Timing the smile

Abstract

Within the general framework of stochastic volatility, the authors propose a method, which is consistent with no-arbitrage, to price complicated path-dependent derivatives using only the information contained in the implied volatility skew. This method exploits the time scale content of volatility to bridge the gap between skews and derivatives prices. Here they present their pricing formulas in terms of Greeks free from the details of the underlying models and mathematical techniques. 1 Underlying or Smile? Our goal is to address the following fundamental question in pricing and hedging derivatives. How traded call options, quoted in terms of implied volatilities, can be used to price and hedge more complicated contracts. One Department of Mathematics, NC State University, Raleigh NC 27695-8205, fouque@math.ncsu.edu. Work partially supported by NSF grant DMS-0071744. Department of Mathematics, Stanford University, Stanford CA 94305, papanico@math.stanford.edu. Department of Operations Research & Financial Engineering, Princeton University, E-Quad, Princeton, NJ 08544, sircar@princeton.edu. Department of Mathematics, University of California, Irvine CA 92697, ksolna@math.uci.edu.