Chp.19 Term Structure of Interest Rates (II). Continuous time models. Term structure models are usually more convenient in continuous time. Specifying a discount factor process and then find bond prices. A wide and popular class models for the discount factor:. Implications.
Vasicekmodel is similar to AR(1) model.
Having specified a discount factor process, it is simple matter to find bond prices
Two way to solve
A second approach is risk-neutral approach
Rearrange we get the ODEs for Affine Model
The risk-neutral probability method rarely make reference to the separation between drifts and market price of risk. This was not a serious problem for the option pricing, since volatility is more important.
However, it is not suitable for the portfolio analysis and other uses. Many models imply high and time-varying market price of risk and conditional Sharpe ratio.
Duffee(1999) and Duarte(2000) started to fit the model to the empirical facts about the expected returns in term structure models.