Pricing European option price in jump-diffusion model / Anisah Abdul Rahman, Siti Salihah Shaffie and Nadzri Mohamad

This research presents a numerical method for pricing European options. The method is based on the jump diffusion process. The Merton’s jump-diffusion model has become a popular model among researchers. The
problem of pricing options with Black-Scholes framework remains a contemporary research topic. The Merton
model extends the Black-Scholes model making iteasy to produce an analytical solution for a variety of option
pricing problems. According to Peter Car, jump-diffusion has become a popular model being used by the
researchers because it is better able to fit smile volatility. There exists a consistent theoretical framework enabling experimentations with adapting the stock hedge or hedging with option.In essence, the Merton model
can be applied directly, given a slight reinterpretation of the parameters of the model. The reinterpretation
requires that we substitute the stock index value, for the stock price in the Merton’s model. We also substitute
the dividend rate on stock index, which we presume to equal risk-free rate. With these substitutions, we can
apply the Merton’s model to price the options.