BFS 2002

Poster Presentation

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 risk-neutral valuation for jump-diffusion processes. By using a recent result of duality by Delbaen et. al. (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.       www.math.ust.hk/~malwu/Publ/JumpDiff.pdf