A Study On Some Exotic Options Pricing Using An Actuarial Approach

An option is a contract that gives the holder the right to buy or sell an underlying asset by a certain time for a predetermined price after paying off the option premium. One important aspect of the research on option pricing theory is focused on how to price the more and more complicated options. Before 1980s, there is an ideal assumption on option pricing research, which is the market is perfect. In these ten years, we made great progress on how to price options under imperfect market, one of important methods is actuarial approach.Actuarial approach turns the option pricing problem into an equivalent insurance or a fair premium determination. There are no economical considerations involved, and our approach is valid even when the market is arbitrage, non-equilibrium and incompleteness. The basic idea is the following: discount risk free (deterministic) future prices according to the risk free interest rate and stochastic prices according to their expected rate of return. With these discounted prices we can calculate the price of a call option as the expected value of the difference between the actual price and the strike price (in present values) when exercising.Exotic options are more complex than vanilla options. Partial differential equation and the binomial tree pricing model are main methods to value exotic options, but the task is difficult and tedious. Choose options, compound options and options to exchange one asset to another are some important exotic options, this paper mostly studies pricing problems on these options by using the stochastic analysis and probability theory. The main work is the following: Firstly, we deal with general pricing formulas of choose options ,compound options , options to exchange one asset to another using physical probability measure of price process and the principle of fair premium- an actuarial approach; Secondly, under the hypothesis of underlying asset price submitting to Geometric Brownian Motion, we obtain the accurate pricing formulas.