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HEDGING WITH ENERGY
Author(s) -
Corielli Francesco
Publication year - 2006
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/j.1467-9965.2006.00280.x
Subject(s) - valuation of options , a priori and a posteriori , volatility (finance) , econometrics , valuation (finance) , robustness (evolution) , stochastic volatility , mathematics , mathematical optimization , mathematical economics , economics , finance , philosophy , biochemistry , chemistry , epistemology , gene
In the setting of diffusion models for price evolution, we suggest an easily implementable approximate evaluation formula for measuring the errors in option pricing and hedging due to volatility misspecification. The main tool we use in this paper is a (suitably modified) classical inequality for the L 2 norm of the solution, and the derivatives of the solution, of a partial differential equation (the so‐called “energy” inequality). This result allows us to give bounds on the errors implied by the use of approximate models for option valuation and hedging and can be used to justify formally some “folk” belief about the robustness of the Black and Scholes model. Surprisingly enough, the result can also be applied to improve pricing and hedging with an approximate model. When statistical or a priori information is available on the “true” volatility, the error measure given by the energy inequality can be minimized w.r.t. the parameters of the approximating model. The method suggested in this paper can help in conjugating statistical estimation of the volatility function derived from flexible but computationally cumbersome statistical models, with the use of analytically tractable approximate models calibrated using error estimates.