Numerical Examples

This chapter presents numerical examples of real-world modeling. First, we give examples within the Gaussian HJM model, working with the Japanese LIBOR swap market data. We calculate the market price of risk from the data, referring to the interpretation of the market price of risk given in Chapter 6. After that, we show numerical examples in the LMRW in parallel to the above. Since the simulation model in the LMRW is more complicated than that of the Gaussian HJM model, we consider four dierent cases in the LMRW to clearly illustrate the properties of the real-world model. In these, Sections 10.1 and 10.2 present de- tailed examinations of the examples given in Yasuoka (2015) and Yasuoka (2012, 2013a), respectively. Next, we present an actual example that admits a positive market price of risk. For this, we employ the Hull{White model, working with data on U.S. Treasury yields. Also, working with long-period observations of U.S. Treasury yields, we calculate the market prices of risk in the Hull{White model. With this, we verify that long-period observation tends to cause a negative market price of risk. We examine the mean price property of the market price of risk by using U.S. Treasury yields. Additionally, Section 10.6 examines the properties of credit exposure calcu- lation in connection with real-world modeling. These examples, in Sections 10.3, 10.4, 10.5, and 10.6 are original to this book.

Keywords: Convexity, Counterparty credit risk, Dimension reduction, Ex- pected exposure, Flat yield model, Gaussian HJM model, HullWhite model, Interest rate swap, LIBOR market model, Market price of risk, Mean rever- sion, Mean price property, Monte Carlo simulation, Negative price tendency, Positive slope model, Potential future exposure, Real-world simulation, Swap rate, U.S. Treasury.