# Questions tagged [vasicek]

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### Affine term structure for CDS

in papres such as https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2686284 (Exploring Mispricing in the Term Structure of CDS Spreads by Robert A. Jarrow, Haitao Li, Xiaoxia Ye, and May Hu) a ...
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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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### Monte Carlo price of European option on ZCB under Vasicek short rate

I'm trying to replicate the analytical result from the closed form Vasicek formula for European options on zero-coupon bonds using Monte-Carlo simulation. The interest rate paths I've simulated seem ...
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### Hazard rate and Term structure model

About the paper of Pan and Singleton 2008 “Default and Recovery Implicit in the Term Structure of Sovereign CDS Spreads”, once the lambdas (hazard rates) for the different tenors of the term structure ...
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### How do I hedge two/three zero coupon bonds with different maturity under Vasicek short rate model?

I am working on the case that I need to hedge two bonds with different maturites under Vasicek model, which is \begin{equation} dr_t=a(b-r_t)dt+\sigma dW^Q_t \end{equation} and I know how to price the ...
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### Calibration and comparison of the Vasicek model and Ho-Lee model

I would like to calibrate the Hoo-Lee model and the Vasicek model to a historical interest rate series and compare the interest rate development of both models with the historical interest rate series....
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### Multi-period Basel/Vasicek formula

I need to apply Basel/Vasicek formula to a 20-years horizon, both from a 20-years cumulative perspective and year-on-year basis. Please find below the formula of the Basel Capital (ie. unexpected loss)...
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### Vasicek credit loss for real portfolio

Consider the Vasicek limiting distribution for losses of a loans portfolio. Now, consider a real portfolio, made of 10 loans each with a different rating class; eg: LN#1 - rating A+ LN#2 - rating BB ...
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### Difference between Vasicek and Gordy models

I'm trying to understand what Gordy  added to Vasicek  model (the core of the IRB formula of Basel Accords). Is it correct to say the Vasicek shows that the portfolio loss conditional on $Y$ ...
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### Vasicek model - Bond price and volatility

Why does the bond price under the Vasicek model increase as the rate volatility increases? What is the intuition behind this?
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### Choosing which interest rate model to go with?

I've been assigned with the task of modelling zero rate curve. I did it with two models: Vasicek and CIR. Looking at the two curves produced, I can see that one is closer to the observed curve than ...
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### Distribution and parameters for the amount at time T of Bond

An investor follows the following investment strategy from time t to time T: buys a 10-year zero coupon bond, holds it for a time-length dt, sells it and buys a new 10-year ZCB with the proceeds. The ...
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### Option pricing PDE Black Scholes one-factor Hull-White (or Vasicek) model

I am trying to find the option pricing PDE of the Black Scholes one-factor Hull-White (or Vasicek) model using a self-financing portfolio strategy. The system is as following \begin{equation*} \begin{...
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### calibration of correlation in vasicek model

how can I calibrate the correlation by numerical integration of the normal bivariate distribution assuming that the standardized asset returns of two firms are described by the single-factor Vasicek ...
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### Python Panel Data Regression for OUP Calibration

I have a model for predicting stock returns that classifies stocks as overbought or oversold, kind of like an RSI. It follows an OUP and I am curious about my $\mu$, $\sigma$, and $\kappa$ parameters, ...
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### Can I use 1M Libor monthly data to estimate Vasicek parameters and use them to price quarterly swap

I am working on CVA algorithm. I am using vasicek model to evolve short rate. At hand, I am supposed to value a fixed to floating IRS quarterly paying. Can I use 1M Libor as surrogate for short ...
330 views

### Bond-price dynamics in the Vasicek model

Hello I am studying about interest rate modeling There is one good source about Vasicek (link: https://web.mst.edu/~bohner/fim-10/fim-chap4.pdf). However there is one equation that I try but unable ...
232 views

### Vasicek model and spot interest rate parametrised by reversion rate

By solving an SDE I want to derive the analytical results for mean and variance of the process of extended Vasicek model. $$dr(t) = \left(\eta - \gamma r(t) \right)dt + c dX(t)$$ where $\gamma$ ...
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### Term structure equation in the Vasicek model

Consider the SDE $$dr_t = (b-ar_t)dt +\sigma dW_t, \text{with } a; b > 0.$$ Let $$F(t; r) = E(\exp(-\int_{t}^{T}r_sds)| r_t = r).$$ (F can be interpreted as price of a zero coupon bond with ...
152 views

### Vasicek and Extended Vasicek Model

I want to ask about basic reasoning in Vasicek and Extended Vasicek model. Why $P(T,T) = 1$ for non arbitrage model? Can we place $P(T,T) = 10$ or other numbers? Is it correlated with The Law of ...
281 views

### Need to solve the stochastic differential equation of Vasicek Model

How to solve the stochastic differential equation of the Vasicek model for the analysis of credit risk? I search in the article "The Distribution of loan portfolio value" (Vasicek) but he doesn't ...
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### Finding B(t) in the Vasicek model relating to the bond equation, more specifcally from the initial condition

In the Vasicek model for derving bond prices, we have the ODE $$\frac{dB}{dt}=\gamma B-1$$ which gives rise to the general solution $$B(t)=C_1 e^{\gamma t}+C_2$$My problem is that we have the "initial"...
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### Vasicek model: joint simulation with discount factor

In Vasicek model, we have the following relation to get Discount factors given the value of short rate: $$P(t\,,T)={{e}^{A(t,T)\,-\,B(t,T){{r}_{t}}\,}}$$ So, Discount factors are known as soon as we ...
141 views

### Derive a mathematical equation for Eurodollar future rate

If we suppose that r(t) follows a Vasicek model, which is: $$dr(t) = (\mu - \kappa r(t))dt + \sqrt\sigma dW(t)$$ How to derive an expression for Eurodollar future rate?
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### Differential of integrating factor $d(e^{at}r_t)$ in Vasicek model

I am attempting to solve the Vasicek model SDE (using Wikipedia parametrisation): $$dr_t = a(b-r_t)dt + \sigma dW_t$$ Every solution is proceeding to multiply both sides of the equation by the ...
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### basic difference between interest rate models

I am reading up on interest rate models, but currently confused about difference in the two types of models: no arb models like ho-lee, vasicek etc. others like nelson siegel, pca models etc. While ...
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