# Questions tagged [short-rate]

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

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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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### 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. ...
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### Delta hedge call option on short rate

Usually delta hedging an european call option in the black-scholes model is constructed of three assets; a call option, the underlying stock and the risk-free asset often assumed to have constant ...
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### Half-life of short rate

The SDE for the short rate r(t) in the Vasicek model is given by: $$d(r) = k(r^* - r)dt + \sigma dW$$ The deterministic part of the above SDE is the following ODE $$d(r) = k(r^* - r)dt,$$ where $k$...
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### Kalman Filtering to estimate parameters of G2++ Model

I'm trying to use Kalman Filtering to estimate the parameters of the G2++ short rate model. For this, I've been using Implementing Short Rate Models: A Practical Guide by F.C. Park. For reference, he ...
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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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### 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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### Bond Options Calibration to market volatility using SABR Model

I'm trying to calibrate bond option implied volatility from SABR model to market volatilities, I tried calibration in python but the smile isn't correctly matching with market volatility? Any help is ...