Peter K. Friz, Jim Gatheral, Radoš Radoičić
Published 2020-02-04Version 1
A general and computable expression for cumulants of a random variables in a semimartingale context is given, with resulting expressions for characteristic and cumulant generating functions. We have been inspired by a formal forest series for expectations of solutions of the Black-Scholes equation [AGR20]. Our proof is of remarkable simplicity and the result is likely to transcend the financial context from which it originates. A variety of examples are presented.
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