scholarly journals BSDEs with terminal conditions that have bounded Malliavin derivative

2014 ◽  
Vol 266 (3) ◽  
pp. 1257-1285 ◽  
Author(s):  
Patrick Cheridito ◽  
Kihun Nam
Keyword(s):  
Malliavin Derivative

scholarly journals Malliavin differentiability of the Heston volatility and applications to option pricing

2008 ◽  
Vol 40 (01) ◽  
pp. 144-162 ◽  
Author(s):  
Elisa Alòs ◽  
Christian-Oliver Ewald
Keyword(s):  
Option Pricing ◽  
Explicit Expression ◽  
Stochastic Volatility ◽  
Malliavin Calculus ◽  
Numerical Results ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Malliavin Derivative ◽  
Volatility Model

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 Alòs (2006) in order to derive approximate option pricing formulae in the context of the Heston model. Numerical results are given.

Discrete Bismut formula: Conditional integration by parts and a representation for delta hedging process

2021 ◽  
pp. 1-9
Author(s):  
Naho Akiyama ◽  
Toshihiro Yamada
Keyword(s):  
Random Walk ◽  
Discrete Time ◽  
Malliavin Calculus ◽  
Random Walk Model ◽  
Integration By Parts ◽  
Exponential Process ◽  
Malliavin Derivative ◽  
Integration By Parts Formula ◽  
Delta Hedging ◽  
New Formula

The paper gives discrete conditional integration by parts formula using a Malliavin calculus approach in discrete-time setting. Then the discrete Bismut formula is introduced for asymmetric random walk model and asymmetric exponential process. In particular, a new formula for delta hedging process is obtained as an extension of the Malliavin derivative representation of the delta where the conditional integration by parts formula plays a role in the proof.

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