Utility-based hedging of exotic options under finite liquidity
: a computational approach

Student thesis: Doctoral ThesisDoctor of Philosophy


We develop computational models for indifference pricing in derivatives markets where price quotes have bid-ask spreads and finite quantities. We first study static hedging where traders only take buy and hold positions. The model quantifies the dependence of the prices and hedging portfolios on investor's beliefs, risk preferences and financial position as well as on the price quotes. Computational techniques of convex optimization allow for fast computation of the hedging portfolios and prices as well as sensitivities with respect to various model parameters. We illustrate the techniques by pricing and hedging of exotic derivatives on S&P index and VIX index using call and put options, forward contracts and cash as the hedging instruments. The optimized static hedges provide good approximations of the options payouts and the spreads between indifference selling and buying prices are quite narrow as compared with the spread between superhedging and subhedging prices. We then study semi-static hedging in derivative markets where the underlying can be traded dynamically while in derivatives we only take buy and hold positions. Galerkin method is used to reduce the infinite dimensional problem to a finite dimensional convex optimization problem which can be solved by an interior point method. We illustrate the technique by indifference pricing of path-dependent options written on S&P 500 options. The indifference prices have smaller spreads compared to the no arbitrage bounds. The semi-static hedging improves considerably on the purely static options strategy and the dynamic trading of the underlying without options. Finally, we extend the model by allowing transaction costs on the dynamically traded underlying.
Date of Award1 May 2020
Original languageEnglish
Awarding Institution
  • King's College London
SupervisorTeemu Pennanen (Supervisor) & John Armstrong (Supervisor)

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