Bayesian Risk Management

Chapter 8Asset-Pricing Models and Hedging

One of the great achievements of modern finance is the analytical derivation of arbitrage-free or equilibrium prices for a variety of financial instruments, including bonds, futures, options, and other derivatives. Beginning from relatively simple primitives about the dynamics of underlying assets and economic fundamentals, pricing formulas can be developed for a variety of instruments, often in closed form.

The prices obtained from equilibrium and arbitrage-free models assume that parameters governing the underlying asset and economic factor dynamics are already known, and that state variables are identifiable without error from available data. The inverse problem of recovering the parameters and state variables that generate observed prices is more difficult. In some cases, the asset price formula may be inverted to solve for an unknown parameter, as with implied volatility in the Black-Scholes-Merton analysis. Other situations allow for static optimization by minimizing the squared differences between model-implied and observed values for a selected data history. However, in instances where inverted formulas give conflicting answers, or when analytical solutions are not available, recovering the parameters governing asset price dynamics becomes an econometric problem. These problems have pushed mainstream econometrics to its limits, relying on simulated and feasible estimators where maximum-likelihood and GMM methods break down (see ...