Novikov, A, Alexander, S, Kordzakhia, N & Ling, T 2017, 'Pricing of asian-type and basket options via bounds', Theory of Probability and Its Applications, vol. 61, no. 1, pp. 94-106.View/Download from: Publisher's site
© 2017 Society for Industrial and Applied Mathematics. This paper sets out to provide a general framework for the pricing of average-type options via lower and upper bounds. This class of options includes Asian, basket, and options on the volume-weighted average price. The use of lower and upper bounds is proposed in response to the inherent difficulty in finding analytical representations for the true price of these options and the requirement for numerical procedures to be fast and efficient. We demonstrate that in some cases lower bounds allow for the dimensionality of the problem to be reduced and that these methods provide reasonable approximations to the price of the option.
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.