Dates First available in Project Euclid: Subscribe to Table of Contents Alerts. The fact that the percentage of times this estimate stays inside the bound is only Then the moments are obtained by inversion. The proof of expression 29 is the same as that of Peng [ 36 ]. The point marked by is the price of the Asian option.
Kolmogorov-Smirnov distance between the true distribution and the different approximations. Finally, in order to have a reference point for comparing the different approximations we use: In section 3 we present the lower and upper bounds given in Rogers and Shi [ 28 ] and in Thompson [ 31 ]. In Section 2 , we use the nonlinear Feynman-Kac formula in the -expectation theory to get the two-dimensional nonlinear PDEs satisfied by the values of the Asian options. This type of option contract is attractive because it tends to cost less than regular American options. For the arithmetic average fixed strike Asian put option with terminal payoff , we will value this option by the following put-call parity.
Patie : Asian options under one-sided Lévy models
Property a is satisfied if we use logarithmic moments [ 14 ] or the moments of the reciprocal, Dufresne [ 12 ] , whilst no result is available about arithmetic moments. Unlike the Black-Scholes model, closed option pricing formulae are not available in exponential Levy models and one must use either deterministic numerical methods see Carr  for the LP model and Benth  for the BNS SV model or Monte Carlo methods. A Probability Density Function Approach. Such assessments are absolutely out of reach of the current published methods for treating Asian Options even in the framework of constant volatility. Hi Samir, First sorry if the qestion apears in two sections.
In the model without volatility uncertainty, there is a vast literature on pricing of Asian options. Basel - Boston - Berlin. The different moments based approximations can be compared in several ways: Let the discretization parameters be given by we use even discretization in time; that is, ,. And they are not linear equations but HJB equations in some sense.