Discrete Time Hedging Errors For European Options Under Stochastic Short Rate Model

This article investigates the asymptotic convergence behavior of the hedging errors of European stock option, bond option and zero coupon bonds due to discrete trading under stochastic interest rates. We prove the convergence speed of the discounted hedging errors is 1/2-order of trading frequency. Following the proof, we study the convergence speed of the final hedging errors (undiscounted) by Monte-Carlo simulation method. In detail, firstly, by using the technique that is introduced in Bertsimas, Kogan, Lo(2000) and F-test, we find the convergence speed of the hedging errs of a European stock option under stochastic interest rate is slightly slower than that of deterministic interest rate, which is 1/2-order. Secondly, interest rate derivatives show different convergence speed from that of stock option. Specifically, the convergence speed is higher than 1/2-order for zero coupon bonds, lower for bond option. The reason relies on the jump delta for option and high volatility of the underlying stock. In the last part of this paper, the sensitivity of the root-mean-squared error to the model parameters is analyzed carefully. All through the paper, we assume the short rates follow the Vasicek interest rate model, the market is complete and the transaction costs are zero.