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The Hull-White model can represents the risk free rate as a stochastic process, that is, in terms of expected return and volatility. The zero curve only gives you expected returns and you have to find a source to calibrate volatility, as FQuant told you. Common volatility sources used for this calibration are historical series of the zero curve or ...


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The one-factor Hull-White model is given by $$dr(t) = (\theta(t) - \alpha\; r(t))\,dt + \sigma\, dW(t)\,\!.$$ The zero curves are only sufficient for the calibration of the parameter $\theta(t)$, which is given in terms of them by $$\theta\mathrm{(t)=}\frac{\partial f(0,t)}{\partial T}+\alpha f(0,t)+\frac{\sigma^2}{2a}(1-e^{-2\alpha t}),$$ where ...


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Here is how I would approach such a calibration. Assuming we have the necessary market data one can easily construct the emprical distribution of the arrival rate. Let $\lambda_{emp}(\delta)$ be the empirical distribution. Then one can define a metric by $$ m(k,A,N)=\sum_{i=1}^N |\lambda_{emp}(i)-\lambda^a(i)| $$ After you have decided upon a suitable ...



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