Estimating Lookback Price Using Monte Carlo Simulation and Binomial Lattice

Lookback options are path-dependent option, whose payoffs depend on the maximum and minimum value of the underlying assets throughout the duration of the contract. Since the payoffs are calculated based on the asset price during the lifetime of the option, there are no analytic formulas yet to evaluate the price of the option. However, the approximation can be obtained using numerial methods. Monte carlo simulation and binomial lattice are two of those numerical methods that will be applied in this paper. Numerical solution using monte carlo is obtained by generating the future price of assets that will be later used in estimating the option and binomial model also does similar action, the only different is all possible paths of the underlying asset are based on the assumption that the stock price for next period will move into two possible values, either up or down. The price lookback option have been computed both for fixed strike lookback call and put; and floating strike lookback call and put, the approximation using the both numerical analysis are compared with analytic Black-School results, and shown that Binomial lattice gives better numerical solution than Monte Carlo. However, the values in Binomial are not entirely close to Black-Scholes, it shows poor performance in Floating Strike Lookback Put Option. Monte Carlo, on the other hand, does not work very well for pricing this option.