# Questions tagged [vasicek]

The Vasicek model is a 1-factor short-rate model.

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### Modeling compounded RFRs with Vasicek

I’m wondering if simple interest rates models, like Vasicek, could be successfully used for modeling compounded setting-in-arrears rates (compounded SOFR for example)? As far as I see I can do that ...
• 31
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### Deriving solution to bond pricing equation

Consider the Vasicek model for the spot model: $$𝑑𝑟 = (𝛼 − 𝛾𝑟)𝑑𝑡 + √𝛽𝑑𝑊$$ Suppose $𝛾 = 0.1, 𝛾 = 0.1$, and the volatility of the process is 0.02. The spot rate is 10%. Assume the form of ...
1 vote
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### ARCH-Vasicek model solution

I understand how we can obtain the solution of Vasicek model $dr_t=\alpha(\mu-r_t)dt+\sigma dW_t$: $$r_t=r_0e^{-\alpha t}+\mu(1-e^{-\alpha t})+\sigma\int_0^te^{-\alpha(t-s)dW_{s}}$$ This easily ...
• 31
1 vote
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### Interest rate models history

I am familiar with some interest rate models, such as the Vasicek, CIR. I also have an understanding of the basic formalization of other models such as Ho-Lee, Hull-White, HJM, Libor market model (LMM)...
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### 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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### 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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### Understanding the application of Asset-Correlation to credit risk models

Suppose we have a portfolio of $n$ credits. In order the estimate the Portfolio Value at Risk (99,9) we use a standard vasicek model with the Ability to pay variable $A_i=\sqrt{\rho}x+\sqrt{1-\rho}z_i$...
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### ATM cap prices in Vasicek model (Filipovic)

I am trying to replicate the ATM cap prices in table 7.1 (see bottom of this post) from Filipovic's book "Term Structure Models - A Graduate Course" which assume the Vasicek model and uses ...
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### How to calibrate an O-U process based on historical data?

Background: I have been working on my master thesis project for the last few months and gave the final presentation on the 2023-06-01. As a part of the master thesis project, I did a complete ...
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### Bond-pricing under the Vasicek short rate model

I'm currently studying the Vasicek model of the short interest rate $$dr_t=a(\mu-r_t)dt+\sigma dW_t$$ I know how to solve this stochastic differential equation (SDE) and how to find expectation and ...
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