20.1 More on models and Numerical Procedures Chapter 20 Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 20.1 More on Models and Numerical Procedures Chapter 20
20.2 Models to be considered Constant elasticity of variance (CEV) Jump diffusion Stochastic volatility Implied volatility function(VF) Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 20.2 Models to be Considered • Constant elasticity of variance (CEV) • Jump diffusion • Stochastic volatility • Implied volatility function (IVF)
20.3 CEV Model (p456 ds=(r-gSsat +os dz When a =1 we have the black- Scholes case When a> 1 volatility rises as stock price rises hen a< 1 volatility falls as stock price rises Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 20.3 CEV Model (p456) – When a = 1 we have the BlackScholes case – When a > 1 volatility rises as stock price rises – When a < 1 volatility falls as stock price rises dS r q Sdt S dz a = ( − ) +
0.4 CEV Models Implied volatilities K Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 20.4 CEV Models Implied Volatilities imp K a < 1 a > 1
20.5 Jump diffusion model (page 457) Merton produced a pricing formula when the stock price follows a diffusion process overlaid with random jumps ds s=(u-nk)dt+odz +dp Ap is the random jump k is the expected size of the jump n dt is the probability that a jump occurs in the next interval of length dt Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 20.5 Jump Diffusion Model (page 457) • Merton produced a pricing formula when the stock price follows a diffusion process overlaid with random jumps • dp is the random jump • k is the expected size of the jump • l dt is the probability that a jump occurs in the next interval of length dt dS / S = ( − lk)dt + dz + dp