# Questions tagged [short-rate]

A short-rate model is a mathematical model that describes the evolution of interest rates

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### Zero-coupon call in CIR model

In an excellent textbook Brigo & Mercurio, I have a difficulty to derive a zero-coupon call option (3.26). What I did here didn't follow a stream of the main text. I assumed (3.28) and derived (3....
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### Understanding simple calibration of Hull-White process

I've encountered issues with understanding how to calibrate the Hull-White model without Quantlib package. I want to calibrate this model for the time series of short-rate ($r_1, \cdots,r_n$). I will ...
1 vote
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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: $$dr(t)=[\nu(t)-ar(t)]dt+\sigma dW(t)$$ 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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### Instantaneous forward rate function to use in HJM framework

HJM framework uses the instantaneous forward rate $f(t,T)$ in the resulting dynamics and pricing formulas (like in Hull-White or Ho-Lee model). But clearly market does not have an $f(t,T)$ formula, so ...
59 views

### Vasicek model calibration to bond prices or rates (no swaptions)

I need to calibrate Vasicek's model $dr_{t} = a(\theta - r_{t})dt + \sigma dW_{t}$ in a market with no swaptions. I was thinking in estimating $\sigma$ with historic data, but I'm in the doubt with ...
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### Simulating the path for Interest Rate

There are many ways to short term rates like Ho-lee process, HW process. However I failed to understand how this information can ...
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### Short rate models practical textbook

Currently working on a validation and testing of a yield curve model (one factor short rate model). Have been reading Andersen and Piterbarg, and Mercurio and Brigo. Good for true understanding, but ...
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### Affine Structure Resolution for the Vasicek model

I would like to now how to solve the PDE of the affine structure under Vasicek.I am delineating the steps: First let's posit the OU process under a Risk Neutral Measure such as : \begin{align*} \...
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### Longstaff and Schwartz example in their paper

I was looking at the well known Longstaff and Schwartz paper "Valuing American Options by Simulation: A Simple Least-Squares Approach". There are a couple of examples where they applied the ...
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### Euro short-term rate (€STR) question

Based on the latest data published by ECB,€STR = -0.56%. Is this the rate a bank would pay to borrow overnight or it's an annualised overnight rate so the actual overnight rate can be approximated ...
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### QuantLib - Calibrating Hull White one-factor on negative interest rates

I have been working with the QuantLib Python package for some days now. Currently, I am working on calibrating a Hull White one-factor model for short rates. I am calibrating the model on the yield-...
1 vote
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### Vasicek Short rate simulation - analytical formula vs discretization

I've been using two approaches to simulate Vasicek short rate paths and I'm wondering if one of them is more correct than the other. The first approach is based on the analytical formula (see code ...
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### Option Valuation With Hard To Borrow Rates

How would you include -in a simple way- high borrow rates, say 10%. Intuitively, for PUTs I'd set r as r - borrow_rate, to include the negative carry of the borrow. So If I'm selling puts, value would ...
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1 vote
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### Hazard process and affine term structure

How can I extrapolate the hazard processes and calibrate an affine term-structure model from the historical series of curves (1y, 2y, ..., 10y tenors) of the CDs spreads of different entities?
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### What is gsr model for short term interest rate

I am looking for a good definition for the GSR model for short rate. As mentioned in the page of https://rkapl123.github.io/QLAnnotatedSource/db/dd8/...
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### Implication of forward-rate dynamics when the short-rate follows a normal process

In the section 3.2.3 of the second edition of "Interest Rate Models - Theory and Practice" by Brigo and Mercurio, the forward-rate dynamics implied by the CIR model is derived as follow: The ...
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