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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.
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.
Graduate School of Engineering Management, Shibaura Institute of Technology. 3-9-14 Shibaura, Minato-ku, Tokyo.