A smiling tree: an empirical evaluation on binomial tree methods for local volatility model
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Date
2009-09
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The British University in Dubai (BUiD)
Abstract
This study compares between the standard Black-Scholes model and two local volatility models of implied binomial trees for PowerShare index options with regards to the pricing accuracy when evaluated against actual market prices. With Black, F. and M. Scholes (1973): The Pricing of Options and Corporate Liabilities. Journal of Political Economy, volume: 81, pp. 637 – 59 model as a benchmark, two local volatility models were analyzed: Derman and Kani's [Derman, E., & Kani, I., 1994. The Volatility Smile and Its Implied Tree. Risk, 7, 32–39] and Barle and Ckici’s [Barle, S and N. Cakici, (1998): How to Grow a Smiling Tree. The Journal of Financial Engineering, Vol. 7, No. 2, June 1998]. The model suggested by Barle and Cakici shows the best performance followed by Derman and Kani. Black-Scholes performance on the other hands was significantly
lower than the two models. This is attributed to the fact that Black-Scholes model adopts a constant volatility regardless of option’s strike price or time to maturity. This finding is consistent at different moneyness levels and for different maturity periods.
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Keywords
empirical evaluation, binomial tree