Fixed income risk model

Fixed Income Risk Modeling for Portfolio Managers... 

Duffie, D., Kan, R., 1996. A yield-factor model of interest rates. Math. Financ. 6 (4), 379-406. Fitton, P., McNatt, J., 1997. The four faces of an interest rate model. In Fabozzi, F. (Ed.), Advances in Fixed Income Valuation Modelling and Risk Management. FJF Associates, New Hope, PA. 

The implications of this new model class are in contrast to most term structure models discussed in the literature, which assume that the bond markets are complete and fixed income derivatives are redundant securities. Collin-Dufresne and Goldstein [ 18] and Heiddari and Wu [36] show in an empirical work, using data of swap rates and caps/floors that there is evidence for one additional state variable that drives the volatility of the forward rates. Following from that empirical findings, they conclude that the bond market do not span all risks driving the term structure. This framework is rather similar to the affine models of equity derivatives, where the volatility of the underlying asset price dynamics is driven by a subordinated stochastic volatility process (see e.g. Heston [38], Stein and Stein [71] and Schobel and Zhu [69]). 

Note that the impact of this correlation effect is not in contradiction to the results found by Bakshi, Cao and Chen [5], Nandi [62] and Schobel and Zhu [69] for equity options. They found higher option prices given positive correlations and vice verca. On the other hand, we have a risk-neutral bond price process, where the source of uncertainty is negatively assigned (see e.g. (7.2)). Thus, assuming a USV bond model with negative correlated Brownian motions is the fixed income market analog of a stochastic volatility equity market model, with positive correlated sources of uncertainty. ... 

Cheyette, O., 1992. Term structure dynamics and mortgage valuation. J. Fixed Income 1 (4), 28 1. Das, S., 1997. A Direct Discrete-Time Approach to Poisson-Gaussian Bond Option Pricing in the Heath-Jarrow-Morton Model Working Paper. Harvard Business School, Boston, MA, pp. 1 14. Das, S., Foresi, S., 1996. Exact solutions for bond and option prices with systematic jump risk. Rev. Deriv. Res. 1, 1-24. 

We compare in Exhibit 23.16 the volatilities of a few selected euro and US dollar factors. The common denominator is that euro volatilities are less than their US dollar counterparts. This is true for all factors if we ignore the volatility bursts sometimes observed over a few months for some factors (for instance the Industrial A factor in Exhibit 23.16). The average level of systematic risk observed amongst euro-denomi-nated fixed income instruments is more generally low compared to other markets. Exhibit 23.16 shows one case where euro volatilities seem to be catching up with US levels. A more systematic analysis of how euro volatilities have recently evolved since 2002 would show that this is an exception. On average, euro volatilities have remained low with respect to US ones. Note that this is consistent first with the predictions of the swap factor model, euro spread levels and swap volatility being low compared to other markets. 

The Monte Carlo method, however, is prone to model risk. If the stochastic process chosen for the underlying variable is unrealistic, so will be the estimate of VaR. This is why the choice of the underlying model is particularly important. The geometric Brownian motion model described above adequately describes the behavior of some financial variables, but certainly not that of short-term fixed-income securities. In the Brownian motion, shocks on prices are never reversed. This does not represent the price process for default-free bonds, which must converge to their face value at expiration. 

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