A Non-parametric Approach to Pricing and Hedging Derivative Securities: With an Application to LIFFE Data

It is important for financial institutions to develop methods to predict their exposure and keep their risk under control. Portfolio managers can insure themselves against the value (of a diversified stock portfolio) dropping below a certain level, by holding in conjunction with the stock portfolio, an index option derivative security. The work reported in this paper is concerned with the study of non-parametric methods for estimating the pricing formula of option derivative securities. Two non-parametric approaches, the projection pursuit method (PPR) and the local polynomial approach (LOESS), are studied and compared to a benchmark parametric Black-Scholes (B-S) approach. The practical relevance of these approaches is tested, when applied to pricing and hedging of real-world LIFFE FTSE 100 index options from April 1997 to November 1997. We compare the two methods by means of constructing a riskless portfolio of stocks, bonds and option derivatives securities. The portfolio is then delta-hedged on a daily basis using a dynamic trading strategy in stocks and bonds during the lifetime of the option instrument. The tests carried out show that both methods generate similar responses, although each method can outperform the others depending on market conditions, such as, time to maturity of the option instrument. Copyright 2002 by Kluwer Academic Publishers