Documentation Help Center. The portfolio pricing functions hjmprice and bdtprice calculate the price of any set of supported instruments, based on an interest-rate tree. Computing Instrument Sensitivities. Overview of Interest-Rate Tree Models.
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In financial mathematics , the Black—Karasinski model is a mathematical model of the term structure of interest rates ; see short rate model. It is a one-factor model as it describes interest rate movements as driven by a single source of randomness. It belongs to the class of no-arbitrage models, i. The model was introduced by Fischer Black and Piotr Karasinski in The main state variable of the model is the short rate, which is assumed to follow the stochastic differential equation under the risk-neutral measure :.
The model implies a log-normal distribution for the short rate and therefore the expected value of the money-market account is infinite for any maturity.
In the original article by Fischer Black and Piotr Karasinski the model was implemented using a binomial tree with variable spacing, but a trinomial tree implementation is more common in practice, typically a lognormal application of the Hull-White Lattice. The model is used mainly for the pricing of exotic interest rate derivatives such as American and Bermudan bond options and swaptions , once its parameters have been calibrated to the current term structure of interest rates and to the prices or implied volatilities of caps , floors or European swaptions.
Numerical methods usually trees are used in the calibration stage as well as for pricing. It can also be used in modeling credit default risk , where the Black-Karasinski short rate expresses the stochastic intensity of default events driven by a Cox process ; the guaranteed positive rates are an important feature of the model here. From Wikipedia, the free encyclopedia. Black, F. July—August Financial Analysts Journal : 52— Damiano Brigo, Fabio Mercurio Springer Verlag.
Stochastic processes. Bernoulli process Branching process Chinese restaurant process Galton—Watson process Independent and identically distributed random variables Markov chain Moran process Random walk Loop-erased Self-avoiding Biased Maximal entropy. List of topics Category. Categories : Short-rate models Financial models. Namespaces Article Talk. Views Read Edit View history. Contribute Help Community portal Recent changes Upload file.
The Black and Karasinski Model
Black-Karasinski Tree Analysis