Pricing exchange options with correlated jump diffusion processes

Abstract

We study the applicability to energy facilities of a model for correlated Poisson processes generated by self-decomposable jumps. In this context, the implementation of our approach, both to shape power or gas dynamics, and to evaluate transportation assets seen as spread or exchange options, is rather natural. In particular we first enhance the Merton market with two underlying assets making jumps at times ruled by correlated Poisson processes. Here however— at variance with the existing literature—the correlation is no longer provided only by a systemic common source of synchronous macroeconomic shocks, but also by a delayed synaptic propagation of the shocks themselves between the assets. In a second step, we consider a price dynamics driven by an exponential mean-reverting geometric Ornstein–Uhlenbeck process plus a compound Poisson process: a combination which is well suited for the energy markets. In our specific instance, for each underlying, we adopt a jumping price spot dynamics that has the advantage of being exactly treatable to find no-arbitrage conditions. As a result we are able to find closed form formulas for vanilla options, so that the price of the spread options can subsequently be calculated (again in closed form) using the Margrabe formula if the strike is zero (exchange options), or with some other suitable procedures available in the literature. The exchange option values obtained in our numerical examples show that, compared to the other Poisson models we analysed, the dependence introduced by the self-decomposition gives more relevance to the timing of the jumps and not only to their frequency.