Natural volatility and option pricing

Carey, Alexander (2008): Natural volatility and option pricing.

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.

• Item Type: MPRA Paper
• Language: English
• 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
• Subjects: G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing ; Futures Pricing

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