a closed-form analytical solution for pricing forward start option under a variance gamma process

In this paper, we are interested in valuation of forward start option under variance gamma (vg) process, a mathematical model that extends traditional brownian motion (bm) by introducing three parameters. this enhancement allows for more flexibility in capturing asset price dynamics, which can exhibit jumps and volatility clustering absent in standard models. we analyze the conditions under which the vg process behaves as a martingale, providing insights into its application in financial derivatives pricing.we conduct extensive computational experiments to assess the accuracy of the vg process in pricing forward start options.the results demonstrate the efficacy of the vg process in capturing the characteristics of market behavior, thereby offering more reliable pricing mechanisms for forward start options. we validate the theoritical finding with the monte carlo (m.c.) simulation.