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2
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2answers
130 views

What is the reasoning to derive this financial model called the Vasicek Model?

The model specifies that the instantaneous interest rate follows the stochastic differential equation $$\mathrm{d}r_t = a(b-r_t)\: \mathrm{d}t + \sigma \: \mathrm{d}W_t$$ where $W_{t}$ is a Wiener ...
5
votes
1answer
184 views

From $AR(p)$ to SDE

Let the Vasicek model to be $$\Delta r_{t}=k(\theta - r_{t-1})\Delta t+\sigma\Delta z_{t}$$ Due to the fact that $$\Delta r_{t}=r_{t}-r_{t-1}$$ if you let $\Delta t=1$, it is easy to see by ...
3
votes
2answers
695 views

Is Vasicek risk neutral?

I am a bit new to this, and am trying to understand the concepts of the risk neutrality in interest-rate models. What I can't seem to understand is why the Vasicek model is risk-neutral? Following ...
3
votes
1answer
199 views

How to design back-testing (validation) for such modified Vasicek model?

Consider a classical Black Scholes model , $$\frac{dS}{S} = \mu dt + \sigma dW$$ , where $dW$ is a Brownian motion, that $W(t_1) - W(t_0) \sim N(0, t_1 - t_0)$. The back-testing strategy is ...
2
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1answer
265 views

Why is the mean time-dependent in the Hull-White interest rate model?

In the Vasicek interest-rate model, the interest rate reverts to a constant mean. This makes sense to me. In my conception, the mean ought to be time-invariant, since interest rates don't follow an ...