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6

You know that the Ho-Lee model is represented by the stochastic differential equations \begin{align} dr_t=\lambda_t\,dt+\sigma\,dW_t \end{align} In order to Implementation our binomial tree, we use the Euler discretization. \begin{align} r_t=r_{t-\Delta t}+\lambda_{t-\Delta t}\,\Delta t+\sigma\,\sqrt {\Delta t} \,Z \end{align} where $Z$ is a standard normal ...

3

You can calibrate the model by discretizing in time, and using a forward induction method as originally proposed by Jamishidian in 1991: F.Jamshidian, Forward Induction and Construction of Yield Curve Diffusion Models, J.Fixed Income 6, 62-74 (1991). Although he formulated this induction in the language of the binomial tree, the method is more general, and ...

1

Yes, this is trivially true once you know that every continuous local martingale is a time-changed brownian motion. Therefore, if you change your time variable $t$ in $dX=a\,dt+b\,dW(t)$ to the right $t^\prime$ you can get a standard tree representation. Now, the correct time change may be difficult or impossible to figure out, so this theorem is of ...

4

For a martingale $dX=a(X,t)\,dt+b(X,t) dW(t)$ where $a$ and $b$ are not constant, your tree will not recombine in general . This is the main issue. See for instance: Florescu, I. and F. G. Viens (2008, March). Stochastic volatility: Option pricing using a multinomial recombining tree. Applied Mathematical Finance 15 (2), 151-181. It deals with the case ...

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