Results 1 
2 of
2
Option pricing under a mixedexponential jump diffusion model
 Management Science
, 2011
"... This paper aims to extend the analytical tractability of the Black–Scholes model to alternative models witharbitrary jump size distributions. More precisely, we propose a jump diffusion model for asset prices whose jump sizes have a mixedexponential distribution, which is a weighted average of expo ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
This paper aims to extend the analytical tractability of the Black–Scholes model to alternative models witharbitrary jump size distributions. More precisely, we propose a jump diffusion model for asset prices whose jump sizes have a mixedexponential distribution, which is a weighted average of exponential distributions but with possibly negative weights. The new model extends existing models, such as hyperexponential and doubleexponential jump diffusion models, because the mixedexponential distribution can approximate any distribution as closely as possible, including the normal distribution and various heavytailed distributions. The mixedexponential jump diffusion model can lead to analytical solutions for Laplace transforms of prices and sensitivity parameters for pathdependent options such as lookback and barrier options. The Laplace transforms can be inverted via the Euler inversion algorithm. Numerical experiments indicate that the formulae are easy to implement and accurate. The analytical solutions are made possible mainly because we solve a highorder integrodifferential equation explicitly. A calibration example for SPY options shows that the model can provide a reasonable fit even for options with very short maturity, such as one day. Key words: jump diffusion; mixedexponential distributions; lookback options; barrier options; Merton’s normal jump diffusion model; first passage times
On the Solution of Complementarity Problems Arising in American Options Pricing
, 2009
"... In the BlackScholesMerton model, as well as in more general stochastic models in finance, the price of an American option solves a system of partial differential variational inequalities. When these inequalities are discretized, one obtains a linear complementarity problem that must be solved at e ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
(Show Context)
In the BlackScholesMerton model, as well as in more general stochastic models in finance, the price of an American option solves a system of partial differential variational inequalities. When these inequalities are discretized, one obtains a linear complementarity problem that must be solved at each time step. This paper presents an algorithm for the solution of these types of linear complementarity problems that is significantly faster than the methods currently used in practice. The new algorithm is a twophase method that combines the activeset identification properties of the projected GaussSeidel (or SOR) iteration with the secondorder acceleration of a (recursive) reducedspace phase. We show how to design the algorithm so that it exploits the structure of the linear complementarity problems arising in these financial models and present numerical results that show the effectiveness of our approach.