Static and dynamic hedging of multi-asset options

Abstract

In this dissertation, we study static and dynamic hedging of multi-asset options. We focus on a general multi-asset option hedging problem to consider various exotic options. In order to deal with the high-dimensional problem, we suggest efficient solution approaches to solve large-scale problems.

First, we compute static-arbitrage bounds on basket option prices. Especially, we focus on the lower bound case and propose a novel efficient solution procedure that is based on the separation problem. The computational burden of the proposed method is polynomial in the input data size. We also discuss the case of possibly negative weight vectors which can be applied to spread options. Additionally, we consider not only exact computation but also approximation of lower bounds when we have market prices of various options.

Next, we consider an hedging problem to minimize the uncertainty caused from multi-asset option trading. We suggest an affine control method to efficiently deal with the high-dimensional problem. First, we compute an optimal hedging strategy based on simulated paths. As the market state changes, the hedging plan is updated at every rebalancing time via online optimization. The hedging performance of the proposed approach is assessed in numerical tests and compared with those of other hedging strategies.

The theoretical and numerical results in this research will provide a better understanding of multi-asset options. Moreover, we expect the suggested approaches to be extended to more general cases.