Simulation and Inference for Stochastic Processes with YUIMA by Stefano M. Iacus & Nakahiro Yoshida

Author:Stefano M. Iacus & Nakahiro Yoshida
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(2.32)

Set the model (2.26) and the functional (2.27) as follows:

This time the setFunctional command fills the appropriate slots inside the yuima object

Then the limit of is easily obtained by calling the function F0 on the yuima object:

Set the function g according to (2.32):

Now we are at the point of computing the coefficients () in the expansion of the price by applying the function asymptotic_term:

Then the sums

give the first- and second-order asymptotic expansions, respectively.

We remark that the expansion of is also possible by the same method for a functional having a stochastic expansion like (2.30). Thus, the method works even under the existence of a stochastic discount factor.

One can compare the result of the asymptotic expansion with other well-known techniques like Edgeworth series expansion for the log-normal distribution as proposed, e.g., in Levy (1992). This approximation is available through the package fExoticOptions (Wuertz 2012).

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