tailieunhanh - Handbook of Economic Forecasting part 83

Handbook of Economic Forecasting part 83. Research on forecasting methods has made important progress over recent years and these developments are brought together in the Handbook of Economic Forecasting. The handbook covers developments in how forecasts are constructed based on multivariate time-series models, dynamic factor models, nonlinear models and combination methods. The handbook also includes chapters on forecast evaluation, including evaluation of point forecasts and probability forecasts and contains chapters on survey forecasts and volatility forecasts. Areas of applications of forecasts covered in the handbook include economics, finance and marketing | 794 T. G. Andersen et al. From the corresponding first order conditions the resulting portfolio weights for the risky assets satisfy Mw W t -4-dp M Mw with the optimal portfolio weight for the risk-free asset given by NL wlt 1 -22 wtf 2-23 i t Moreover from the portfolio Sharpe ratio equals SR pp Wf t i tW . Just as in the CAPM pricing model discussed above both volatility and covariance dynamics are clearly important for asset allocation. Notice also that even if we rule out exploitable conditional mean dynamics the optimal portfolio weights would still be time-varying from the second moment dynamics alone. . Option valuation with dynamic volatility The above tools are useful for the analysis of primitive securities with linear payoffs such as stocks bonds foreign exchange and futures contracts. Consider now instead a European call option which gives the owner the right but not the obligation to buy the underlying asset say a stock or currency on a future date T at a strike price K. The option to exercise creates a nonlinear payoff which in turn requires a special set of tools for pricing and risk management. In the Black-Scholes-Merton BSM option pricing model the returns are assumed to be normally distributed with constant volatility a along with the possibility of costless continuous trading and a constant risk free rate rf .In this situation the call price of an option equals ct BS l v a2 K rf T st d - K exp -rfT d - a VT where st denotes the current price of the asset d ln st K T rf a 2 2 T and refers to the cumulative normal distribution function. Meanwhile the constant volatility assumption in BSM causes systematic pricing errors when comparing the theoretical prices with actual market prices. One manifestation of this is the famous volatility-smiles which indicate systematic underpricing by the BSM model for in- or out-of-the-money options. The direction of these deviations however are readily explained by the presence of .