Pricing Asian Options with Monte-Carlo Method

Abstract

The paper is the Computational Finance project on pricing Asian options with the Monte-Carlo method. The certain discounted payoff formula is given under the risk-neutral density. The author reviews the arithmetic sampling payoff formula for fixed and floating strikes; the geometric sampling payoff formula for the fixed and floating strikes. In both cases the author use the Euler-Maruyama scheme for simulating the underlying stock price using the following set of data: today’s stock price S0 = 100; strike K = 100; time to expiry (T − t) = 1 year; volatility σ = 20%; constant risk-free interest rate r = 5%. As a result following is produced: outline of the numerical procedure; appropriate tables, comparisons and error graphs; analysis of observations and problems encountered.