Ho–Lee model: Difference between revisions

In financial mathematics, the Ho-Lee model is a short-rate model widely used in the pricing of bond options, swaptions and other interest rate derivatives, and in modeling future interest rates.^[1]^: 381 It was developed in 1986 by Thomas Ho^[2] and Sang Bin Lee.^[3]

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. This calibration, and subsequent valuation of bond options, swaptions and other interest rate derivatives, is typically performed via a binomial lattice based model. Closed form valuations of bonds, and "Black-like" bond option formulae are also available.^[4]

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 and mean reverting) and Hull–White (mean reverting with lognormal variant available) are often preferred.^[1]^: 385 The Kalotay–Williams–Fabozzi model is a lognormal analogue to the Ho–Lee model, although is less widely used than the latter two.

References

Notes

^ ^a ^b Pietro Veronesi (2010). Fixed Income Securities: Valuation, Risk, and Risk Management. Wiley. ISBN 0-470-10910-6
^ Thomas S.Y. Ho Ph.D, thcdecisions.com
^ Sang Bin Lee, shanghai.nyu.edu
^ Graeme West, (2010). Interest Rate Derivatives Archived 2012-04-17 at the Wayback Machine, Financial Modelling Agency.

Primary references

T.S.Y. Ho, S.B. Lee, Term structure movements and pricing interest rate contingent claims, Journal of Finance 41, 1986. doi:10.2307/2328161
John C. Hull, Options, futures, and other derivatives, 5th edition, Prentice Hall, ISBN 0-13-009056-5

External links

Valuation and Hedging of Interest Rates Derivatives with the Ho-Lee Model, Markus Leippold and Zvi Wiener, Wharton School
Term Structure Lattice Models, Martin Haugh, Columbia University

Online tools

Binomial Tree – Excel implementation, thomasho.com

v t e Bond market
Bond Debenture Fixed income
Types of bonds by issuer	Agency bond Corporate bond Senior debt Subordinated debt Distressed debt Government bond Infrastructure bond Municipal bond Global bond
Types of bonds by payout	Accrual bond Auction rate security Commercial paper Consol Convertible bond Contingent Reverse Exchangeable bond Extendible bond Fixed rate bond Floating rate note Inverse Inflation-indexed High-yield debt Lottery bond Perpetual bond Zero-coupon bond
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Fields and other	Dirichlet process Gaussian random field Gibbs measure Hopfield model Ising model Potts model Boolean network Markov random field Percolation Pitman–Yor process Point process Cox Poisson Random field Random graph
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@@ Line 1: / Line 1: @@
 {{Short description|Short-rate model in financial mathematics}}
-In [[financial mathematics]], the '''Hooli model''' is a [[short-rate model]] widely used in the pricing of [[bond option]]s, [[swaptions]] and other [[interest rate derivatives]], and in modeling future [[interest rate]]s.<ref name="Veronesi"/>{{rp|381}} It was developed in 1986 by Thomas Ho<ref>[https://www.thcdecisions.com/thc/team.asp Thomas S.Y. Ho Ph.D], thcdecisions.com</ref> and Sang Bin Lee.<ref>[https://shanghai.nyu.edu/academics/faculty/directory/sang-bin-lee Sang Bin Lee], shanghai.nyu.edu</ref>
+In [[financial mathematics]], the '''Ho-Lee model''' is a [[short-rate model]] widely used in the pricing of [[bond option]]s, [[swaptions]] and other [[interest rate derivatives]], and in modeling future [[interest rate]]s.<ref name="Veronesi"/>{{rp|381}} It was developed in 1986 by Thomas Ho<ref>[https://www.thcdecisions.com/thc/team.asp Thomas S.Y. Ho Ph.D], thcdecisions.com</ref> and Sang Bin Lee.<ref>[https://shanghai.nyu.edu/academics/faculty/directory/sang-bin-lee Sang Bin Lee], shanghai.nyu.edu</ref>
 Under this model, the short rate follows a [[gaussian|normal process]]:

Revision as of 16:32, 12 April 2023

References

External links