Numerical Examples

This chapter presents numerical examples of real-world modeling using actual market data. First, we show 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 different cases in the LMRW to clearly illustrate the properties of the real-world model. In these, Sections 10.1 and 10.2 present detailed examinations of the examples given in Yasuoka (2015) and Yasuoka (2012, 2013a), respectively.

Additionally, 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. Finally, 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. These examples, in Sections 10.3 and 10.4, are original to this book.

Keywords: Dimension reduction, Drift term, Flat yield model, Full-factor model, Gaussian HJM model, Historical trend, Hull-White model, Implied forward LIBOR, Implied forward rate, LIBOR, LIBOR market model, LMRW, Long-period observation, Market price of risk, Mean reversion, Monte Carlo simulation, Negative price tendency, PCA, Real-world model, Real-world simulation, Swap rate, U.S. Treasury.