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Hedging performance of utility indifference pricing of European call options

Köroğlu, Can
Hedging performance of the Utility Indifference Pricing model presented by Davis et. al [European option pricing with transaction costs, SIAM J. Con. & Opt., 31(2), 1993] is studied in this thesis. Their indifference pricing approach is based on utility indifference of an investor towards portfolios with and without a short position in the European call option contract. The option price is defined as a difference of the minimum amount of initial endowments that make the maximum utilities from these portfolios equal to zero. Furthermore, Davis et al. considered an incomplete market where transaction costs are included. They worked with an exponential utility function which eliminates the dependence of investments in stocks to total wealth. This framework is adopted and hedging strategy is defined as a difference of two control variables that solves the utility maximization problems for the portfolios. Thus, finding the call option price embedded in utility maximization problems is studied via Optimal Control Theory. Markov Chain Approximation is utilized to compute the problem numerically and the option price is derived. Ending wealth from the portfolio consisting of short position in the option is measured. Hedging error is defined as the losses incurred in this portfolio. Furthermore, hedging performance is measured by computing the conditional expected value of losses as a percentage of the option price. Hedging performance is evaluated against different levels of transaction costs, degree of risk aversion, volatility and option moneyness. Our findings suggest that hedging performance measure is large when volatility and risk aversion rates are low, and when transaction costs are high. We also find that moneyness of option has a decreasing effect on the hedging performance measure.