Risk-Neutral Option Pricing for Log-Uniform Jump-Amplitude Jump-Diffusion Model

44 Pages Posted: 28 Jan 2013

See all articles by Floyd B. Hanson

Floyd B. Hanson

University of Illinois at Chicago

Zongwu Zhu

University of Illinois at Chicago

Date Written: January 28, 2013

Abstract

Reduced European call and put option formulas by risk-neutral valuation are given. It is shown that the European call and put options for log-uniform jump-diffusion models are worth more than that for the Black-Scholes (diffusion) model with the common parameters. Due to the complexity of the jump-diffusion models, obtaining a closed option pricing formula like that of Black-Scholes is not tractable. Instead, a Monte Carlo algorithm is used to compute European option prices. Monte Carlo variance reduction techniques such as both antithetic and optimal control variates are used to accelerate the calculations by allowing smaller sample sizes. The numerical results show that this is a practical, efficient and easily implementable algorithm.

Keywords: option pricing, jump-diffusion model, Monte Carlo method, antithetic variates, optimal control variates, variance reduction

Suggested Citation

Hanson, Floyd B. and Zhu, Zongwu, Risk-Neutral Option Pricing for Log-Uniform Jump-Amplitude Jump-Diffusion Model (January 28, 2013). Available at SSRN: https://ssrn.com/abstract=2208191 or http://dx.doi.org/10.2139/ssrn.2208191

Floyd B. Hanson (Contact Author)

University of Illinois at Chicago ( email )

1200 W Harrison St
Chicago, IL 60607
United States

HOME PAGE: http://www.math.uic.edu/~hanson

Zongwu Zhu

University of Illinois at Chicago ( email )

1200 W Harrison St
Chicago, IL 60607
United States

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