Pricing index options by static hedging under finite liquidity

TL;DR

This paper introduces a model for pricing and hedging index options in markets with bid-ask spreads and finite liquidity, using convex optimization to efficiently compute prices and sensitivities.

Contribution

It develops a novel indifference pricing framework accounting for market frictions and investor preferences, with practical computational methods for exotic derivatives.

Findings

Narrow bid-ask spreads for indifference prices compared to super- and subhedging prices.

Efficient convex optimization techniques enable fast computation of prices and hedges.

Static hedging approximates exotic option payouts effectively.

Abstract

We develop a model for indifference pricing in derivatives markets where price quotes have bid-ask spreads and finite quantities. The model quantifies the dependence of the prices and hedging portfolios on an investor's beliefs, risk preferences and financial position as well as on the price quotes. Computational techniques of convex optimisation 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 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 super- and subhedging prices.