Using program synthesis to price derivatives

ABSTRACT The authors demonstrate the use of software synthesis to produce finite-difference code for a variety of option pricing problems. In this approach, pricing models are specified in a concise language that mirrors the mathematical and financial statement of the problem. Specifications typically occupy less than a half page. An intelligent software synthesis system then automatically translates these specifications into codes of thousands lines in a conventional programming language such as C or Fortran. Option features for which pricing code can be automatically synthesized include discrete dividends and early exercise, discretely or continuously sampled stationary or moving barriers, stochastic volatility and interest rate models, multiple underlying assets, and more. A method of parametrizing an arbitrary functional dependence on the underlying assets enables synthesis of code for standard path dependent options such as Asian and lookbacks as well as for much more complex path-dependent options.