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

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Abstract
In this paper we recover the BlackScholes 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 Europeanexercise 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 pathconditional forward volatility, via which the natural volatility can be directly specified in an economically meaningful way.
Item Type:  MPRA Paper 

Original Title:  Natural volatility and option pricing 
Language:  English 
Keywords:  natural filtration, natural volatility, stochastic volatility, local volatility, pathdependent volatility, change of measure, change of filtration, martingale valuation, BlackScholes, pathconditional forward price, pathconditional forward volatility 
Subjects:  G  Financial Economics > G1  General Financial Markets > G13  Contingent Pricing; Futures Pricing 
Item ID:  6709 
Depositing User:  Alexander Carey 
Date Deposited:  13. Jan 2008 05:16 
Last Modified:  11. Feb 2013 20:40 
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URI:  http://mpra.ub.unimuenchen.de/id/eprint/6709 