## The One Factor Ho-Lee Interest Rate Model

The applet on this page constructs a binomial tree of spot interest
rates using the Ho-Lee model. Suppose t =1,2,3,..,n (where n >=2)
and we are given

- D(1),..,D(n) where D(t) is the discount factor over the time
period [0, t]. It is assumed that interest is compounded continuously.
Hence if r(2) is the interest rate over [0,2]. Then D(2) =
exp(-2*r(2)).
- sigma(1), sigma(2),..,sigma(n-1), the volatilities of the spot
interest rates at time t=1,2,..,n-1 respectively.

The computed spot interest rate at time t and state j, r(t,j),
satisfies

- r(t+1, j+1) - r(t+1,j) = 2 *sigma(t+1) for 0 < =
t <= n-2, 0 <= j
< = t-1.
- There is no arbitrage opportunity among all the discount rates.

Note that the discount factor D(t,j) at time t and state j over
[t,t+1], is given by D(t,j) = exp(-r(t,j)). The computed r(t,j) is a
discretisation of the Ho-Lee model

dr = theta(t) d(t)+ sigma(t) dW

Testing Done

- Verify example on p456-p461 in [1]

For more details on Ho-Lee model, please see Chapter 15 of

[1]. A description on the algorithm
employed is given in

HoLeeImp.pdf.

**JRE 1.4 or later is required to run the following applet. **

[1]
R.Jarrow and S.Turnbull, Derivative Securities (second edition),
South-Western College Publishing