins Robert G.
Published: May 2010

It is well known that prices of foreign exchange options systematically diverge from those consistent with the Garman‐Kohlhagen and Black option‐pricing models. The implied volatilities of options on the same underlying foreign exchange rate differ across strike prices and terms to expiration. When implied volatilities for the same expiration are plotted
versus
strike prices and a corresponding function relationship is determined, the result is a convex pattern, which is commonly known as a
smile
. A logical first step in formulating a theory to explain this phenomenon would be to better understand the empirical record of implied volatility smiles. If time invariant regularities are discovered, this will provide a benchmark to compare implied volatility smiles associated with alternative models. In this article, we summarize the empirical record of implied volatility smiles for four alternative currency pairs: British pound, Swiss franc, Deutsche mark, and Japanese yen all
versus
the US dollar. The time period of analysis is from 1985 to 2000 and it considers options on futures traded at the Chicago Mercantile Exchange.

This article then considers models that have been proposed to explain the existence of implied volatility smiles. Neither stochastic volatility model nor jump‐diffusion models are able to generate similar implied volatility smile dynamics. An alternative model that combines both stochastic volatility and jump processes appears to explain the smile surfaces better. While the dynamics are matched, the smiles are not as extreme (in curvature) as the empirical smiles. The differences between the empirical and model generated smile patterns suggest a systematic and substantive negative risk premium. Finally, transaction costs are added to the best fitting theoretical model and the risk premium is substantially reduced. We conclude that both an alternative process for foreign exchange returns and transaction costs explain why implied volatility smiles for options on foreign exchange exist.
Foreign Exchange Smile Interpolation
Authors: Wystup Uwe
Published: May 2010

This article provides a short introduction into the handling of FX‐implied volatility market data–especially their inter‐ and extrapolation across delta space and time. We discuss a low‐dimensional Gaussian kernel approach as the method of choice showing several advantages over usual smile interpolation methods such as cubical splines.
Margrabe Formula
Authors: Poulsen Rolf
Published: May 2010

The Margrabe formula for valuation of exchange options is described and extensions to other contracts such as spread, compound, and traffic light options are discussed.
Foreign Exchange Options: Delta‐ and At‐the‐money Conventions
Authors: Beier Claus Christian , Renner Christoph
Published: May 2010

In foreign exchange (FX) markets, option volatilities are generally quoted in terms of option delta sensitivities. As various delta conventions (spot and forward deltas with and without premium adjustment) have been established in the markets, care has to be taken when retrieving volatilities in accordance with market conditions.

In this article, we summarize the various delta and at‐the‐money conventions used in FX markets, highlight their intuition, and give formulas and methods for the conversion of option deltas to strikes and
vice versa
. We point out some mathematical problems and pitfalls when retrieving volatilities in accordance with market conditions and give criteria under which these problems surface.
Stochastic Volatility Models: Foreign Exchange
Authors: Griebsch Susanne A. , Pilz Kay F.
Published: May 2010

We discuss the application of stochastic volatility models, in particular the Heston model, to foreign exchange (FX) markets. In this context, the valuation of contingent claims is considered by giving an overview of numerical and analytical methods. The calibration of the Heston model to FX market data and the pricing of barrier options are discussed.
Foreign Exchange Basket Options
Authors: Hakala Jürgen , Wystup Uwe
Published: May 2010

We explain the valuation and correlation hedging of foreign exchange basket options in a multidimensional Black–Scholes model that allows to include the smile. The technique presented is a fast analytic approximation to an accurate solution of the valuation problem.
Call Options
Authors: Madan Dilip B.
Published: May 2010

The information content of call option prices is summarized along with conditions for the absence of static arbitrage among quoted option prices.
Barrier Options
Authors: Qian Michael
Published: May 2010

Some common barrier options are discussed including their basic risk profiles and application.
Corridor Options
Authors: Fusai Gianluca
Published: May 2010

Corridor options are path‐dependent options characterized by having their settlement based on the time spent by a reference index inside a given range. In this contribution, we describe the most important payoff structures and provide some pricing formulae. A discussion of the main references in the literature, including non‐Gaussian models, is also provided.
Lookback Options
Authors: Fusai Gianluca
Published: May 2010

Lookback options are path‐dependent options characterized by having their settlement based on the minimum or the maximum value of an underlying index as registered during the lifetime of the option. In this contribution, we provide pricing formulae for lookback under the geometric Brownian motion (GBM) dynamics. In addition, we discuss different approaches to deal with discrete monitoring of the underlying and with non‐Gaussian models.
Parisian Option
Authors: Labart Céline
Published: May 2010

In this article, a type of path‐dependent options called
Parisian
options is presented. These options are barrier options that are activated (or canceled) if the underlying asset continuously remains above (or below) a barrier long enough. Pricing Parisian options is a challenging issue, and the different methods proposed in the literature, such as, Monte Carlo simulations, Laplace transforms, lattices, and partial differential equations, are surveyed.
Cliquet Options
Authors: Shypit Rick L.
Published: May 2010

Cliquet options are customized derivatives contracts, which can be tailored to provide a rich variety of risk‐reward profiles. The defining characteristic of cliquet options is a series of periodic settlement values with a strike that resets at the start of each period. Often caps and/or floors are added to achieve the desired risk‐reward characteristics. We present an overview of cliquet options and discuss some of their applications in the market for financial products.
Call Spread
Authors: Liverance Eric
Published: May 2010

A call spread is an option strategy with limited upside and limited downside that uses call options of two different strikes but the same maturity on the same underlying. This produces a structure that at maturity pays off only in scenarios where the price of the underlying is above the lower strike. One can think of this strategy as buying a low‐strike call option and financing part of the upfront cost by selling a higher strike call option. The effect of selling the higher strike option is to limit the upside potential, but to reduce the cost of the structure. It should be used for expressing a bullish view that the underlying will rise in price above the lower strike. By using two strike very close together and leveraging up the size of the trade, a digital option can be replicated by a call spread.
Delta Hedging
Authors: Joseph Viju
Published: May 2010

The article describes the concept of delta hedging for portfolios as well as financial derivatives. It discusses the different factors to consider while hedging the delta of financial derivatives and provides some examples of the same.
Dispersion Trading
Authors: Ren Yong
Published: May 2010

This article explains dispersion trading and its relationship with correlations. We give the definition of the correlation proxy and mention the mean variance ratio which is more commonly used in practice than correlation itself. We briefly discuss the reason behind dispersion trading. Finally, we discuss the some methods and issues in dispersion trading.
Static Hedging
Authors: Poulsen Rolf
Published: May 2010

Barrier options can be statically hedged with plain vanilla puts and calls.
Corridor Variance Swap
Authors: Lee Roger
Published: May 2010

A corridor variance swap with corridor
C
is a weighted variance swap, with weight given by the indicator of
C
. We discuss the corridor variance swap's motivations, model‐free replication and valuation, relation to local time, valuation via characteristic function, and issues of discretization.
A
tlas Option
Authors: Gharavi Reza K.
Published: May 2010

An Atlas option is a regular option on a small basket where a contractual number of best‐performing and worst‐performing assets are removed from the basket. This article provides an overview of the product. It describes the motivation behind the product, discusses its valuation, and describes its risk profile.
Equity Default Swaps
Authors: Chen Oliver
Published: May 2010

Equity default swaps (EDS) are defined as far out‐of‐the‐money American‐style binary puts with periodic swap payments rather than an up‐front premium. Applications of EDS are given to illustrate why EDS have been introduced to the market. Although the payout of an EDS is triggered by a fall in the equity price, we show why this has been described as a credit–equity hybrid. Finally, pricing of EDS is described.
Put–Call Parity
Authors: Bossu Sébastien
Published: May 2010

Put–call parity is a fundamental relationship connecting European calls, puts, and forward contracts together.
Weighted Variance Swap
Authors: Lee Roger
Published: May 2010

After defining weighted variance swaps, we present examples (variance swaps, corridor variance swaps, and gamma swaps), formulas for model‐free replication and valuation under nonzero interest rates and dividends, and features of weighted variance swap contracts as specified in practice.
Dupire Equation
Authors: Dupire Bruno
Published: May 2010

Under very general conditions, the cross section of European call and put prices on any underlying asset follows, as a function of strike and maturity, a partial differential equation commonly named the
Dupire equation
. This equation can be used to obtain price‐ and time‐dependent instantaneous volatilities, also named
local volatilities
, which provide a simple model consistent with all European option prices. The local variances, square of the local volatilities, can be interpreted as instantaneous forward variances conditional on a given underlying price.
Implied Volatility in Stochastic Volatility Models
Authors: Carr Peter , Lee Roger
Published: May 2010

We survey how implied volatility relates to realized volatility, under general stochastic volatility dynamics. We consider implied volatility according to the Black–Scholes definition and also two model‐free definitions.
Local Volatility Model
Authors: Luo Chiyan , Liu Xinming
Published: May 2010

In this article, the local volatility surface is presented as a general framework for equity derivatives modeling. In particular, efficient volatility calibration techniques with parametric local volatility models are presented, along with methodologies for handling discrete dividends and stochastic interest rates. The importance of these models is demonstrated in realistic pricing examples with data from the S&P 500 index options market.
Dividend Modeling
Authors: Shepeleva Anna , Verberkmoes Alain
Published: May 2010

Dividend modeling is a topic specific to equity derivatives pricing. Here “the devil is in the details”: one should clearly understand how the underlying process is influenced by the presence of dividends. Complexity of dividend assumptions varies a lot: in practice one has to choose complexity of the model depending on the dividend exposure of the derivative to be priced. We also discuss some unexpected pitfalls even in the most common models.
Implied Volatility: Long Maturity Behavior
Authors: Tehranchi Michael R.
Published: May 2010

We discuss some properties of implied volatility surfaces for large times to maturity. The implied volatility smile flattens at long maturities in a rather precise manner. An asymptotic formula for the long implied volatility is given and is illustrated by examples. The long implied volatility is almost surely nondecreasing as a function of calendar time, in analogy with the Dybvig–Ingersoll–Ross theorem on long interest rates.
Implied Volatility: Large Strike Asymptotics
Authors: Friz Peter K.
Published: May 2010

We discuss how tail asymptotics of some risky asset under the pricing measure translate directly to large strike asymptotics of the implied volatility smile. In many models, the tail behavior (to relevant leading order) is either known (e.g., from the vast literature on probability distributions) or can be derived from the moment generating function.
Bates Model
Authors: Bates David S.
Published: May 2010

This article reviews the Bates and Scott option pricing models, which capture both stochastic volatility and jump risk within a tractable affine specification.
Barndorff‐Nielsen and Shephard (BNS) Models
Authors: Tankov Peter
Published: May 2010

Barndorff‐Nielsen and Shephard models are stochastic volatility models where the volatility follows a non‐Gaussian Ornstein–Uhlenbeck type process. This article briefly reviews the construction of such models and discusses their application to option pricing and hedging.
H
eston Model
Authors: Buehler Hans
Published: May 2010

We discuss Heston's stochastic volatility model for equity markets. This model features a very efficient numerical method of computing vanilla option prices and can therefore be calibrated very quickly to market data. The article describes the basic model, option pricing, Monte Carlo and partial differential equation (PDE) approaches and related models.
Variance‐Gamma Model
Authors: Seneta Eugene
Published: May 2010

The variance‐gamma (VG) process is a stochastic process with independent stationary increments, which allows for flexible parameterization of skewness and kurtosis and is analytically tractable. It can be represented either as a Lévy process with VG increments or as a subordinated Brownian motion. We briefly discuss the VG model, parameter estimation issues, applications to option pricing, and extensions allowing for dependence in increments.
Jump‐Diffusion Models
Authors: Gatheral Jim
Published: May 2010

Jump‐diffusion option pricing models are generalizations of the Black–Scholes model, generalizations in which the underlying asset price can jump. The dynamics of the log‐price is given by the sum of Brownian motion and an independent compound Poisson process. Some examples of jump size distributions, such as normal or double exponential, lead to analytically tractable option pricing models that can generate implied volatility smiles.
Time‐Changed Lévy Process
Authors: Madan Dilip B.
Published: May 2010

If
L
is a Lévy process and (
T

t

)

t
 ≥ 0

is a positive increasing process,
X

t

 = 
L
(
T

t

) is called a
time‐changed Lévy process
with time change (
T

t

)

t
 ≥ 0

. When the time change is an affine process independent from
L
, many properties of
X
can be derived from those of
L
. We discuss various examples of such constructions.
Kou Model
Authors: Kou Steven
Published: May 2010

The double exponential jump‐diffusion model (or Kou model) is an exponential Lévy model (seeExponential Lévy Models) with finite jump intensity, whose jump size distribution follows a two‐sided exponential distribution. We give an overview of properties related to the double exponential jump‐diffusion model. Certain difficulties in applying the model, such as the lack of volatility clustering, extension to multiple underlying assets, and the difficulty in distinguishing the tail behavior of asset returns, are also discussed.
Uncertain Volatility Model
Authors: Martini Claude , Jacquier Antoine
Published: May 2010

The everyday worry of an option trader is to make sure its profit and loss stays nonnegative.

In the framework of a delta‐hedged dynamic buy or sell strategy computed with the parameters of a complete model (like the Black–Scholes model), the P&L at maturity will in fact be zero, under the assumption that the underlying follws the model dynamic. Of course this assumption is
very
unrealistic. In a seminal paper, El Karoui, Jeanblanc and Shreve study the robustness of the B&S strategy in the context of an unknown volatility. The uncertain volatality model (UVM) setting, pioneered independently by T. Lyons and M. Avellaneda, goes one step further by finding the cheapest selling price of an option for a totally risk‐averse trader in the much more realistic setting where there is almost no information on the volatility, except that it lies in a prespecified range. Even if its concrete implementation at the level of an option portfolio is tricky, the UVM setting is a milestone in the pricing and risk management of derivatives. It also raises theoretical issues when one tries to formalize a general framework for option pricing in the context of model uncertainty.
Implied Volatility: Market Models
Authors: Durrleman Valdo
Published: May 2010

We survey the different approaches to modeling option prices, which take the implied volatility as the modeling variable. These approaches all face the difficult task of handling and understanding the important relations among implied volatilities and between the implied and the spot volatilities.
Rating Transition Matrices
Authors: Lando David
Published: May 2010

Rating transition matrices play an important role in credit risk management both as a method for summarizing the empirical behavior of a rating system and as a tool for computing probabilities of rating migrations in, for example, a portfolio of risky loans. Analysis of statistical properties of rating transition matrices is intimately linked with Markov chains. Even if rating processes in general are not Markovian, statistical analysis of rating systems often focuses on assessing a particular deviation from Markovian behavior. Furthermore, the tractability of the Markovian setting can be preserved in some simple extensions.
Credit Migration Models
Authors: Straumann Daniel , Finger Christopher C.
Published: May 2010

This article provides a short survey on credit‐migration‐based portfolio models, and on CreditMetrics®in particular. Mathematical properties and estimation and supply references are also discussed.