Numerical Analysis: Quadratic hedging

Figure 1. Empirical histogram of hedging errors for a certain category of options when using quadratic hedging in a stochastic volatility (left image) model compared to hedging in the standard Black-Scholes model (right image).

The classic financial theory that started with the arbitrage free pricing theory of Black, Scholes and Merton (1973) deals with markets that are complete in the sense that every financial contract in the market can be perfectly (“almost surely”) replicated by a dynamic portfolio of other contracts. It is generally recognized that this is not the case in real financial markets, and stochastic models for markets that are not complete are frequently used by financial institutes. The academically well established concept of quadratic hedging provides a natural framework for hedging the risk of financial contracts in cases where the market is not complete. Yet, quadratic hedging has been largely overseen by market practitioners. In this project we thus try to illustrate what the advantages could be if hedging of standard European options were made with quadratic hedging in models with stochastic volatility rather than in a standard Black-Scholes framework.



Love Lindholm