Stochastic regression and its application to hedging in finance

In this paper we investigate how to employ stochastic regression to hedge risks in finance, where the risk of a security is measured by its quadratic variation process. Mykland and Zhang used this technique to demonstrate how to reduce the risk of a given security by introducing another security. In this paper, we investigate how to further reduce the remaining unhedgable risk by adding more hedging securities. Some practical guidelines on how to choose those hedging securities in practice is also given. Jing’s research was partially supported by Hong Kong RGC (Grant Nos. HKUST6011/07P, HKUST6015/08P), and Zhang’s research was supported in part by National Natural Science Foundation of China (Grant No. 10771214)