# Tag Info

### Two papers - two different solutions of the Ornstein-Uhlenbeck process

Note that the Ito integral of a deterministic integrand $f: \mathbb{R}_+ \rightarrow \mathbb{R}$ is normally distributed \begin{equation} \int_0^t f(u) \mathrm{d}W_u \sim \mathcal{N} \left( 0, \...

### What is the purpose of short rate models?

Short rate models were first used in the 1970s and 1980s to try to fit and explain the term structure of interest rates - they went beyond simple parametric shapes (polynomials and exponential forms). ...
Accepted

### Vasicek short rate: Risk-neutral measure into real-world measure

Vasnicek by itself does not specify what form the change of measure should be and how you should parameterise the market price of risk. A very natural parameterisation is affine in the factor, i.e., ...

### Why isn't the Vasicek model arbitrage-free?

Short rate models are broadly divided into equilibrium models and no-arbitrage models. The models from Vasicek, Dothan and Cox, Ingersoll and Ross are examples of equilibrium short rate models. The ...
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### Problem with pricing a call option using the Monte Carlo Vasicek model

To make sure that I understand the problem: you are trying to price a call option expiring at time 0.5, which will exercise into a unit notional zero-coupon bond with a maturity of 1.0 at a strike (...

### What is the purpose of short rate models?

I might get down-voted for this, but in my opinion, short-rate models are not very useful for any practical pricing problems in today's finance. Even for simple vanilla rate derivatives (i.e. Caplet ...
Accepted

Accepted

### Difference between the Basel IRB and the Vasicek formula

The paper continues "The quantity p(Y) provides the loan default probability under the given scenario." But the default probability is 0.001, not 0.999 as in the IRB version. So G(0.999) = -G(1 - 0....

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### How to find the transition distribution functions of these two processes?

Here is a derivation for the Ornstein-Uhlenbeck process. Solution to the SDE $$dX_t = \theta(\mu-X_t) dt + \sigma dW_t$$ subject to the initial condition $X_0=x$ has the form X_t= \mu + (x - \mu)e^{-...
Accepted

### Hull-White Extension of Vasicek Model

$\theta(t) - a(t) r(t)$ is the risk neutral drift. The Hull & White models posits the dynamics $dr(t) = (\theta(t) - a(t) r(t)) dt + \sigma dW(t)$ under the risk neutral measure $P$ and then ...

### Term structure used in Geometric Brownian Motions under Risk Neutral Measure?

It should be time dependent and set to the spot forward rate $= -\frac{\partial}{\partial t} \ln(\text{discount}(t))$ when simulating in continuous time. When discretizing the simulation use the ...
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### Derive a mathematical equation for Eurodollar future rate

there are many ways to solve Vasicek system, for me personally I markov short rate approach. Without going into the details of proofs: Note that eurodollar future is calculated under risk neutral Q ...
that symbol means "the min of". So for example, if: $s<t$, then $s$ ^ t = s. If you look in any book for the Covariance of a BM, you will see that same symbol and how to work with it. Cheers.