Options are a type of financial derivative that has enjoyed an immense boom in the past 40 years. Asian option are a class of path-dependent options, whose payoff depends on the average value of the underlying asset during the option's duration. This feature drastically increases the difficulty of their valuation. In this work, a basic mathematical framework is presented to develop the classic theory of option valuation, and both the Black-Scholes model binomial tree approach are described. The latter is then modified into a method to value Asian options using an idea first presented by Hull and White in [8], where a table is added to each node of the tree that tracks the potential values of the average. To avoid the exponential increase in size each table only contains a small set of representative values, which are used to interpolate the missing values. Valuation then proceeds via standard backward recursion towards the base of the tree and the desired initial option price. The error incurred by using interpolation is mitigated by having a sufficient number of representative values. An efficient implementation of this method is presented and its performance further improved with the use of Richardson extrapolation. The method is then tested on options for which the correct value is known analytically and proves to be both fast and precise.
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