Compound Cox processes and option pricing (Q1600611)

The author uses a compound Cox process to obtain a new model for the description of a financial -- asset progress employing the limit theorem for a random sum of random variables. The obtained Levy process has increments with symmetrized Gamma distribution. By applying various statistical tests it is shown that the new introduced model provides a more accurate statistical model for daily exchange rates than the geometric Brownian motion. Esscher transform has been used to find an equivalent martingale measure and the option pricing formula for a European call option.