An interest rate option model (originally appeared in 1986) which uses short rates in pricing interest rate derivatives such as bond options and swaptions or in valuing fixed income securities with embedded options such as callable bonds, puttable bonds, etc. In other words, it models the uncertain behavior of the interest rate structure as a whole, not a certain point on the curve. To that end, this arbitrage-free, term-structure model assumes that interest rates along the yield curve are correlated and don’t revert to their mean.

The derivation of interest rate follows a process of four steps: 1) building the perturbation function (a mathematical method that is used to obtain an approximate solution to a problem due to inability to find an exact one. By doing so, it builds on the exact solution of a related problem). 2) calculating the risk-neutral probabilities depending on the Cox-Ross-Rubinstein model. 3) deriving the path-dependence conditions using a binomial tree. And 4) combining the previous steps together.

The Ho and Lee model is also built on another set of assumptions for simplicity’s sake. 1) there are no market frictions, i.e. no transaction costs or taxes. 2) all assets are perfectly divisible. 3) trading takes place at discrete times. 4) the market is complete in the sense that there exists for every time period a fixed income security (bond) with the respective maturity. And 5) for every time period, the state-space is finite. The Ho and Lee option model, which is also known as “term-structure option pricing model”, paved the way for more complicated, but more flexible option models like Hull-White (1990) and Heath-Jarrow-Morton (1992). Originally, this model can be viewed as an equivalent of the Cox-Ross-Rubinstein model (1979) for stock options but with a focus on interest rate contingent claims.

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