Title :
American Put Option Pricing for Stochastic-Volatility, Jump-Diffusion Models
Author :
Hanson, Floyd B. ; Yan, Guoqing
Author_Institution :
Univ. of Illinois at Chicago, Chicago
Abstract :
The numerical treatment for the American put option pricing is discussed for a stochastic-volatility, jump- diffusion (SVJD) model with log-uniform jump amplitudes. Heston´s (1993) mean reverting, square-root stochastic volatility model is used along with our uniform jump-amplitude model. However, computation is needed for nonlinear and multidimensional terms with dependence on the combined stock and volatility state space. A systematic finite difference formulation of the American put partial integro-differential complementary problem (PIDCP) is implemented using a successive over-relaxtion method projected on the maximum payoff function. Interpolation is used to construct the smooth transition to the payoff of the corresponding free boundary problem. Also, a fast, but less accurate, heuristic quadratic approximation, originally due to MacMillan (1986), is corrected and extended from pure diffusion models. The fast and simple quadratic approximation is compared with a more accurate PIDCP formulation. The simple quadratic approximation is briefly compared with market data.
Keywords :
approximation theory; finite difference methods; integro-differential equations; partial differential equations; pricing; quadratic programming; share prices; stochastic processes; American put option pricing; heuristic quadratic approximation; jump-diffusion model; log-uniform jump amplitude model; maximum payoff function; mean reverting; partial integro-differential complementary problem; square-root stochastic volatility model; systematic finite difference formulation; Approximation methods; Cities and towns; Contracts; Finite difference methods; Interpolation; Multidimensional systems; Pricing; Security; State-space methods; Stochastic processes; American option put pricing; jump diffusion; linear complementary problem; quadratic approximation; stochastic volatility; uniform jump-amplitudes;
Conference_Titel :
American Control Conference, 2007. ACC '07
Conference_Location :
New York, NY
Print_ISBN :
1-4244-0988-8
Electronic_ISBN :
0743-1619
DOI :
10.1109/ACC.2007.4283124