Numerical Methods for Pricing Exotic Options

Derivative securities, when used correctly, can help investors increase their expected returns and minimize their exposure to risk. Options offer leverage and insurance for risk-averse investors. For the more risky investors, they can be ways of speculation. When an option is issued, we face the problem of determining the price of a product which depends on the performance of another security and on the same time we must make sure to eliminate arbitrage opportunities. Due to the nature of those contracts, over the past decades a lot of research has focused on finding accurate valuation models for options. Popular pricing methods such as Black-Scholes PDE have proven to be inefficient for pricing exotic options as it is impossible to express their price in an analytic solution In this project, we investigate two recently proposed valuation techniques. They approach the problem of pricing an option by approximating upper and lower bounds for the option price using semidefinite programming. We will explore the price dynamics of options and the efficiency of these methods for pricing European and Exotic options. www.doc.ic.ac.uk/~db04/project/ 4 Numerical Methods for Pricing Exotic Options 5 1BAcknowledgements