Natural volatility and option pricing

Carey, Alexander

Natural volatility and option pricing

MPRA Paper from University Library of Munich, Germany

Abstract: In this paper we recover the Black-Scholes and local volatility pricing engines in the presence of an unspecified, fully stochastic volatility. The input volatility functions are allowed to fluctuate randomly and to depend on time to expiration in a systematic way, bringing the underlying theory in line with industry experience and practice. More generally we show that to price a European-exercise path-(in)dependent option, it is enough to model the evolution of the variance of instantaneous returns over the natural filtration of the underlying security. We call the square root of this new process natural volatility. We develop the associated concept of path-conditional forward volatility, via which the natural volatility can be directly specified in an economically meaningful way.

Keywords: natural filtration; natural volatility; stochastic volatility; local volatility; path-dependent volatility; change of measure; change of filtration; martingale valuation; Black-Scholes; path-conditional forward price; path-conditional forward volatility (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2008-01-12
New Economics Papers: this item is included in nep-fmk, nep-ore and nep-rmg
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