Pricing of Discretely Sampled Asian Options Under Levy Processes

Pricing Discretely Monitored Asian Options under Lévy Processes

We present methodologies to price discretely monitored Asian options when the underlying evolves according to a generic Lévy process. For geometric Asian options we provide closed-form solutions in terms of the Fourier transform and we study in particular these formulas in the Lévy-stable case. For arithmetic Asian options we solve the valuation problem by recursive integration and derive a rec...

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

This paper considers the pricing of discretely sampled Asian and lookback options with ̄oating and ®xed 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 n...

Pricing Discretely Sampled Path-dependent Exotic Options Using Replication Methods

A semi-static replication method is introduced for pricing discretely sampled path-dependent options. It depends upon buying and selling options at the reset times of the option but does not involve trading at intervening times. The method is model independent in that it only depends upon the existence of a pricing function for vanilla call options which depends purely on current time, time to ...

A General Framework for Pricing Asian Options Under Markov Processes

Efficient Pricing of European-Style Asian Options under Exponential Lévy Processes Based on Fourier Cosine Expansions

We propose an efficient pricing method for arithmetic and geometric Asian options under exponential Lévy processes based on Fourier cosine expansions and Clenshaw–Curtis quadrature. The pricing method is developed for both European-style and American-style Asian options and for discretely and continuously monitored versions. In the present paper we focus on the European-style Asian options. The...