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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.e. it can fit today's zero-coupon bond prices, and in its most general form, today's prices for a set of caps, floors or European swaptions. The model was introduced by Fischer Black and Piotr Karasinski in 1991. ==Model== 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): : where ''dW''''t'' is a standard Brownian motion. 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Black–Karasinski model」の詳細全文を読む スポンサード リンク
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