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Zbl 0908.90012
Hobson, David G.; Rogers, L.C.G.
Complete models with stochastic volatility. (English)
[J] Math. Finance 8, No.1, 27-48 (1998). ISSN 0960-1627; ISSN 1467-9965/e

Summary: The paper proposes an original class of models for the continuous-time price process of a financial security with nonconstant volatility. The idea is to define instantaneous volatility in terms of exponentially weighted moments of historic log-price. The instantaneous volatility is therefore driven by the same stochastic factors as the price process, so that, unlike many other models of nonconstant volatility, it is not necessary to introduce additional sources of randomness. Thus the market is complete and there are unique, preference-independent option prices. We find a partial differential equation for the price of a European call option. Smiles and skews are found in the resulting plots of implied volatility.

MSC 2000:: *91B28 Finance etc.

Keywords: continuous-time price process; nonconstant volatility; option prices; European call option

Cited in: Zbl 1160.35457 Zbl 1187.91211 Zbl 1066.91081 Zbl 1098.91052 Zbl 1153.91474

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