Selfsimilar Additive Processes and Financial Modeling

Craig Nolder

We present here theoretical reasons to use selfsimilar additive processes to model asset prices and a program for calibrations and implementations. L\'evy processes are stationary additive processes and are selfsimilar only in the stable case. In contrast any selfdecomposable distribution will generate selfsimilar additive processes with any positive exponent of selfsimilarity. Selfsimilar additive processes due to nonstationarity need not adhere to a Central Limit Theorem. It is hoped that because of this these models will exhibit implied volitility smirks at high maturities.