Pricing Discretely Monitored Asian Options by Maturity Randomization

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...

Pricing Discretely Monitored Barrier Options by a Markov Chain

We propose a Markov chain method for pricing discretely monitored barrier options in both the constant and time-varying volatility valuation frameworks. The method uses a time homogeneous Markov Chain to approximate the underlying asset price process. Our approach provides a natural framework for pricing discretely monitored barrier options because the discrete time step of the Markov chain can...

Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options — Online Supplementary Material

Spitzer identity, Wiener-Hopf factorization and pricing of discretely monitored exotic options

TheWiener-Hopf factorization of a complex function arises in a variety of fields in applied mathematics such as probability, finance, insurance, queuing theory, radio engineering and fluid mechanics. The factorization fully characterizes the distribution of functionals of a random walk or a Lévy process, such as the maximum, the minimum and hitting times. Here we propose a constructive procedur...

Closed-Form Expansions of Discretely Monitored Asian Options in Diffusion Models

In this paper we propose a closed-form asymptotic expansion approach to pricing discretely monitored Asian options in general one-dimensional diffusion models. Our expansion is a small-time expansion because the expansion parameter is selected to be the square root of the length of monitoring interval. This expansion method is distinguished from many other pricing-oriented expansion algorithms ...