Abstract
We prove that the Heston volatility is Malliavin differentiable under the classical Novikov condition and give an explicit expression for the derivative. This result guarantees the applicability of Malliavin calculus in the framework of the Heston stochastic volatility model. Furthermore, we derive conditions on the parameters which assure the existence of the second Malliavin derivative of the Heston volatility. This allows us to apply recent results of Alos (2006) in order to derive approximate option pricing formulae in the context of the Heston model. Numerical results are given.
Original language | English |
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Pages (from-to) | 144-162 |
Number of pages | 19 |
Journal | Advances in Applied Probability |
Volume | 40 |
Issue number | 1 |
DOIs | |
Publication status | Published - Mar 2008 |
Keywords
- Malliavin calculus
- stochastic volatility model
- Heston model
- Cox-Ingersoll-Ross process
- Hull and White formula
- option pricing
- STOCHASTIC VOLATILITY
- FORMULA