Efficient pricing of asian options by the pde approach

Version pdf de ce document Efficient pricing of Asian options by the PDE approach. Pascal, Champs-sur-Marne, France. We then propose a scheme which is able to produce very quickly in less than one second on a PC equipped with a 1 GHz Intel Pentium III microprocessor accurate results at least 5 digits of precision.

We compare our approach with the schemes proposed in the litterature. Asian Options, Partial Differential Equation, Characteristic method.

We will focus on numerical methods based on this PDE. The advantage of the PDE approach is that it is generally faster than Monte Carlo methods, and than it gives the results for all initial prices S 0 and even for all strikes K or all maturities T in some cases.

The drawback is usually that the numerical methods are more complicated to implement for PDE, but we give here a numerical scheme which is really simple to code. The process S t is solution of the following stochastic differential equation under IP: We are interesting in computing the price of an Asian option with maturity Twhich means that the option payoff g S,A depends on the price S T of the risky asset and on the mean A Rapidshare stock market books of the price S stock for savage 11/111 The price at time t is given by: When one wants to compute the solution of the classical Black-Scholes equation: Results obtained with a finite element scheme, or, equivalently, a centered scheme for the advection operator.

The numbers I and N denote respectively the number of space steps and the number of time steps.

Solving an Asian option PDE via the Laplace transform — The National University of Malaysia

Values of other parameters: This means that we perform the change of variable: The PDE satisfied by g is such that when the advective term r is small, the diffusion term is also small. The drawback of this change of variable is that the advective and diffusion terms now depend on time: This means efficient pricing of asian options by the pde approach the size of the matrices we build depend on the timestep.

Efficient pricing of Asian options by the PDE approach.

Since the mesh is uniform, it is really easy to discretize the operators involving derivatives of x. What we use is the following equation on gequivalent to 7: The matrices obtained are tridiagonal, so that they can be inverted with Vix options trade hours method with linear complexity.

Comparison of the results for different values of J. Default values of parameters: We have also performed a rate of convergence analysis. We have found that both the price and the delta values converge with a rate O.

The results from Zvan et al.

Efficient Pricing of Asian Options by the PDE Approach by François Dubois, Tony Lelievre :: SSRN

Comparisons of the prices obtained with other methods. N computational time 0.

One can see from this comparisons that our method is accurate both for small or large volatilities. For any value of the parameters, one obtains at least 5 digits of precision in less than one second. It seems also that our method is faster than the other, but this would have to be checked carefully since it depends on the computers used.

We can also conclude from these experiments that, as expected, the accuracy is better for strikes less than S 0as well as for large volatilities. It also works with null or negative interest rate, which is of interest if one takes into account some dividend rate.

Fast narrow bounds on the value of asian options. Working paper Judge Institute U. The value of an asian option. Version pdf de ce document. Efficient pricing of Asian options by the PDE approach.