Option pricing under stock market cycles with jump risks: evidence from the S&P 500 index

Abstract

This study incorporates the Markov switching model with return jumps to depict the behavior of stock returns. Based on the daily Standard & Poor’s 500 index (hereafter SPX) and the daily closing price of the call option, we use the particle filtering algorithm to fit the parameter of the model. The joint log-likelihood evaluates the model performance: the weighted average log-likelihood with the rate of return of the SPX and the relative implied volatility root-mean-squared error for the SPX call options. The empirical results identify that the pricing model with jump risks improves the pricing performance to the median-term call options. According to the sensitivity analysis, option prices increase with the probability of remaining in the recession state but decrease with the probability of remaining in the expansion state. Moreover, the call option prices are positively associated with the volatility in each market state and the factors of jump risk.