Drishtikon: A Management Journal

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Discrete-Time Hedging for European Contingent Claims via Risk Minimization in Market Measure


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1 Tata Consultancy Services, No. 1, Software Units Layout, Madhapur, Hyderabad 500081
2 Tata Consultancy Services No. 1, Software Units Layout, Madhapur, Hyderabad 500081
3 Tata Consultancy Services No. 1, Software Units Layout, Madhapur,Hyderabad 500081
     

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In this work, we propose a discrete-time hedging strategy for a European contingent claim (ECC) that reduces risk in the market measure. To this end, we minimize the second-moment of the hedging error in the market measure and give computable expressions for the positions that the seller must hold in the underlying asset (of the ECC) at any given hedge time. The minimization of the second-moment of the hedging error also yields an expression for the price of the option. The expressions obtained can be evaluated using Monte-Carlo methods. A noteworthy feature of the framework is that, it does not assume any specific model for the underlying asset price or involve any assumptions on the underlying market probability measure.

Keywords

European Contingent Claims (ecc), Discrete-time Hedging, Market Measure, Second-moment, Risk-minimization, Path-dependent Options, Martingale Measure, Geometric Brownian Motion (gbm)
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  • Discrete-Time Hedging for European Contingent Claims via Risk Minimization in Market Measure

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Authors

Easwar Subramanian
Tata Consultancy Services, No. 1, Software Units Layout, Madhapur, Hyderabad 500081
Vijaysekhar Chellaboina
Tata Consultancy Services No. 1, Software Units Layout, Madhapur, Hyderabad 500081
Anil Bhatia
Tata Consultancy Services No. 1, Software Units Layout, Madhapur, Hyderabad 500081
Sanjay P. Bhat
Tata Consultancy Services No. 1, Software Units Layout, Madhapur,Hyderabad 500081

Abstract


In this work, we propose a discrete-time hedging strategy for a European contingent claim (ECC) that reduces risk in the market measure. To this end, we minimize the second-moment of the hedging error in the market measure and give computable expressions for the positions that the seller must hold in the underlying asset (of the ECC) at any given hedge time. The minimization of the second-moment of the hedging error also yields an expression for the price of the option. The expressions obtained can be evaluated using Monte-Carlo methods. A noteworthy feature of the framework is that, it does not assume any specific model for the underlying asset price or involve any assumptions on the underlying market probability measure.

Keywords


European Contingent Claims (ecc), Discrete-time Hedging, Market Measure, Second-moment, Risk-minimization, Path-dependent Options, Martingale Measure, Geometric Brownian Motion (gbm)

References