bluuebunny/crossref_metadata_2025_split huggingface dataset:
Semimartingale
Authors: Podolskij Mark 
Published: May 2010

Abstract

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

AbstractFinancial 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

Abstract
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.
Recursive Preferences
Authors: Schroder Mark 
Published: May 2010

Abstract
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

Abstract
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

Abstract
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

AbstractA 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

Abstract
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.
Complete Markets
Authors: Rutkowski Marek 
Published: May 2010

Abstract
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

Abstract

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.
Utility Indifference Valuation
Authors: Becherer Dirk 
Published: May 2010

AbstractUnder 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

Abstract
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.
Exchange Options
Authors: Jamshidian Farshid 
Published: May 2010

AbstractThe 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

AbstractWe 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

Abstract
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 Smiles
Authors: Tompkins Robert G. 
Published: May 2010

Abstract

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 Options: Delta‐ and At‐the‐money Conventions
Authors: Beier Claus Christian , Renner Christoph 
Published: May 2010

Abstract
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

Abstract
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.
Lookback Options
Authors: Fusai Gianluca 
Published: May 2010

Abstract
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

Abstract

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

Abstract
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

Abstract
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.
Equity Default Swaps
Authors: Chen Oliver 
Published: May 2010

Abstract
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.
Dupire Equation
Authors: Dupire Bruno 
Published: May 2010

Abstract

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.
Local Volatility Model
Authors: Luo Chiyan , Liu Xinming 
Published: May 2010

AbstractIn 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

Abstract
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

AbstractWe 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

Abstract
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.
Variance‐Gamma Model
Authors: Seneta Eugene 
Published: May 2010

AbstractThe 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

Abstract
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

Abstract

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.