PRICING BONDS AND EUROPEAN OPTIONS IN A MILD STOCHASTIC ENVIRONMENT

The paper deals with the problem of pricing derivative financial products. The most frequently used option pricing method is that given by the well-known Black-Scholes model (1973). This model starts from the assumption that the market uncertainty can be modeled by a white noise (Wiener process). The Black-Scholes option price results as a solution of a second order partial differential equation. The present paper starts from an idea of the late Professor Aristide Halanay from Bucharest University. The idea consists of considering a more regular behaviour of the market, called "mild stochastic environment". In this framework, the "fair" price of an option is the solution of a first order partial differential equation.