high performance computing on graphics processing units: hgpu.org

We present a language for specifying stochastic processes, called SPL. We show that SPL can express the price of a range of financial contracts, including so called exotic options with path dependence and with multiple sources of uncertainty. Jones, Eber and Seward previously presented a language for writing down financial contracts in a compositional manner [JES00], and specified a pricer for these contracts in terms of an abstract financial model and abstract stochastic processes. For the subset of prices that do not require nested forecasting, these can be specified in SPL, and we show an example of how to do this. The ease of writing a model that matches reality and the speed of computing the expected price is then highly dependent on the properties of SPL. SPL is declarative in the sense that it is agnostic of the computational model. It is designed with the goal of matching the notation used in mathematical finance, which allows a high level specification of stochastic processes. The language is embedded in Haskell, and we have given the language formal semantics in terms of the probability monad [Gir82], as well as a type system in terms of Haskell’s type system. We provide an implementation of SPL that performs Monte Carlo simulation on the GP-GPU, and we present data indicating that this implementation scales linearly with the number of available cores.