# Asian option code

Numerical inversion of the Laplace transform for pricing Asian options The Geman and Yor model Numerical inversion is done by Talbot's method. Pflug , Artur Swietanowski , Engelbert J. As mentioned in the class on option pay-off hierarchies we are able to create an abstract base class called PayOff , which defines an interface that all subsequent inherited pay-off classes will implement. The listings for the AsianOptionArithmetic and AsianOptionGeometric classes are analogous to those in the PayOff hierarchy, with the exception that their constructors take a pointer to a PayOff object. First, we examine how the two semi-analytical i. This entails the usage of an ever larger summation, or in other words the value of precision parameter M and thus the calculation time needs to be increased as. This estimator has a variance of.

## Brent Average Price Option

The following is code for generating a user specified number of simulated asset paths and then using those paths to price a standard Asian Put and Call option. In this case, the estimator is. Features Channels vendor extension Double-precision floating-point Multiple device execution Multiple kernels, including single work-item kernels Downloads The design example provides source code for the OpenCL device. Thus, before waving aside the Laplace transform inversion methods for their notorious sensitivity to small values of , we should remember that in valuation problems where there is no such control variate available these numerical algorithms could serve as a valuable pricing tool. Before proceeding with the empirical analysis of our valuation framework in the next section, let us make a few notes with regard to the practical implementation of the simulation methods discussed above. It is called flexible when the payoff is a weighted average, and equally weighted when all the weights are equal. Before making a comparison with the simulation approach, let us look into the latter on its own and examine the three Monte Carlo algorithms introduced in Section 2.

### Pricing Asian options using mpmath « Python recipes « ActiveState Code

Striving to cut this variance to a minimum level, we study in details how the variance reduction techniques of antithetic variates and control variates work in the case of financial derivative valuation. Also, by looking at the above calculations, where is multiplied by in the antithetic and by in the control variate case, we understand why the simulation error of the latter grows faster as. In order to do the discretization we started with the formula: It is quite straightforward and we're not using any real advanced features beyond abstract base classes and pure virtual functions. To achieve this, we need to set the simulation parameters so that the confidence interval 7 around the estimated option value is sufficiently small to ensure the desired precision. Instead it provides an interface through which all inherited classes will be bound to. You can analyze options prices at different levels of the underlying asset.
Asian options are path-dependent options whose payoff depends on the average value of the underlying asset during a specific set of dates across the life of the option. Comparing these simulation errors with the variance of the basic method, which is. We make use of the operator to turn our pay-off classes into a functor i. Striving to cut this variance to a minimum level, we study in details how the variance reduction techniques of antithetic variates and control variates work in the case of financial derivative valuation. Zvan, Forsyth, and Vetzal have introduced a modified finite difference method, which seems to be more efficient. In the continuous case. The payoff of the fixed strike Asian option at maturity given as.
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### asian+option+code

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