The pricing of discretely sampled Asian and lookback options: a change of numeraire approach

Abstract

This paper considers the pricing of discretely sampled Asian and lookback options with floating and fixed strikes. In the modelling framework of Black and Scholes (1973), it is shown that a change of numeraire of the martingale measure can be used to reduce the dimension of these path-dependent option pricing problems to one in addition time. This means that the pricing problems can be solved by numerically solving onedimensional partial differential equations. The author demonstrates how a Crank‐ Nicolson scheme can be applied to the numerical solution. Finally, the methodology is extended to the case when the underlying stock exhibits discontinuous returns, and it is shown that in this case the Asian and lookback option pricing problems can be solved by numerically solving one-dimensional partial integrodifferential equations.