Option Hedging in Jump-Diffusion Markets by Malliavin Calculus

Subject Areas : Journal of Investment Knowledge

Minoo  Bakhsh Mohammadlou ¹ (PhD student, Iran University of Science and Technology)
Rahman  Farnoosh ² (Associated Professor, Iran University of Science and Technology (Corresponding Author))

Received: 2017-09-19 Accepted : 2018-01-20 Published : 2019-09-23

Keywords: Jump diffusion market, Hedging strategy, Malliavin calculus, Clark-Ocone formula, Residual risk,

Abstract :

We obtain the hedging strategy in a jump-diffusion market by minimizing the variance of the residual risk. We calculate the residual risk by two formulas: the Ito's formula and the jump-diffusion version of the Clark-Ocone formula. The results show that Malliavin calculus can generate the hedging strategy under weaker assumptions. Thus afterward we do not require to check the strong condition  on  and the condition  with bounded derivative is sufficient.    

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