Comptes Rendus
no. 7
Mathematical Economics
Risk premium and fair option prices under stochastic volatility: the HARA solution
[Prime de risque et prix de l'option sous l'hypothèse de volatilité stochastique]

Présenté par : Pierre-Louis Lions

Srdjan D. Stojanovic1
1 Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, USA
Comptes Rendus. Mathématique, Volume 340 (2005) no. 7, pp. 551-556.

Nous résolvons le problème de la détermination du prix de l'option sous un modèle général de volatilité stochastique. Pour une fonction d'utilité HARA, « la prime de risque », i.e. le prix du marché associé au risque de volatilité, est déterminé en utilisant la solution d'une EDP non linéaire. De la même façon, le prix de l'option est déterminé comme solution d'un système découplé d'une EDP non linéaire et d'une EDP de type Black–Scholes.

We have solved the problem of finding (HARA) fair option price under a general stochastic volatility model. For a given HARA utility, the ‘risk premium’, i.e., the ‘market price of volatility risk’ is determined via a solution of a certain nonlinear PDE. Equivalently, the fair option price is determined as a solution of an uncoupled system of a non-linear PDE and a Black–Scholes type PDE.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.11.002
Srdjan D. Stojanovic 1

1 Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221-0025, USA 
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Srdjan D. Stojanovic. Risk premium and fair option prices under stochastic volatility: the HARA solution. Comptes Rendus. Mathématique, Volume 340 (2005) no. 7, pp. 551-556. doi : 10.1016/j.crma.2004.11.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.11.002/

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