Remarks on Real-World Models

This chapter presents some remarks about real-world modeling. First, we examine the numerical differences between real-world simulations and riskneutral simulations, comparing the drift terms in each type of model. Next, we investigate the reason that the market price of risk is negative by using a simplified model, which we refer to as a flat yield model. This subject is motivated by the following research question: Why does long-period observation tend to imply a negative value for the market price of risk? We obtain an answer to this question by introducing simplified models (specifically, the flat yield model and the positive slope model). Through this book, we have estimated the market price of risk under the assumption that it is constant in the sample period. Addressing this, we examine the validity of the constancy assumption for risk management by using a simplified model. It is worth nothing here that Section 7.1 is basically the contents of Yasuoka (2015), and Sections 7.2 and 7.3 are newly written for this book.