# Tag Info

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### What mathematical theory is required for high frequency trading?

Hah! There is no such thing as the “rigorous mathematical underpinning” of high frequency trading - because HFT, like all trading, is not primarily a mathematical endeavour. It’s true that many ...
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### Long Gamma vs Vega

Long gamma is being long realized volatility. Long vega is being long implied volatility. Long gamma positions benefit when realized volatility goes up or the actual underlying has volatility. Long ...
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### What mathematical theory is required for high frequency trading?

I would argue, taking a note from John von Neumman, that quantitative finance lacks rigorous underpinnings. Von Neumann warned in 1953 that many things that look like proofs in economics and finance ...
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### What is the difference between pull to par and roll down in both mathematics and conceptual?

Pull-to-par just says that a bond's (clean) price will converge towards its face value as the bonds approaches maturity. There is nothing really interesting about pull-to-par - a bond's (clean) price ...
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### What is the difference between pull to par and roll down in both mathematics and conceptual?

Pull-to-par says that the bond's price will gradually converge toward par (100% of face value) when yield is unchanged. This process is also known as accretion for a bond trading at a discount (since ...
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I am one of the two authors of the paper. The continuity in time of the path of the underlying suggests that at every trading time, the strategy is self-financing. In fact, if the underlying random ...
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### Mathematical equation relating $\frac{dV}{dS}$ to $\frac{dV}{dK}$

If your working modelling assumptions are such that the dynamics of the log price process $\ln(S_t)$ is space homogeneous, you have that the price of a European vanilla option is itself a space-...
• 13.9k
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### What is an adapted process

Let $\{X_t\}$ be a stochastic process and $\mathcal{F}$ be a filtration. The intuitive idea is that for $\{X_t\}$ to be adapted, it can't reveal what's unknowable (according to the filtration). By ...
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### Cadlag Property of Jump Proccesses

Intuitively, cadlag expresses the fact that we know a jump has occurred after the fact, but we never have advance knowledge that the jump is about to occur (i.e no knowledge of the starting point for ...
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### How to check if $E [\exp \{ \int_0^t \frac{Y_u^2}{1+Y_u^2}du \}]< \infty$

If you make the change of variable $Y_t = \sinh U_t$ and apply Ito then you immediately get $$dU_t = 2dW_t$$ so the solution of your SDE is $$Y_t = \sinh\left(2W_t + C\right)$$ with $C$ a constant. ...
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### Zero coupon bond calculations

The notations in the snapshot are pretty messy. I prefer to proceed as follows. Let $X_t = -\int_t^T f(t, u)du$. Note that \begin{align*} f(t, u) - f(0, u) = \frac{\partial }{\partial u}\left(\int_0^...
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### Quantitative finance for physicists

Physicists typically know PDEs but not stochastic calculus I have a masters in physics, so have a reasonable idea of the usual skillsets a physicist will know (at least at undergraduate level), and ...
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### Interpolation of $\mu(t,X(t))dt+\sigma(t,X(t))dW(t)$
That is a tricky question because interpolation seems to be ok if you need one point $\tau$ between $t_k$ and $t_{k+1}$ but it is not. The difficulty arise a direct way if you want two points inside \$[...