Research on the indexed stock options’ quadratic hedging under jump-diffusion settings

Abstract

This paper studied the hedging of European indexed stock options, whose exercise price is a variable varying with the market index. Firstly, using the expectation of the squared error between option’s terminal value and hedging portfolio to measure market risk , and with the constraint of self-financing, a squared hedge decision model was built; Then, by using the Dynamic Programming Principle and backward recursion method, the optimal hedging positions’ analytical expressions were acquired; Lastly, all hedging results with different option maturities and different position rebalancing frequencies show that there is dependent relationship between hedging positions and option’s maturity time limit; hedging positions also rely on the relative variation of the underlying asset price.