An enhanced implied tree model for option pricing: A study on Hong Kong property stock options

Abstract

This paper empirically tests the practicability of the implied tree models on pricing the major HK real estate stock options and Hang Seng Index (HSI) Options, as an attempt to deal with the problem haunting the Black–Scholes Model in “volatility smiles”. Further, an iterative search procedure is originated to incorporate the idea of node-dependent interest rates to the implied binomial tree model. The results would then be compared with the original Cox, Ross, and Rubinstein (1979) [Cox, J., Ross, S. and Rubinstein, M. (1979), Option pricing: A simplified approach, Journal of Financial Economics, vol.7, no.3 (September), 229–264] tree models (CRR) in order to assess its performance, through an out-of-sample fitness test. The findings illustrate that the implied binomial trees, with node-dependent interest rates, provide a closer estimate of option prices than the original CRR tree models, when options are frequently traded in the market. Encouraging results are obtained from the in-sample fitness test on the implied trees to simulate the spot evolution of HSI options within a short period of time. However, the original CRR tree models outperform the implied tree models on either inactively traded property stock options, or options with distant time-to-maturity. Misrepresentation of future local volatilities, implied by the prices, and data constraints are likely the reasons hindering the development of the implied tree models.