Valuation of Asian Options by Monte Carlo Simulation

Ayako Fukui

Mathematics

Asian options are very useful in the financial industry and are one of the most popular path-dependent exotic options today. They can be used to hedge an asset over a certain period of time. The hedge is cheaper than a portfolio of plain vanilla options. In addition to the cost-effectiveness, the Asian options have another advantage over the

plain vanilla options in that they can be used to protect against price manipulation by either contract party on the maturity date. The main focus of my research will be on continuously sampled European style arithmetic average rate options, one of numerous versions of Asian options.

The pricing of an Asian option is known to be computationally hard and a great deal of literature deals with this problem, using either analytic methods, numerical methods based on the associated partial differential equation, or Monte Carlo methods. I will introduce and discuss different valuation methods with the focus on Monte Carlo methods.

Monte Carlo methods are known to be useful when the state dimension is large. This is widely true, but in my paper, I will give an example of a small dimension problem where a Monte Carlo method can be more efficient than other known methods. I will show that, when we use a suitable scheme and variance reduction, a Monte Carlo method can be more competitive than other methods under some circumstances. Surprisingly, really high precision (10^-4) can only be reached by a Monte Carlo method with a relatively large time step (approximately one month).