On the Conditional Moment-Generating Function of a Three-Factor Variance Gamma Based Process and Its Applications to Forward and Futures Pricing

#### R.V. Ivanov, G. Temnov

2016, v.22, №4, 737-758

ABSTRACT

In this paper we present an analytical formula for the conditional
moment-generating function of a sum of the variance gamma process and several diffusion processes.
The result is applicable to the problem of futures and forward pricing in models with stochastic interest rates,
where log-returns of a stock are supposed to follow the variance gamma distribution.
The obtained formulas are dependent on evaluations of the parabolic cylinder function.

Keywords: variance gamma process, Ornstein\tire Uhlenbeck process, forward, futures, moment-generating function, stochastic interest rate