Delta Hedging in Discrete Time under Stochastic Interest Rate
We examine the e?ect of stochastic interest rate on the Delta hedging strategy in discrete time when hedging a contingent claim written on a risky asset. The performance of the hedging is mainly measured by the variance of the error. We consider a simple two-dimensional model of the type Black-Scholes combined with the Vasicek model, allowing for correlation between the stock and the interest rate. Within this model, we perform the Delta hedging ?rst by implementing the strategy by taking into account the stochasticity of interest rate and then by using a plain Black-Scholes Delta with deterministic rate. The di?erences between the two performances can be relevant, mainly depending on the correlation and on the relation between the standard deviation of the risky asset and that of the interest rate. We also consider Delta hedging for an interest rate option in the Cox-Ingersoll and Ross model. The analysis is done by applying a general result for the e?cient computation of expected value and variance of the hedging error of a certain class of strategies, which include the Delta strategy.
|Date of creation:||19 Oct 2012|
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