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Towards a self-consistent theory of volatility. (English) Zbl 1127.91027

The present paper continues the authors’ previous one [C. R. Acad. Sci., Paris, Sér. I, Math. 331, No. 11, 879–885 (2000; Zbl 0971.49015)]. It aims to construct a theoretical model for pricing and hedging with the volatility determined endogenously through the investors’ actions. A self-consistent theory of volatility incorporating the effects of large number of the agents and their actions has been established via a self-consistent volatility equation (SCV equation), which is derived by using an utility function maximal approach on the hedging rate. The SCV equation is well-posed and can be solved through a nonlinear parabolic equation.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
91B70 Stochastic models in economics

Citations:

Zbl 0971.49015
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References:

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