Questions tagged [short-rate]
A short-rate model is a mathematical model that describes the evolution of interest rates
125 questions
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Obtaining the dynamics of the LGM (Hull-White) short rate (Brigo and Mercurio Toolkit)
I'm struggling with the following problem: I have a diffusion of the short rate under a numeraire associated measure $Q^N$ of the form: $dr(t) = (...)dt+ H'(t)\alpha(t)dW_t^N$ This is the short rate ...
1 vote
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Modeling the Yield Curve with Short-Rate Models
I have been reading Gregory Counterparty Credit Risk. In the book he criticizes one-factor short-rate models for their limited ability to capture realistic yield curve movements. While they allow for ...
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Relation between short term rate and forward rates
I'm trying to understand relationship between short rates and forward rates Let $f(t,T)$ is forward rates compounding at $T$ as seen from $t$, and $r(t)$ just a short rate For a Zero Coupon Bond ...
3 votes
1 answer
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The converse to Cheyette's Ansatz
It is well known that if the HJM volatility function $\sigma(t,T) = g(t)h(T)$ where $g(t)$ is a random process then the short rate is Markovian on two state variables. One can show that this ...
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What type of interest rate data can the Euler-M discretization of the Vasicek interest rate be used to model?
I'm looking at analysing the Vasicek model via its EM discretization. I know the model represents instantaneous short rates but would it be valid to take US tbills (3 month) historical daily rates as ...
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Can I use the Gsr short-rate model in quantlib to find the OAS of callable bonds
I am trying to find the OAS of callable/puttable bonds using TreeCallableFixedRateBondEngine. This works when I use the HullWhite or BlackKarasinski short-rate models, but they do not allow for time-...
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1 answer
157 views
Link between short rate model and Nelson-Siegel
I have just read the paper about the Nelson-Siegel model and I am a bit confused about its relation to short rate models, such as the Vasicek model. Nelson-Siegel model The Nelson-Siegel model is a ...
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Jamshidian's formulation of Black Derman Toy
In his 1991 paper on forward induction of binomial tree calibration on BDT model, it is stated that $$r(t) = U(t)\exp(\sigma(t)W(t))$$ where $r$ is the short rate modelled by Black Derman Toy. It is ...
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Why use instantaneous forward rates?
My question is why we need instantaneous forward rate $f_t$? What is the usage? I know that some stochastic rate models model this one, and we easily integrate to get spot rate $r_t$, since $f_t=(tr_t)...
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Calibrating CIR to bond prices
Consider the Hull-White model - $$dr_t = (\theta_t - kr_t)dt + \sigma_tdw_t$$ We can/have to calibrate $\theta_t$ to the current bond prices $P(0,t)$ and make it consistent with the HJM framework. For ...
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Step by step integration of the Hull-White SDE
I'm struggling to understand the integration process of the Hull-White equation: \begin{equation} dr(t)=[\nu(t)-ar(t)]dt+\sigma dW(t) \end{equation} In the majority of the references that I have ...
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EURIBOR dependent product pricing
3M Euribor rates still exists (see https://www.ice.com/) and there still exist structured products depending on them : for instance a CMS spread whose udnerlying CMS rates depend on it. But also range ...
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Multiple factor Hull-While and yield curve deformation
I am currently studying rate models and I understand that the One-Factor model has some incompleteness: The yield-curve can only be shifted. But I don’t understand what parameter controls this shift ( ...
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Are instantaneous short rates compatible across models?
If I calibrate the Vasicek's yield curve to the Nelson-Siegel's (NS) yield curve, can I assume that $r_V(0) = r_{NS}(0) = \beta_0 + \beta_1$ or not? NS short rate: $r_{NS}(S) = β_0 + β_1 e^{-S/\tau} + ...
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How to convert the parameters of multi-factors cheyette model (quasi-Gaussian model) from tenors to factors?
The book "Interest Rate Modeling" by Andersen and Piterbarg is an extermely fascinating book on interest rate derivatives. Recently, I have encoutered some issues while reading this book. ...
