Average Rate Option Pricing: Approximate Analytical Methods

When attempting to price average rate options, a few approximate analytical solutions have been developed to provide alternatives to Monte Carlo simulation, which can be computationally exhaustive. We discuss some variance reduction techniques, such as antithetic variates, control variates, importance sampling, and stratified sampling, and then examine in more detail the Levy method of option pricing. We describe the intuition behind Levy's method, and demonstrate how a risk-neutral transformation is applied to value average rate and average strike options.