Methods of Risks Estimation and Analysis of Business Processes

This chapter provides various alternatives to the Black–Scholes model for the pricing of derivative securities. The purpose of such extensions is to make pricing models more realistic in order to incorporate the so-called smile effect and volatility clustering. Stochastic volatility and interest-rate models as well as models with Levy processes are explained in detail. Keywords: hedging strategies; volatility; constant elasticity models; Levy process models; transform techniques; stochastic differential equation; fundamental theorem of asset pricing

[1]  David D. Yao,et al.  A Regime-Switching Model for European Options , 2006 .

[2]  T. Alderweireld,et al.  A Theory for the Term Structure of Interest Rates , 2004, cond-mat/0405293.

[3]  M. Yor,et al.  Stochastic Volatility for Lévy Processes , 2003 .

[4]  Steven Kou,et al.  A Jump Diffusion Model for Option Pricing , 2001, Manag. Sci..

[5]  P. Carr,et al.  Time-Changed Levy Processes and Option Pricing ⁄ , 2002 .

[6]  Vadim Linetsky,et al.  Pricing and Hedging Path-Dependent Options Under the CEV Process , 2001, Manag. Sci..

[7]  Pricing Equity Swaps in a Stochastic Interest Rate Economy , 2001 .

[8]  Equilibrium Positive Interest Rates: A Unified View , 2001 .

[9]  D. Madan,et al.  Spanning and Derivative-Security Valuation , 2000 .

[10]  P. Carr,et al.  Option valuation using the fast Fourier transform , 1999 .

[11]  Nicolas P. B. Bollen Valuing Options in Regime-Switching Models , 1998 .

[12]  Emanuel Derman,et al.  STOCHASTIC IMPLIED TREES: ARBITRAGE PRICING WITH STOCHASTIC TERM AND STRIKE STRUCTURE OF VOLATILITY , 1998 .

[13]  P. Carr,et al.  The Variance Gamma Process and Option Pricing , 1998 .

[14]  D. Duffie,et al.  A YIELD-FACTOR MODEL OF INTEREST RATES , 1996 .

[15]  N. Touzi,et al.  Option Hedging And Implied Volatilities In A Stochastic Volatility Model , 1996 .

[16]  S. Heston A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options , 1993 .

[17]  E. Seneta,et al.  The Variance Gamma (V.G.) Model for Share Market Returns , 1990 .

[18]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[19]  Oldrich A. Vasicek An equilibrium characterization of the term structure , 1977 .

[20]  S. Ross,et al.  The valuation of options for alternative stochastic processes , 1976 .

[21]  R. C. Merton,et al.  Option pricing when underlying stock returns are discontinuous , 1976 .

[22]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.