Selfsimilar Additive Processes and Financial Modeling

C.A. Nolder (USA)


selfsimilar additive processes, option pricing


We present here theoretical reasons to use selfsimilar ad ditive processes to model asset prices and a program for calibrations and implementations. Levy processes are sta tionary additive processes and are selfsimilar only in the stable case. In contrast any selfdecomposable distribution will generate selfsimilar additive processes with any pos itive exponent of selfsimilarity. Selfsimilar additive pro cesses due to nonstationarity need not adhere to a Central Limit Theorem. It is hoped that because of this these mod els will exhibit implied volitility smirks at high maturities.

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