MA 374 Financial Engineering Lab Lab 11
1. Consider the Vasicek model
dr = β(µ − r)dt + σdWQ.
For the three parameter sets [β, µ, σ, r(0)] given by [5.9, 0.2, 0.3, 0.1], [3.9, 0.1, 0.3, 0.2] and
[0.1, 0.4, 0.11, 0.1], plot the term structure up to 10 time units (i.e, plot yield versus time). Now for each of
the three parameter sets, plot yield curves versus maturity up to 500 time units for ten different values of r(0).
Put down your observations in the report.
2. Consider the CIR model
dr = β(µ − r)dt + σ
√
rdWQ.
For the three parameter sets [β, µ, σ, r(0)] given by [0.02, 0.7, 0.02, 0.1], [0.7, 0.1, 0.3, 0.2] and
[0.06, 0.09, 0.5, 0.02], plot the term structure up to 10 time units (i.e, plot yield versus time). For the parameter
set [β, µ, σ] given by [0.02, 0.7, 0.02] and with r(0) = 0.1 : 0.1 : 1, plot yield curves versus maturity for 600
time units. Put down your observations in the report.
Note that WQ in the above models denotes the Brownian motion under the risk-neutral measure Q. For the termstructure results, you may refer to Bjork.
