5.1.2 Parameters illustrated with VMARKET experiments

[ SLIDE parameters - discounting - price of risk - drifts || VIDEO modem - LAN - DSL ]

Since the terminal value of the discount function at the maturity is simply , the parameters characterize either the forecast of the spot rate or the numerical method that will be examined later in sect.5.3.1. The financial parameters that are relevant in the applet are:

- the
**lifetime or maturity date**( or`RunTime`

) of a bond in years, e.g. 10 for a bond reaching its maturity in a decade, - the
**maximum volatility**( or`Volatility`

) of a bond estimated from historical values, e.g. 0.02 for a two percent volatility peak that will be reached after one third of the bond lifetime (5.1.1#fig.1), - the
**market price of risk**( or`MktPriceRsk`

) measuring the reward expected by the investors for taking an investment risk, e.g. -0.25 in a risk averse market with little appetite for risk. In the applet, the effect is further modulated by a cosine function reproducing ( or`UserDouble`

)**economic cycles**during the lifetime of the bond, - the
**mean reversion target rate**( or`MeanRevTarg`

) is the value towards which the spot rate returns to after a long time, e.g. 0.05 for a market with a 5% average rate, - the
**mean reversion velocity**( or`MeanRevVelo`

) measures the speed of the process, e.g. 0.5 [1/year] for a mean reversion taking about years. - the
**spot rate**( or`SpotRate`

) used to plot the term structure of the interest rates.

as expected for a risk free investment (1.3#eq.6). The bond yield is equal to the spot rate and the term structure of the interest rates is constant .

The second applet below illustrates the effect of a large volatility in the spot rate and accounts for the extra return investors expect from the market through the so-called market price of risk .

Although this is not immediately apparent in the simulation, the main effect of the volatility is to reduce the curvature of the discount function by smearing out irregularities in the yield curves , : if the forecast rate changes rapidly, the yield curves do not follow immediately everywhere. The reward payed to the investor who accepts the risk associated with fluctuations in the spot rate is clearly visible, with an effective yield that increases with time for a positive value of the market price of risk .

The applet above illustrates the effect of evolving drifts in the forecast rates, here modeled with two economic cycles during the lifetime of the bond: recession cut rate over-heated economy rise rate... or rather the opposite when the time runs backward in the applet.

The third applet below finally illustrates the effect of a mean reversion, which accounts for the tendency of the forecasted rates to fall back to a long term average value.

Experimenting with the applet enables you to develop an intuitive understanding for the fundamental processes that characterize the credit market. The experiments also prepare you also for the inverse problem, where the term structure of the interest rates is known from the market (e.g. 2.2.2#fig.1) and the drift / volatility parameters are matched in order to extrapolate into the future (exercise 5.01).

**SYLLABUS** ** Previous:** 5.1.1 Term structure models
**Up:** 5.1 Discound bonds
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