On option pricing in local volatility models using parallel computing

Pricing of options and other financial instruments is one of the most important problems in finance. To price an option, one needs first to choose the model of underlying asset price dynamics, usually in the form of a stochastic differential equation depending on market parameters such as interest rate, asset volatility, etc., then find a solution of the chosen model in some form, and finally obtain the required option price. The asset volatility can be constant (Black-Scholes model), depend on the value of the underlying asset and time (local volatility model), or satisfy some other stochastic differential equation (stochastic volatility model). Exact analytical formula for option price was obtained for Black-Scholes model and a few other models with local and stochastic volatility, but in general case one has to use approximations or numerical methods to evaluate options. We study the problem of European option pricing when volatility is a function of underlying asset value and time. To solve the problem, we use Monte Carlo method to construct the empirical distribution density of underlying asset and then determine the option value using Feynman-Katz formula. The issues of parallelization of the option pricing algorithm and its implementation on computers with multicore processors are discussed. Possible applications of local volatility models with parallel computing include modeling and management of large equity portfolios, assessing and managing market and credit risks. © 2020 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings (CEUR-WS.org)