Chapter 10

Numerical Examples

Takashi Yasuoka

Abstract

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 di erent 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.

Total Pages: 235-279 (45)

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