Real-World Model in The Gaussian HJM Model
Pp. 111-148 (38)
This chapter theoretically investigates a real-world model within the
Gaussian HJM model. In order to construct the real-world model, it is vital to
estimate the market price of risk. For this purpose, we assume that the market
price of risk is constant during each observation period. Representing the forward
rate process in a principal component space, we introduce a formula for the market
price of risk as the maximum likelihood estimate.
Next, we investigate the numerical properties of the market price of risk, after
which we give an interpretation of that price with respect to the historical trend
of the forward rates. Furthermore, we show that the interest rate simulation
admits historical drift and volatility. Finally, we present a numerical procedure
for real-world modeling. These results are essentially those from Yasuoka (2015).
Of particular note, however, is that applying maximum likelihood estimation to
finding the market price of risk is newly written for this book, in Section 6.2.
Additionally, a numerical procedure is introduced in Section 6.9 for implementing
the real-world model.
Butterfly trading strategy, Dimension reduction, Flattening strategy,
Forward rate curve, Full-factor model, Gaussian HJM model, Market price
of risk, Monte Carlo simulation, Maximum likelihood estimation, Musiela’s
parametrization, Numerical procedure, Observable trend, PCA, Principal volatility
component, Real-world simulation, Rolled trend, Rolled trend score, Rolldown,
Roll-up, State price deflator, State space, Steepening strategy.
Graduate School of Engineering Management, Shibaura Institute of Technology. 3-9-14 Shibaura, Minato-ku, Tokyo.