IJPAM: Volume 94, No. 2 (2014)

PERFORMANCE MEASURE OF LAPLACE TRANSFORMS
FOR PRICING PATH DEPENDENT OPTIONS

Chuma Raphael Nwozo$^1$, Sunday Emmanuel Fadugba$^2$
$^1$Department of Mathematics
University of Ibadan
Oyo State, NIGERIA
$^2$Department of Mathematical Sciences
Ekiti State University
Ado Ekiti, NIGERIA


Abstract. This paper presents a performance measure of Laplace transforms for pricing path dependent options. We obtain a simple expression for the double transform by means of Fourier and Laplace transforms, (with respect to the logarithm of the strike and time to maturity) of the price of continuously monitored Asian options. The double transform is expressed in terms of Gamma functions only. The computation of the price requires a multivariate numerical inversion. Under jump-diffusion model, we show that the Laplace transforms of lookback options can be obtained through a recursion involving only analytical formulae for standard European call and put options. We also show that the numerical inversion can be performed with great accuracy and low computational cost.

Received: February 11, 2014

AMS Subject Classification: 11A25, 44A10, 42A38, 91G20, 91G80, 91G99

Key Words and Phrases: Asian option, exotic option, Laplace transform, lookback option, path dependent option

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DOI: 10.12732/ijpam.v94i2.5 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 94
Issue: 2
Pages: 175 - 197

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).