## 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
1. r(t+1, j+1) - r(t+1,j) = 2 *sigma(t+1) for 0 < = t <= n-2, 0 <= j < = t-1.
2. 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