Pricing Jump Risk with Utility Indifference
34 Pages Posted: 21 Feb 2005
Date Written: February 21, 2002
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
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