Author : Orcan Ogetbil
Publisher :
ISBN 13 :
Total Pages : 16 pages
Book Rating : 4.:/5 (129 download)
Book Synopsis Extensions of Dupire Formula by : Orcan Ogetbil
Download or read book Extensions of Dupire Formula written by Orcan Ogetbil and published by . This book was released on 2020 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: We derive generalizations of Dupire formula to the cases of general stochastic drift and/or stochastic local volatility. First, we handle a case in which the drift is given as difference of two stochastic short rates. Such a setting is natural in foreign exchange context where the short rates correspond to the short rates of the two currencies, equity single-currency context with stochastic dividend yield, or commodity context with stochastic convenience yield. We present the formula both in a call surface formulation as well as total implied variance formulation where the latter avoids calendar spread arbitrage by construction. We provide derivations for the case where both short rates are given as single factor processes and present the limits for a single stochastic rate or all deterministic short rates. The limits agree with published results. Then we derive a formulation that allows a more general stochastic drift and diffusion including one or more stochastic local volatility terms. In the general setting, our derivation allows the computation and calibration of the leverage function for stochastic local volatility models.