Cumulant Expansion and Monthly Sum Derivative

Details Cumulant Expansion and Monthly Sum Derivative Cumulant Expansion and Monthly Sum Derivative

2010-11-17

arxiv.org/abs/1011.3975v3

Economy

Quantitative Finance

Pricing of Securities

8 pages, 2 figures

Scientific paper

Cumulant expansion is used to derive accurate closed-form approximation for Monthly Sum Options in case of constant volatility model. Payoff of Monthly Sum Option is based on sum of $N$ caped (and probably floored) returns. It is noticed, that $1/\sqrt{N}$ can be used as a small parameter in Edgeworth expansion. First two leading terms of this expansion are calculated here. It is shown that the suggest closed-form approximation is in a good agreement with numerical results for typical mode parameters.

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