# Tag Info

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### Processes used in quant finance

Here is a short list (to be edited and improved - community wiki) : Standard brownian motion (also called Wiener process) for which: $d\, W_t \sim \mathcal N(0, \sqrt{d t})$ Geometric brownian ...

### 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). ...
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### Dynamics of FX rate

I am answering now instead of commenting. The rate of change in FX is naturally forward looking in this case. What you confuse is what happened to Spot due to changes in interest rate environments ...

### How do you find variance of a sde?

Here are two approaches that you could take to compute the variance of $X_t$. I am not making the conditioning explicit as it just complicates the notation but doesn't really add any additional ...
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### Stochastic differential equation of a Brownian Motion

In stochastic calculus, only stochastic integrals are defined. The differential form is just a notation. That is, $$dF=g(t)dW_t$$ is just another expression for the integral $$F=\int_0^t g(s) dW_s.$$ ...
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### Solving $dX_{t} = \mu X_{t} dt + \sigma dW_{t}$

It appears that you need to read some books such as Stochastic Differential Equations. For such type of equations, you need to use something called integrating factor such as the function $e^{-\mu t}$ ...