Canonical valuation of options in the presence of stochastic volatility

Abstract

Proposed by M. Stutzer (1996), canonical valuation is a new method for valuing derivative securities under the risk-neutral framework. It is nonparametric, simple to apply, and, unlike many alternative approaches, does not require any option data. Although canonical valuation has great potential, its applicability in realistic scenarios has not yet been widely tested. This article documents the ability of canonical valuation to price derivatives in a number of settings. In a constant-volatility world, canonical estimates of option prices struggle to match a Black-Scholes estimate based on historical volatility. However, in a more realistic stochastic-volatility setting, canonical valuation outperforms the Black-Scholes model. As the volatility generating process becomes further removed from the constant-volatility world, the relative performance edge of canonical valuation is more evident. In general, the results are encouraging that canonical valuation is a useful technique for valuing derivatives. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:1–19, 2005

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