Department of Mathematics, University of Ibadan, Oyo State, Nigeria; Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria
Nwozo, C.R., Department of Mathematics, University of Ibadan, Oyo State, Nigeria; Fadugba, S.E., Department of Mathematical Sciences, Ekiti State University, Ado Ekiti, Nigeria
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. © 2014 Academic Publications, Ltd.