Pricing Jump Risk with Utility Indifference

34 Pages Posted: 21 Feb 2005

See all articles by Lixin Wu

Lixin Wu

Hong Kong University of Science & Technology - Department of Mathematics

Min Dai

National University of Singapore (NUS) - Department of Mathematics

Date Written: February 21, 2002

Abstract

In an incomplete market, option prices depend on investors' utility functions. In this paper, we establish the connection between risk preference and optimal hedging strategy, and price options according to the principle of utility indifference. Taking the exponential utility function, we completely characterize the risk-neutral valuation for jump-diffusion processes. By using a recent result of duality by Delbaen (2000) we prove that pricing measure for the risk neutral valuation is just the equivalent minimal entropy martingale measure. We show that risk aversion contributes a price spread from the risk neutral price. We also show that, however, risk-neutral valuation does not correspond to any practical hedging strategy. Minimal variance hedging strategy is discussed. Parallel analysis is carried over to discrete setting with multi-nomial random walks, and efficient numerical methods are developed. Numerical examples show that our model reproduces crash-o-phobia and other features of market prices of options.

Keywords: Utility maximization, utility indifference prices, minimal entropy martingale measure, jump-diffusion processes, risk neutral valuation

JEL Classification: C61, G13

Suggested Citation

Wu, Lixin and Dai, Min, Pricing Jump Risk with Utility Indifference (February 21, 2002). Available at SSRN: https://ssrn.com/abstract=663442 or http://dx.doi.org/10.2139/ssrn.663442

Lixin Wu (Contact Author)

Hong Kong University of Science & Technology - Department of Mathematics ( email )

Clearwater Bay
Kowloon, 999999
Hong Kong
2358-7435 (Phone)
2358-1643 (Fax)

Min Dai

National University of Singapore (NUS) - Department of Mathematics ( email )

Singapore

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