Natural volatility and option pricing
AbstractIn 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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 6709.
Date of creation: 12 Jan 2008
Date of revision:
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;
Find related papers by JEL classification:
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-01-19 (All new papers)
- NEP-FMK-2008-01-19 (Financial Markets)
- NEP-ORE-2008-01-19 (Operations Research)
- NEP-RMG-2008-01-19 (Risk Management)
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