Essays on risk management and valuation of derivatives

Abstract

This thesis deals with two subjects. The first subject is a strategy of hedging bond portfolios with interest rate futures. Traditional duration assumes that the term structure is flat and all shifts in the term structure are parallel and infinitesimal. This thesis derives a general hedging strategy with interest rate futures when the yield curve changes are nonparallel, noninfinitesimal, and noninstantaneous at the present. For considering nonparallel changes of the yield curve, a simple polynomial structure of the yield curve changes is assumed, and for considering noninfinitesimal changes, the higher derivative terms of the Taylor expansion of the change in bond price are included. Also, it is assumed that the yield curve changes between present time and an investor``s planning horizon. This thesis presents a general hedging strategy with interest rate futures under polynomial approximations to the shape of the yield curve changes. It differs from previous approaches to immunizing against nonparallel shifts in that the duration vectors considering that the yield curve changes once in the future are defined, and the simultaneous equations to calculate hedge ratios for hedging at an investor``s planning horizon are derived using the definition of forward prices. The second subject of this thesis is a binomial model for pricing Asian options. Asian options are path-dependent contingent claims whose payoffs depend on the average prices of underlying asset. This thesis has developed a lattice model to price Asian options. First, the algorithm to price geometric average options is derived. The accuracy of the algorithm has been tested against closed form solutions of Turnbull and Wakeman, and the numerical results show that the algorithm approximates well the closed form solution. Thus, the algorithm can be used successfully to the valuation of American geometric average options. Next, the algorithm to price arithmetic average options is derived. The algorithm o...