TRADING OPTION MODEL PARAMETERS AND CLIQUET PRICING USING OPTIMAL TRANSPORT

Abstract

This dissertation consists of two independent topics. Chapter 1 titled, “Trading Option Model Parameters” describes two methods of constructing a portfolio of vanilla options that is sensitive to only one parameter for any kind of option pricing model. These special portfolios can be constructed for any parameter and move in the same direction as that specific parameter, while being resistant to changes in all others. We use the Variance Gamma model and Bilateral Gamma model as examples and show both methods yield portfolios with similar payoff structure at maturity. In addition we show that the value of these portfolios remains unchanged when all but one parameter is perturbed. We conclude by assessing the viability of using these methods as a trading or hedging strategy. Chapter 2 titled “Pricing Cliquets using Martingale Optimal Transport” applies the theory of Optimal Transport to pricing forward starts and cliquets. We develop models based on relative entropy minimization that provide close fits to market data using information based on just the marginal distributions. We prove a duality result that provides an explicit form of the optimal distribution. Furthermore we provide an algorithm and a convergenceresult for iteratively computing the dual. Chapter 3 titled “Martingale Optimal Transport under Acceptability” addresses the issue of narrowing the no arbitrage price bounds for a cliquet by introducing the concept of acceptable risk. We prove a duality result based on acceptability and show how to numerically compute acceptable bounds.