Pricing Options Using Implied Trees:

Previously, few, if any, comparative tests of performance of Jackwerth’s (1997) generalized binomial tree (GBT) and Derman and Kani (1994) implied volatility tree (IVT) models were done. In this paper, we propose five different weight functions in GBT and test them empirically compared to both the Black-Scholes model and IVT. We use the daily settlement prices of FTSE-100 index options from January to November 1999. With both American and European options traded on the FTSE-100 index, we construct both GBT and IVT from European options and examine their performance in both the hedging of European option and the pricing of its American counterpart. IVT is found to produce least hedging errors and best results for American call options with earlier maturity than the maturity span of the implied trees. GBT appears to produce better results for American ATM put pricing for any maturity, and better in-sample fit for options with maturity equal to the maturity span of the implied trees. Deltas calculated from IVT are consistently lower (higher) than Black-Scholes deltas for both European and American calls (puts) in absolute term. The reverse holds true for GBT deltas. These empirical findings about the relative performance of GBT, IVT, and Standard Black-Scholes models are important to practitioners as they indicate that different methods should be used for different applications, and some cautions should be exercised. Since the market crash of October 1987, the volatility smile for most world equity markets has become more pronounced. The constant volatility assumption underpinning the Black-Scholes options pricing model (1973)[4] is violated if we assume that the option market is efficient and the options are correctly priced. Tompkins (1998)[35] documents volatility smiles in the UK, Japan, and Germany and compares them with similar smiles in US markets. Studies have extended the Black and Scholes model to account for the volatility smile and other related empirical violations. Jackwerth and Buraschi (1998)[24] group them into two main approaches: Stochastic Volatility models and Deterministic Volatility models. In Stochastic Volatility models, the evolution of the stock price volatility can be modeled to follow a certain process. Two examples are Brownian motion and mean-