1 The Model; 2 Euler Scheme for the Black-Karasinski() Model; 3 Theta.m Simulation of Short Rates using Euler Scheme; 4 References. Pricing and Hedging a Portfolio Using the Black-Karasinski Model. This example illustrates how MATLAB® can be used to create a portfolio of interest-rate. In this paper, we compare two one-factor short rate models: the Hull White model and the Black-Karasinski model. Despite their inherent.
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Black-Karasinski Tree Analysis – MATLAB & Simulink
All registered users please make sure to provide a valid email address. The general formulation for the Black-Karasinski model [1] is as follows. This is a great advantage over other short rate models such as Vasicek model and Hull-White model where short rates can possibly turn negative due to the additive noise processes.
However, the drawback for the Black-Karasinski Model [1] is that the analytical tractability is lost, when computing bond and bond option prices. To obtain bond and bond option prices, we have to use numerical procedures, such as tree and Monte Carlo simulation. To simulate future short rates driven by the dynamics as mdel equation BK.
Black–Karasinski model – Wikipedia
One such a numerical scheme is the Euler scheme. Specifically, applying the Euler scheme to equation BK.
Other numerical schemes with stronger path convergence are available, examples are the Milstein scheme, the strong Taylor scheme, and so on. For the Black-Karasinski model [1]the noise part is a deterministic function of time only, as such, the Euler scheme and the Milstein scheme are the same. More discussions about numerical discretization schemes for SDEs can be found in Kloeden [2].
The following is a Theta. Note however, due to the log-normal process assumed in the Black-Karasinski model, simulated short rates can eventually explode or have infinite values.
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