Change of Time Methods in Quantitative Finance by Anatoliy Swishchuk

Author:Anatoliy Swishchuk
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(5.14)

with

we obtain the value of volatility swap.

5.3.5 The Calculation of E{V } in a Discrete Case

The realized discrete sampled variance is

where we neglected the following term for simplicity reason only. We note that

We know the expressions for and for and the fourth expression is equal to zero. Hence, we can easily calculate all the expressions above and, thus, E{Var n (S)} and variance swap in this case.

Remark 1.

Some expressions for the price of the realized discrete sampled variance (or pseudo-variance) were obtained in the Proceedings of the Sixth Annual PIMS Industrial Problems Solving Workshop, PIMS IPSW 6, UBC, Vancouver, Canada, May 27-31, 2002. Editor: J. Macki, University of Alberta, Canada, June, 2002, pp. 45–55.

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