bluuebunny/crossref_metadata_2025_split huggingface dataset:
Credit Default Swaption
Authors: Laurent Jean‐Paul 
Published: May 2010

Abstract

Credit default swap (CDS) options, also called
credit swaptions
, allow an investor to buy protection on a reference name at a specified spread. We define the cash flows associated with the option and describe a method for obtaining a Black formula for CDS options. One could think of other specifications, for instance associated with a shifted square root process for the short‐term credit spread of the reference entity, which can be put within a convenient Cox process framework. We discuss the merits of the two approaches.
Forward‐Starting
CDO
Tranche
Authors: Baheti Prasun , Mashal Roy , Naldi Marco 
Published: May 2010

Abstract
Reset tranches are a class of default‐path‐dependent structures that include forward‐starting contracts and subordination/leverage step‐ups. The attachment and/or width of the tranche are reset at a predetermined time (the reset date) as deterministic functions of the random amount of losses incurred by the reference portfolio up to that time. We discuss a simple algorithm for fast quasi‐analytical valuation of these products.
Leveraged Super‐Senior Tranche
Authors: Arnsdorf Matthias 
Published: May 2010

Abstract
A leveraged super‐senior (LSS) note is a structure that allows investors to take a leveraged exposure to the super‐senior (SS) part of a collateralized debt obligation (CDO). This provides an enhanced level of return while typically maintaining a AAA rating. Leverage is achieved by posting an initial collateral amount that is less than the notional of the underlying SS tranche. All credit losses to the investor are capped at the collateral amount, but the coupon is paid on the full notional. Early unwind clauses are typically included in the trade to mitigate the risk to the issuer that losses exceed the collateral amount. Compared to a standard SS tranche the investor is exposed to mark‐to‐market (MTM) risk as well as credit risk, that is, for certain market moves his/her principal could be reduced even if no credit losses have occurred owing to a forced unwind. The issuer faces a so‐called gap risk, the risk that the MTM of the tranche will fall below the initially posted collateral amount before a trade unwind can take place.
Modeling Correlation of Structured Instruments in A Portfolio Setting
Authors: Yahalom Tomer , Levy Amnon , Kaplin Andrew S. 
Published: May 2010

Abstract
Traditional approaches to modeling economic capital, credit‐VaR (Value‐at‐Risk), or structured instruments whose underlying collateral is composed of structured instruments treat structured instruments as a single‐name credit instrument (i.e., a loan‐equivalent). Though tractable, the loan‐equivalent approach requires appropriate parameterization to achieve a reasonable description of the cross‐correlation between the structured instrument and the rest of the portfolio. This article provides an overview of how to calibrate loan‐equivalent correlation parameters. Results suggest that structured instruments have far higher correlation parameters than single‐name instruments.
Credit Portfolio Insurance
Authors: Islam Saiyid S. 
Published: May 2010

AbstractStructured credit portfolio insurance products such as credit constant proportion portfolio insurance (CPPI) have emerged as alternative investment products to more traditional structured assets in the past few years. Related products in the form of constant proportion debt obligations (CPDOs) added further variety to the set of structured credit products. From the perspective of the investor, while credit CPPIs have the appealing feature of providing principal protection through part investment in risk‐free assets, CPDOs are designed to return high coupon payments through leveraged exposure to investment grade risk. This article compares and contrasts the similarities and differences between credit CPPIs and CPDOs, briefly describes their structures, summarizes the risks in these securities in the form of downgrade and default risk, spread risk, and interest rate risk, and presents ideas around how to model these assets in a Monte Carlo simulation framework.
Nested Simulation
Authors: Gordy Michael B. , Juneja Sandeep 
Published: May 2010

Abstract

We discuss nested simulation methods for computing loss distributions and Value‐at‐Risk (VaR) for a portfolio containing CDO tranches as well as single‐name CDS and bonds. When these instruments are modeled
via
correlated stochastic default‐intensity models, estimation of VaR requires a nested simulation procedure: in the outer step of the simulation one draws realizations of all default intensities up to the horizon, and in the inner step one uses simulation to reprice each instrument in the portfolio at the horizon conditional on the realized intensities. We analyze how a fixed computational budget may be allocated to the inner and the outer steps to minimize the mean square error (MSE) of the resultant estimator. We also review how importance sampling may be used to increase the efficiency of the inner step.
Convertible Bonds
Authors: Ayache Élie 
Published: May 2010

Abstract

A convertible bond (CB) is a
corporate bond
that may be converted into a certain number of shares of the issuing company, also known as the
underlying equity
. Pricing and hedging of convertible bonds involves accounting for the volatility of the underlying stock as well as the credit risk of the firm's debt. Convertible bonds are examples of equity–credit hybrids.
Bond
Authors: Priaulet Stéphane 
Published: May 2010

Abstract

A
bond
, or a
debt security
, is a financial claim by which the
issuer
, or the borrower, is committed to paying back to the
bond holder
or the lender, the cash amount borrowed, called
principal
, plus periodic coupon interests calculated on this amount during a given period. It can have either a standard or a nonstandard structure. A
standard bond
is a fixed coupon bond without any embedded option, delivering its coupons on periodic dates and principal on the maturity date. Nonstandard bonds include, among others, zero‐coupon bonds, floating rate notes, inflation‐linked bonds, callable and putable bonds, and convertible bonds. Bonds are usually quoted in price, yield, or spread against an underlying benchmark bond or reference swap rate. The
quoted price
(or
market price
) of a bond is usually its
clean price
, that is, its gross price minus the accrued interest. The quoted
yield to maturity
of a bond is the discount yield that equalizes its gross price times its nominal amount to the sum of its discounted cash flows.

A decline (rise) in interest rates will cause a rise (decline) in bond prices, with highest volatility occurring for long‐maturity bonds and bonds with low coupons. A bond price risk is most often measured by the bond interest rate sensitivity or
duration
. The duration concept is an instantaneous risk measure. It assumes a flat yield curve, solely affected by parallel shifts with small magnitude. Relaxing the assumption of small shifts in the yield curve leads to the introduction of a convexity adjustment in the price risk measure.
H
eath–
J
arrow–
M
orton Approach
Authors: Björk Tomas 
Published: May 2010

Abstract
We give an overview of the Heath–Jarrow–Morton (HJM) approach used in interest‐rate modeling. In particular, we cover absence of arbitrage, the HJM drift condition, the Musiela parameterization, consistency, and existence of finite Markovian representations.
Forward and Swap Measures
Authors: Jamshidian Farshid 
Published: May 2010

AbstractForward and swap measures are defined and some of their main applications illustrated. The development is based on the construction of general numeraire measures from a state price density. Using the numeraire‐invariance theorem and the fact that forward asset prices are martingales under the forward measure, we indicate how a call option is replicated when the forward asset price process is a diffusion. The standard pricing formula is derived in the deterministic‐volatility case. Caps and swaptions are treated similarly, using that forward Libor and swap rates are martingales under the forward and swap measures, respectively. As another application, we calculate, in the continuous case, the risk‐neutral drift of the instantaneous forward rate and the terminal‐measure drift of the Libor forward rate.
Cox–Ingersoll–Ross (
CIR
) Model
Authors: Alfonsi Aurélien 
Published: May 2010

Abstract
This article intends to give a short presentation of the Cox– Ingersoll– Ross (CIR) model, giving the main features that have contributed to its success. It provides the basic mathematical knowledge on this model and the fundamental pricing results for caps and swaptions. Finally, it hints at practical questions such as calibration and Monte Carlo simulation.
QuadraticGaussian Models
Authors: Durand Philippe 
Published: May 2010

AbstractQuadratic Gaussian (QG) models are factor models for the pricing of interest‐rate derivatives, where interest rates are quadratic functions of underlying Gaussian factors. We discuss analytical properties of these models and their application to the pricing of interest‐rate derivatives. Owing to its capacity to fit to implied volatility smiles and to correlation term structures, the QG model has been used for pricing and hedging exotic interest‐rate options.
Alternating Direction Implicit (
ADI
) Method
Authors: Villeneuve Stéphane 
Published: May 2010

Abstract
In the Black–Scholes model option values are characterized as solutions of certain partial differential equations for European options or partial differential inequalities for American options. In general and in particular for American options, there is no closed‐form formulae and the option values have to be evaluated numerically, for example using the finite difference method. Unfortunately, when considering the pricing of options depending on several assets, the finite difference method suffers from the curse of dimensionality.
To circumvent this difficulty, it has been known for more than 50 years that the alternating direction implicit (ADI) algorithm is an efficient procedure for solving a large‐scale system of linear equations arising from the finite difference discretization of elliptic or parabolic equations. We describe here the ADI methods and discuss some of their features.
Conjugate Gradient Methods
Authors: Wan Justin W.L. 
Published: May 2010

Abstract
In option pricing on the basis of the Black–Scholes model, the value of an option is governed by a partial differential equation. Numerical approximations of the solution by the finite difference or finite element methods on a mesh of discrete asset prices result in a linear system to be solved in each time step. In this article, we introduce the conjugate gradient (CG) methods for fast solution of the option pricing equations. CG methods generate “optimal” approximate solutions by performing simple vector operations and matrix–vector multiply. We derive the method for symmetric problems and extend the idea to the nonsymmetric case. Convergence and preconditioning issues are discussed. As an example, a preconditioned CG method is used to efficiently price European options in a general exponential Levy model.
Crank–Nicolson Scheme
Authors: Giles Michael B. 
Published: May 2010

AbstractWe describe the Crank–Nicolson method for the numerical solution of parabolic partial differential equations, its numerical properties and its application to the Black–Scholes equation. We also present the Rannacher start‐up procedure that is required to achieve second‐order accuracy for the option value and its first and second derivatives, and discuss extensions to nonlinear and multifactor applications.
Lattice Methods For Path‐Dependent Options
Authors: Kwok Yue‐Kuen 
Published: May 2010

Abstract
In this article, we discuss the lattice tree methods that are augmented with the forward shooting grid technique for pricing strongly path‐dependent options. Typical examples of options whose payoffs depend on the path dependence of the underlying asset price processes are Asian options, lookback options, and occupation time derivatives. The essence of the forward shooting grid approach is to append an auxiliary state vector at each node in the lattice tree that models the correlated evolution of the path dependence function with the underlying asset price process. We illustrate how to apply the forward shooting grid approach to price Asian options, lookback options, soft call requirement in callable convertible bonds, and call options with strike reset feature. Techniques of interpolating nodal values in the lattice tree and the associated convergence of numerical calculations are also discussed.
Wavelet Galerkin Method
Authors: Hilber Norbert , Reich Nils , Winter Christoph 
Published: May 2010

AbstractIn this article, we provide an overview of wavelet methods for asset pricing. Wavelet methods are a particular realization of the finite element method. They provide a very general PDE‐based numerical pricing technique. We describe the general setup and admissible market models. The fundamental concepts of the wavelet‐based finite element implementation are described. Furthermore, we illustrate the pricing of American contracts as well as the computation of sensitivities and Greeks. Numerical illustrations are given.
Tree Methods
Authors: Lelong Jérôme , Zanette Antonino 
Published: May 2010

AbstractTree methods are among the most popular numerical methods to price financial derivatives. Mathematically speaking, they are easy to understand and do not require severe implementation skills to obtain algorithms to price financial derivatives. Tree methods basically consist in approximating the diffusion process modeling the underlying asset price by a discrete random walk. In this contribution, we provide a survey of tree methods for equity options, which focus on multiplicative binomial Cox–Ross–Rubinstein model.
Partial Integro‐Differential Equations (PIDES)
Authors: Voltchkova Ekaterina 
Published: May 2010

AbstractOption pricing in models with jumps leads to the solution of partial integro‐differential equations (PIDEs). We present the specific features of the PIDEs compared with the partial differential equations. In particular, we highlight the difficulties that arise for the numerical solution of these equations. We show that the use of standard methods, such as finite differences or finite elements, is not straightforward. We then present a simple explicit–implicit finite difference scheme for pricing European vanilla and barrier options in exponential Lévy models and survey the other existing numerical techniques. We also discuss American option pricing, which leads to variational inequalities with the same integro‐differential operator.
Method of Lines
Authors: Seydel Rüdiger U. 
Published: May 2010

Abstract

The valuation of vanilla options is considered under the one‐dimensional Black–Scholes model; a continuous dividend yield is allowed. Only the time variable is discretized, which defines a set of parallel “lines” (parallel to the
S
‐axis, where
S
is the price of the underlying). Replacing the time derivative of the Black–Scholes partial differential equation by a difference quotient establishes a system of coupled linear ordinary differential equations, one equation for each line. The ordinary differential equations can be solved analytically. This is done one line after the other in a backward fashion, starting with the payoff. The solution on each line serves as inhomogeneous term for the next line's equation. An approximation of the early exercise curve is obtained as well. Triple sums must be evaluated. The resulting set of involved analytical formulas is used along with extrapolation, which provides a fairly accurate approximation with only three lines. Using more lines, the accuracy of this method fulfills higher demands.
Monte Carlo Simulation for Stochastic Differential Equations
Authors: Bruti‐Liberati Nicola , Platen Eckhard 
Published: May 2010

Abstract
We introduce Monte Carlo simulation for stochastic differential equations, which is a much simpler task than scenario or pathwise simulation. A weak convergence criterion is used to classify various discrete‐time approximations and numerical schemes. Higher weak order Taylor schemes, implicit methods, and predictor–corrector methods are described.
Stochastic Differential Equations: Scenario Simulation
Authors: Platen Eckhard , Bruti‐Liberati Nicola 
Published: May 2010

Abstract
We consider pathwise converging simulation methods that use discrete‐time approximations for the solution of stochastic differential equations. These are different to Monte Carlo simulation methods, where probabilities and expectations but not sample paths are approximated. Scenario simulation is a more demanding task than Monte Carlo simulation. Various numerical schemes are examined and some examples are considered that can be handled by the simulation of discrete‐time approximations of trajectories. Higher order strong convergence and questions on numerical stability are discussed.
Pseudorandom Number Generators
Authors: L'ecuyer Pierre 
Published: May 2010

AbstractWe review the basic principles underlying the design of uniform random number generators, their main quality requirements, theoretical analysis, and empirical testing. The main construction techniques of algorithmic generators are discussed, with an emphasis on the most common ones, the linear generators. Nonlinear generators, as well as hardware‐based generators, are also briefly discussed. For simulation, we explain why we favor generators that can offer multiple streams and substreams, and we recommend specific ones.
B
ermudan Options
Authors: Kolkiewicz Adam 
Published: May 2010

Abstract
Pricing Bermudan options that depend on multiple assets is a challenging computational problem. Algorithms based on a discretization of the state space typically suffer from the “curse of dimensionality”, meaning that the computational effort grows exponentially with the number of state variables. Regression‐based methods address this problem first by simulating trajectories of the underlying process and then by estimating continuation values through the regression of option values at the next time step on a set of regressors that depend on the current state. In principle, these methods can be applied to any situation where trajectories of the underlying process can be simulated, since no other information about the process is required. In particular, they can be applied to path‐dependent options.
Simulation of Square‐Root Processes
Authors: Andersen Leif B.G. , Jäckel Peter , Kahl Christian 
Published: May 2010

Abstract
We discuss methods for time discretization and simulation of square‐root stochastic differential equations (SDEs), both in isolation (CIR (Cox–Ingersoll–Ross) process) and as part of vector SDEs modeling stochastic volatility (Heston model). Both exact and biased discretization methods are covered.
Stochastic Mesh Method
Authors: Kolkiewicz Adam 
Published: May 2010

Abstract
Pricing options that depend on multiple assets and allow the owner to exercise early are challenging computational problems. Deterministic algorithms based on a discretization of the state space typically become ineffective, as the computational effort grows exponentially with the dimension of the problem. The stochastic mesh method has been designed to address these challenges. It approximates the dynamic programming representation of the price by randomly generating a mesh of points and then using weighted sums to calculate continuation values. The desirable feature of the method is that it provides lower and upper bounds for the true price and is asymptotically consistent.
Stochastic Taylor Expansions
Authors: Platen Eckhard 
Published: May 2010

AbstractIn quantitative finance, it is essential to be able to approximate quantities that can be represented as functions of solutions of stochastic differential equations. If a function is sufficiently smooth and the underlying process satisfies a stochastic differential equation, then one can use a stochastic Taylor expansion. Such expansions generalize the deterministic Taylor formula as well as the Itô formula. They allow various kinds of higher order approximations of solutions of stochastic differential equations.
Mutual Funds
Authors: Gambera Michele 
Published: May 2010

AbstractMutual funds provide expert asset management, and give diversified exposure to investments. Open‐end mutual funds are investment companies that sell individual investors a variable number of shares of a pool of assets. Closed‐end mutual funds are just like holding companies: the number of shares is predetermined, and shares trade on the stock market. Exchange‐traded funds (ETFs) are a special type of closed‐end fund.Equity funds invest in stocks, bond funds invest in debt instruments, and money market funds invest in short‐term bonds. Hybrid funds, also calledbalancedorasset allocation funds, invest in a mix of stocks, bonds, and money market instruments.Open‐end funds are calledno‐loadif they only charge an annual management fee, which is a percentage of assets. A load is a commission that is charged when the investor either buys (front load) or sells (back load) shares. The loads generally compensate brokers and management companies.
Style Analysis
Authors: Meier Iwan 
Published: May 2010

Abstract
Style describes the exposures of an investment to different sources of risk. The style of a fund can be inferred from past returns or from portfolio holdings. Return‐based style analysis uses a constrained regression to estimate the risk exposures to different asset classes. The quality of the analysis crucially hinges on the selection of benchmark indices. An alternative approach is to perform a fundamental analysis of portfolio holdings data. Style benchmarks can be applied to evaluate the performance and to monitor the style consistency of a fund.
Sharpe Ratio
Authors: Alexander Gordon J. , Baptista Alexandre M. 
Published: May 2010

Abstract

The
ex post
Sharpe ratio (SR) is a measure of a portfolio's performance over an evaluation period that is expressed as the portfolio's average excess return per unit of risk. Risk is measured by the portfolio's standard deviation of returns over the evaluation period. The ratio is widely used in practice to compare a portfolio's performance relative to a market index and relative to other portfolios. Similarly, a portfolio's
ex ante
SR indicates its expected excess return per unit of risk as measured by its standard deviation of future returns. This ratio can be used to make portfolio construction decisions.
Risk–Return Analysis
Authors: Markowitz Harry M. 
Published: May 2010

AbstractA risk–return analysis analyzes the trade‐off of some measure of risk and some measure of return. Almost universally, the measure of return used is the mean or expected value. Various measures of risk have been proposed including variance (or, equivalently, standard deviation), semivariance (which is the same as variance, but only considers the downside), absolute deviation, and probability of loss. This article considers the merits of each, how trade‐off curves (also known asefficient frontiers) of these are computed, and how one gets (or can get) data for these.
Fixed Mix Strategy
Authors: Mulvey John M. , Kim Woo Chang 
Published: May 2010

Abstract

An advantage of adopting multiperiod portfolio models is improved investment performance
via
the fixed mix rule. Owing to its similarity to the “buy low/sell high” strategy, it is often misunderstood that it requires mean‐reverting processes for the assets. We show that mean reversion is not necessary to benefit from the fixed mix rule,
via
a simple multidimensional geometric Brownian motion. We also list successful examples from the domain of equities, commodity futures, alternative investments, and momentum strategies.