Bounds On Prices For Asian Options Via Fourier Methods

Publisher:
Australian Mathematical Society
Publication Type:
Journal Article
Citation:
ANZIAM Journal, 2016, 57 (3), pp. 299 - 318
Issue Date:
2016-01-03
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The problem of pricing arithmetic Asian options is nontrivial, and has attracted much interest over the last two decades. This paper provides a method for calculating bounds on option prices and approximations to option deltas in a market where the underlying asset follows a geometric L´evy process. The core idea is to find a highly correlated, yet more tractable proxy to the event that the option finishes in-the-money. The paper provides a means for calculating the joint characteristic function of the underlying asset and proxy processes, and relies on Fourier methods to compute prices and deltas. Numerical studies show that the lower bound provides accurate approximations to prices and deltas, while the upper bound provides good though less accurate results.
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