Math @ Duke

Publications [#296272] of Harrison Potter
Papers Published
 VX Dang, H Potter, S Glasgow and S Taylor, Pricing the Asian Call Option,
Electronic Proceedings of Undergraduate Mathematics Day, vol. 3 no. 3
(February, 2008),
pp. 26 [available here]
(last updated on 2016/02/14)
Abstract: Background material on measuretheoretic probability theory and stochastic
calculus is provided in order to clarify notation and inform the reader unfamiliar with
these concepts. These fields are then employed in exploring two distinct but related approaches
to fair option pricing: developing a partial differential equation whose solution,
given specified boundary conditions, is the desired fair option price and evaluating a riskneutral
conditional expectation whose value is the fair option price. Both approaches are
illustrated by example before being applied to the Asian call option.
Two results are obtained by applying the latter option pricing approach to the Asian call
option. The price of an Asian call option is shown to be equal to an integral of an unknown
joint distribution function. This exact formula is then made approximate by allowing one
of the random variables to become a parameter of the system. This modified Asian call
option is then priced explicitly, leading to a formula that is strikingly similar to the Black
ScholesMerton formula, which prices the European call option. Finally, possible methods
of generalizing the procedure to price the Asian call option both exactly and explicitly are
speculated.


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