Testing the alternative two-state options pricing models: An empirical analysis on TXO

Considering the volatility in two states, the option pricing models involved constant volatility can be extended to two-state lognormal model (TLN), two-state constant-elasticity-variance model (TCEV) and two-state jump-diffusion model (TJD). Using Taiwan stock index, the parameters of transition between high- and low-volatility of the three two-state option pricing models are all estimated significant and then using TXO, we examine the three two-state models compared with the Black-Scholes model from two perspectives: strike prices and maturities in TXO. Overall, the option pricing performance of the four models in descending order are TLN, Black-Scholes, TCEV, and TJD in both call and put options while they have better pricing performance in put options than in call options. With the same strike price, the series of pricing errors across different maturities are nonstationary for the four models based on the unit root-test. However, with the different strike prices, the Johansen co-integration test of the different series of pricing errors are stationary and have finite variance. It appears that the spreads of pricing errors between different strikes are stable and mean reverse in the long run and the short run divergences from the equilibrium are vanished after all.