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# Questions tagged [hullwhite]

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Let's take the following three SDEs: $$dr=u(r,t)dt + w(r,t)dX$$ $$u(r,t)=a(t)-br$$ $$w(r,t)=c$$ where $b$ and $c$ are constants and $a(t)$ an arbitrary function of time $t$. If Zero Coupon Bond $Z(... 1answer 581 views ### Hull-White formula on wikipedia, correct? The distribution for the short rate in Hull-White model on Wikipedia is: But the same equation in Damiano's Interest Rate Models - Theory and Practice is: Q: I ... 1answer 608 views ### zero coupon bond pricing formula using Hull White I am having some trouble to understand the derivation of the parameters of zero coupon pricing formula using Hull White. Specifically I am trying to understand how to get --[1] where is the ... 1answer 1k views ### How to get set the theta function in the Hull-White model to replicate the current yield curve I want to calibrate the HW one factor model to current market data. How do I set the function$\theta(t)$in $$\mathrm{d}r(t) = \kappa(\theta(t)-r(t))\mathrm{d}t+\sigma\mathrm{d}W(t)$$ to ... 1answer 357 views ### Estimation of market price of risk of short interest rate under the Hull-White model I think I am a bit confused. I intend to estimate the market price of risk the short interest rate, say, under the Hull-White model. I have the following two questions. Is it correct to state state ... 2answers 12k views ### How to calibrate Hull-White from zero curve? I am interested in calibrating a Hull-White model to the market. I do not, however, have data on anything except the market zero curves, as all derivatives are being traded OTC. My plan is to ... 1answer 797 views ### Instruments for calibrating Hull White Model I have a few questions regarding hull white calibration, specificly for the trinomial tree model. 1.I am wondering what are the ideal instruments could be used for hull white model calibration? Cap, ... 1answer 554 views ### Hull White Tree Calibration 2 This is actually to extend the question I asked previously and to follow up Bernd's answers. This is the original link: Instruments for calibrating Hull White Model 1. As Bernd mentioned, it's ... 2answers 829 views ### Why does the short rate in the Hull White model follow a normal distribution? Consider Hull White model$dr(t)=[\theta(t)-\alpha(t)r(t)]dt+\sigma(t)dW(t)$when we solve the SDE above we have$r(t)=e^{-\alpha t}r(0)+\frac{\theta}{\alpha}(1-e^{-\alpha t})+\sigma e^{-\alpha t}\...
I have been trying to understand the H&W model expression for zero coupon bond price volatilities: $\nu_B(t_0,t_M)=-\frac{\nu_r}{m}(1-e^{-m\tau_{0,M}})$, where $\nu_B(t_0,t_M)$ is zero coupon ...