Numerical Procedures

Q: What are the methods available to value derivatives contracts?

A: When the Black-Scholes formula is not applicable i.e the option payoff is path dependent and the option can be exercised prior to maturity as in the case of American options, there are three methods available. First, Binomial tree approach where the movement of the asset price is mapped on a tree. Second, Monte Carlo simulation where simulated value of future asset price is used to value derivatives. Third, Finite Difference Method where the differential equation is converted to a set of difference equations and then solved iteratively.

Q: What are the conditions under which these methods are applied?

A: MCS works from the beginning to the end of the life of the derivative. While both tree and FDM work in reverse. But MCS becomes less time consuming and more efficient when the number of underlying variable increases. But all three methods can be applied to both American and European options.