Cumulant Expansion and Monthly Sum Derivative
V.M. Belyaev
TL;DR
This paper develops a closed-form approximation for Monthly Sum Options using cumulant expansion and Edgeworth series, providing accurate results under constant volatility assumptions.
Contribution
It introduces a novel application of cumulant expansion and Edgeworth series to derive a closed-form approximation for Monthly Sum Options.
Findings
Approximation aligns well with numerical results for typical parameters.
Edgeworth expansion effectively captures the distribution of sum of capped returns.
Method offers a computationally efficient alternative to numerical methods.
Abstract
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 caped (and probably floored) returns. It is noticed, that 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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Taxonomy
TopicsStochastic processes and financial applications · Monetary Policy and Economic Impact · Financial Markets and Investment Strategies