Journal ArticleDOI
Volatility Skews and Extensions of the Libor Market Model
TLDR
In this article, the authors consider extending the Libor market model to markets with volatility skews in observable option prices and discuss efficient techniques for calibration to quoted prices of caps and swaptions.Abstract:
This paper considers extensions of the Libor market model (Brace et al (1997), Jamshidian (1997), Miltersen et al (1997)) to markets with volatility skews in observable option prices. We expand the family of forward rate processes to include diffusions with non-linear forward rate dependence and discuss efficient techniques for calibration to quoted prices of caps and swaptions. Special emphasis is put on generalized CEV processes for which exact closed-form expressions for cap prices are derived. We also discuss modifications of the CEV process which exhibit appealing growth and boundary characteristics. The proposed models are investigated numerically through Crank-Nicholson finite difference schemes and Monte Carlo simulations.read more
Citations
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Journal ArticleDOI
The dynamics of stochastic volatility: evidence from underlying and options markets
TL;DR: In this article, a more general parametric stochastic variance model of equity index returns is proposed and estimates using data from both underlying and options markets, and the model fails to explain the implied volatility smile for short-dated options and conditional higher moments in returns.
Journal ArticleDOI
Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options
Leif B. G. Andersen,Mark Broadie +1 more
TL;DR: The proposed algorithm can handle virtually any type of process dynamics, factor structure, and payout specification, and gives valid confidence intervals for the true value of the Bermudan option price.
Book
A Benchmark Approach to Quantitative Finance
Eckhard Platen,David Heath +1 more
TL;DR: Preliminaries from Probability Theory and Statistical Methods are used in this article to estimate the probability that a stock market will be a buy or sell in the next five years.
Journal ArticleDOI
Pricing and Hedging Path-Dependent Options Under the CEV Process
Dmitry Davydov,Vadim Linetsky +1 more
TL;DR: It is demonstrated that the prices of options, which depend on extrema, can be much more sensitive to the specification of the underlying price process than standard call and put options and show that a financial institution that uses the standard geometric Brownian motion assumption is exposed to significant pricing and hedging errors when dealing in path-dependent options.
Journal ArticleDOI
Fast strong approximation Monte Carlo schemes for stochastic volatility models
Christian Kahl,Peter Jäckel +1 more
TL;DR: In this paper, numerical integration methods for stochastic volatility models in financial markets are discussed, where the volatility is either directly given by a mean-reverting CEV process or as a transformed Ornstein-Uhlenbeck process.
References
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Numerical recipes in C
TL;DR: The Diskette v 2.06, 3.5''[1.44M] for IBM PC, PS/2 and compatibles [DOS] Reference Record created on 2004-09-07, modified on 2016-08-08.
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Brownian Motion and Stochastic Calculus
TL;DR: In this paper, the authors present a characterization of continuous local martingales with respect to Brownian motion in terms of Markov properties, including the strong Markov property, and a generalized version of the Ito rule.
Book
Continuous univariate distributions
TL;DR: Continuous Distributions (General) Normal Distributions Lognormal Distributions Inverse Gaussian (Wald) Distributions Cauchy Distribution Gamma Distributions Chi-Square Distributions Including Chi and Rayleigh Exponential Distributions Pareto Distributions Weibull Distributions Abbreviations Indexes
Journal ArticleDOI
A Theory of the Term Structure of Interest Rates.
TL;DR: In this paper, the authors use an intertemporal general equilibrium asset pricing model to study the term structure of interest rates and find that anticipations, risk aversion, investment alternatives, and preferences about the timing of consumption all play a role in determining bond prices.
Book
Numerical Solution of Stochastic Differential Equations
Peter E. Kloeden,Eckhard Platen +1 more
TL;DR: In this article, a time-discrete approximation of deterministic Differential Equations is proposed for the stochastic calculus, based on Strong Taylor Expansions and Strong Taylor Approximations.