Modelling of Bonds, Term Structure and Interest Rate Derivatives
Exercises 1
1. You have £1000 that you wish to invest for two years in a savings account. Which of the following
options would you prefer?
(a)
(b)
(c)
(d)
(e)
A simple interest rate of 10%.
9.5%, compounded annually.
9%, compounded monthly for the rst year and six-monthly for the second year.
9.2%, compounded three-monthly for the rst year and monthly for the second year.
Continuously compounded rate of 9%.
2. Fix any r > −1 and suppose that
B(t, T ) =
1
(1 + r)T −t
for all t ≤ T .
(a) Compute all simple and continuously compounded forward and spot rates at time t.
(b) Assume that this model is discrete in time with time steps 0 = t0 < t1 < · · · < tn = t. Express
the value B(t) of the money market account in terms of r and t.
3. Fix any r ∈ R and any time t ≥ 0, and suppose that
B(t, T ) = e−r[T −t]
for all T ≥ t.
(a) Compute all simple and continuously compounded forward and spot rates at time t.
(b) Assuming that this is a model in continuous time, compute all instantaneous forward rates as
well as the short rate at time t. Can you give an expression for the value of the money market
account?
E1.1