Sato Processes and the Valuation of Structured Products

41 Pages Posted: 15 Jan 2007

See all articles by Dilip B. Madan

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Ernst Eberlein

University of Freiburg

Date Written: July 3, 2007

Abstract

We report on the adequacy of using Sato processes to value equity structured products. An analysis of the variance of realized variance for Sato processes shows that these processes may be suited to option contracts on realized volatility. Nonlinear pricing principles based on hedging to acceptability are outlined for the purpose of pricing structured transactions. It is shown that typically different products should be priced using different models. Pricing comparisons of Sato process prices with other standard models like Heston stochastic volatility, with and without jumps, VGSA, local volatility and local CGMY are also provided. Sato processes tend to overprice cliquets relative to other models. They also maintain the value of long dated out-of-the-money realized variance options.

Keywords: Options on Realized Variance, Forward Starts, Ziggurat for Levy Processes

JEL Classification: G10, G12, G13

Suggested Citation

Madan, Dilip B. and Eberlein, Ernst, Sato Processes and the Valuation of Structured Products (July 3, 2007). Available at SSRN: https://ssrn.com/abstract=957167 or http://dx.doi.org/10.2139/ssrn.957167

Dilip B. Madan (Contact Author)

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

Ernst Eberlein

University of Freiburg ( email )

Department of Mathematical Stochastics
Eckerstrasse 1
D-79104, Freiburg
Germany
++49 761 203 5660 (Phone)
++49 761 203 5661 (Fax)

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