# Tag Info

Accepted

### 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 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 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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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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### 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 ...
• 11.8k
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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-...
• 14.7k
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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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### Long Gamma vs Vega

Vega (denoted by $\nu$ in what follows) is the first order sensitivity of the option price with respect to volatility $\sigma$. Gamma (denoted by $\Gamma$ in what follows), is the second order ...
• 14.7k
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### Does financial math benefit society?

It is not financial mathematics in general, but a scientific approach that is beneficial: quantitative views and open objective tools make transactions more transparent. It decreases information ...
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### Implied Volatility of stock on Think or Swim

What they gave you is Newton's formula. If you have a function $f(x)$ then you can find the value $x_0$ such that $f(x_0) = 0$ by this method. It uses the derivative $f'$ which in your case is the ...
• 13.7k
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### Periodic functions when determining No Arbitrage price

It is, of course, possible to price such a contract in a no-arbitrage market. Indeed, if $f$ is a sufficiently smooth function, then you can price all contracts paying $f(S_T)$. Note that your ...
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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. ...