Utility indifference pricing theory with applications in weather derivatives

Abstract

The aim of this dissertation is to explore a particular method, known as utility indifference pricing, for pricing derivatives in incomplete markets. Using the exponential family of utility functions to model investor preferences, an explicit representation of the indifference price is derived. After exploring the necessary theory from stochastic optimal control, the price is derived by first formulating a stochastic optimal control problem and then applying stochastic dynamic programming techniques. The pricing formula is derived for 2 cases; when the investor has a previous risk exposure to the underlying phenomenon on which the derivative is written (the underlying), and when there is no such prior risk exposure to the underlying. After modelling a temperature process using temperature data taken from Luqa weather station, simulations are done to determine the behaviour of the price as various parameters in the model were varied. It is shown how the behaviour of the indifference price of a buyer is greatly affected by the existence of a prior risk exposure to the underlying on which the derivative is written, and how both the writer and buyer of a derivative stand to gain from a trade when the buyer feels that the derivative is effectively reducing any risk exposure to the underlying.