financial mathematics Mathematical finance, also known as quantitative finance and financial mathematics, is a field of applied mathematics, concerned with mathematical modeling in the Finance#Quantitative_finance, financial field. In general, there exist two separate ...

, the Ho-Lee model is a

short-rate model A short-rate model, in the context of interest rate derivatives, is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written r_t \,. The short rate Under a sh ...

widely used in the pricing of

bond option In finance, a bond option is an option to buy or sell a bond at a certain price on or before the option expiry date. These instruments are typically traded OTC. *A European bond option is an option to buy or sell a bond at a certain date in fu ...

s, swaptions and other interest rate derivatives, and in modeling future

interest rate An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, ...

s. It was developed in 1986 by Thomas Ho and Sang Bin Lee. Under this model, the short rate follows a normal process: :

dr_t = \theta_t\, dt + \sigma\, dW_t

The model can be calibrated to market data by implying the form of

\theta_t

from market prices, meaning that it can exactly return the price of bonds comprising the

yield curve In finance, the yield curve is a graph which depicts how the Yield to maturity, yields on debt instruments – such as bonds – vary as a function of their years remaining to Maturity (finance), maturity. Typically, the graph's horizontal ...

. This calibration, and subsequent valuation of

s, swaptions and other

interest rate derivative In finance, an interest rate derivative (IRD) is a derivative whose payments are determined through calculation techniques where the underlying benchmark product is an interest rate, or set of different interest rates. There are a multitude of dif ...

s, is typically performed via a binomial lattice based model. Closed form valuations of bonds, and " Black-like" bond option formulae are also available.Graeme West, (2010)
''Interest Rate Derivatives''
, Financial Modelling Agency. As the model generates a symmetric ("bell shaped") distribution of rates in the future, negative rates are possible. Further, it does not incorporate mean reversion. For both of these reasons, models such as Black–Derman–Toy (

lognormal In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normal distribution, normally distributed. Thus, if the random variable is log-normally distributed ...

and mean reverting) and Hull–White (mean reverting with lognormal variant available) are often preferred.Pietro Veronesi (2010). ''Fixed Income Securities: Valuation, Risk, and Risk Management''. Wiley. The Kalotay–Williams–Fabozzi model is a

analogue to the Ho–Lee model, although is less widely used than the latter two.

References

Notes Primary references * T.S.Y. Ho, S.B. Lee, ''Term structure movements and pricing interest rate contingent claims'', ''

Journal of Finance ''The Journal of Finance'' is a peer-reviewed academic journal published by Wiley-Blackwell on behalf of the American Finance Association. It was established in 1946. The editor-in-chief is Antoinette Schoar. According to the ''Journal Citation R ...

'' 41, 1986. * John C. Hull, ''Options, futures, and other derivatives'', 5th edition,

Prentice Hall Prentice Hall was a major American publishing#Textbook_publishing, educational publisher. It published print and digital content for the 6–12 and higher-education market. It was an independent company throughout the bulk of the twentieth cen ...

External links

Valuation and Hedging of Interest Rates Derivatives with the Ho-Lee Model
Markus Leippold and Zvi Wiener,

Wharton School The Wharton School ( ) is the business school of the University of Pennsylvania, a private Ivy League research university in Philadelphia. Established in 1881 through a donation from Joseph Wharton, a co-founder of Bethlehem Steel, the Wharton ...

Term Structure Lattice Models
, Martin Haugh,

Columbia University Columbia University in the City of New York, commonly referred to as Columbia University, is a Private university, private Ivy League research university in New York City. Established in 1754 as King's College on the grounds of Trinity Churc ...

Online tools
Binomial Tree – Excel implementation
thomasho.com Fixed income analysis Short-rate models Financial models {{Econ-theory-stub