Pricing and hedging bond options in the presence of transaction costs.

摘要

This dissertation studies how to price and hedge European bond options in the presence of transaction costs. When transactions cannot be made costless, the Black and Scholes' continuous rebalancing argument suffers from potentially huge transaction costs. Although this subject has been extensively studied for the case of equity options since Leland (1985)'s first groundwork, no research has been performed on the case of bond options to my knowledge. We formulate the problem of interest on pricing and hedging bond options with transaction costs mainly in two different ways---as an extension of Lai and Lim (2004) and of Hodges and Neuberger (1989) to the case of bond options.; In our formulations, we propose to hedge a bond option with a futures contract on the underlying bond. This approach has two main advantages over a hedging strategy with an underlying bond. First, a futures contract is traded on exchanges while a bond is not; thus, a futures contract has less risk of illiquidity, which is a critical property of a hedging vehicle. Second, no initial capital is required to long or short futures contracts, which is advantageous to investors with a limited access to capital. When we use a futures contract as a hedging vehicle, we hedge a bond option by replicating not the option itself but a "forward contract" on the option. This is analogous to hedging a commodity position with a forward contract on the commodity.; A difficulty unique to our formulations is that we work with two diffusion processes; one is for a short rate and the other is for a futures price. The construction of a binomial lattice for the two processes is not as simple as one might expect. We propose an approximate binomial lattice approach to retain the lattice structure. Using this lattice, we solve the two main formulations for the problem we address and compare the results.