Numerical options models without programming

We describe the automatic generation of nite diierence codes for solving the Black-Scholes and related equations for option valuation using the SciNapse software synthesis system. Analysts can specify codes at a very high level that mirrors the mathematical description of the problem. A typical option pricing speciication occupies less than a half page. From such concise input, the system automatically generates validated, documented codes of several hundred lines of either C or Fortran in minutes, codes of several thousand lines in about an hour. 1 The Opportunity Rapid development of numerical models for pricing and hedging has become essential to the derivatives industry. New types of derivatives proliferate as customers demand instruments structured to speciic requirements. Analysts must generate pricing models for the new instruments quickly and inexpensively, often within days or hours. The current method of developing nancial models, and scientiic modeling software in general, is a tedious cycle of programming, debugging, and re-testing, quite ill-suited to this new environment. Software synthesis can deliver an order of magnitude increase in software productivity. Software synthesis is the process of transforming high level speciications that mirror the mathematical description of the problem into eecient code in a conventional programming language such as C or Fortran. In this paper, we describe how analysts can specify options models to the SciNapse software synthesis system and display results from the generated codes. We also outline how SciNapse synthesizes programs. Modeling codes that have been synthesized by SciNapse include simple European and American put and call options, compound options, Asians and lookbacks with continuous and discrete sampling, inside and outside barrier options, convertible bonds with stochastic interest rate models, many types of rainbow options, and more. Underlying equities may pay continuous or discrete dividends of very general forms. Equation parameters may have arbitrary functional forms and dependencies, or may be even interpolated from tabular data. Volatilities, for example, may be assigned price and time structures obtained from current market data. In short, any option pricing problem that can be posed in terms of a PDE (possibly nonlinear) is suitable for SciNapse. In this section we illustrate how to specify pricing models to SciNapse. We begin with a simple speciication of an American put and discuss some basic speciication features. Then we discuss some additional features in a more complex speciication for a program that allows run-time European/American and put/call choices, discrete dividends, and calculation of …