A main device in the theoretical analysis is finding the small interval asymptotic distribution for the estimation error of . Finally we discuss the implications of residual variation on the volatility model, and carry out numerical experiments and a data analysis with S P500 data. In this talk I will introduce the origin of the BSDE and some basics of the theory, and then give a survey of finance problems where BSDEs have proved to be useful. When this bound is compared to observed futures prices, one nevertheless finds that the theoretical bound is sometimes violated by market prices. The main consequence of this observation is that virtually all of the important fixed income models have theoretical implications that are sometimes at odds with market realities, at least when they are applied to futures markets.
Local times play a key role.
The work of Markowitz and the later work by William Sharpe on the Capital Asset Pricing Model is based on the premise that the benefit of diversification is the driving force behind investor risk preferences and decision making. The players have changed, the rules have changed and the incentives have changed. Stock specific risk and its corresponding return are now key factors, and shareholders have given executives incentives to optimize these two factors. The inputs for the model are derived from traded market instruments, and the model provides a metric system that incorporates the probability of future outcomes and time. The resulting term structure of equity from the model answers many of the paradoxes encountered previously when applying CAPM metrics to issues in corporate finance.