# Tag Info

### Why Ito calculus?

My understanding is because the Ito's integration definition keeps the martingale property. With Brownian motion $W(t, \omega)$ defined, to define stochastic integration in a Riemann–Stieltjes style:...
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### Why Ito calculus?

In fact Ito and Stratonovich calculus are both mathematically equivalent. In the following paper you can e.g. see that both derivations lead to the same result, i.e. the Black-Scholes equation: Black-...
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### What the expectation of S^2 is from GBM?

As Sanjay said, you can apply Itô's Lemma to $f(t,x)=x^2$ and obtain \begin{align*} \mathrm{d} S^2_t=\left(2\mu S_t^2+\sigma^2S_t^2\right)\mathrm{d}t+\left(2\sigma S_t^2\right)\mathrm{d}W_t. \end{...
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### Proof that no trading system always wins

At the first glance, what you are asking for is a model admitting arbitrage, so there is a zero chance of losing money and positive chance of yielding profits. Well, many equilibrium models start with ...
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### Preparation for interview: influx of power of the moon

Here's how i'd have at it; * I happen to know these are okay guesses. ** Let's assume it's just the potential energy, and that ...
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Let define $\mathbb{Q}$ and $\mathbb{P}$ two equivalent probabilities on a filtered space $(\Omega,(\mathcal{F}_t)_{t\geq 0})$ Let define $Z_T=\frac{d\mathbb{Q}}{d\mathbb{P}}$ restricted to $\mathcal{... • 2,362 5 votes Accepted ### Do we have a Brownian motion Aside from the independence requirement for the increments, that is, the independence of$X_{s+t}-X_s$and$\mathcal{F}_s$, you can check whether the increment$X_{s+t}-X_s$has the distribution of$N(...
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It is actually rather simple. Lets start with the fixed rate market. A can borrow at 5% while B can borrow at 7%. Simply said, A has a comparative advantage of 2% in the fixed rate market. In the ...
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### Abstract algebra in economics and finance

Yes, I've seen some interesting papers that improve one's insight into how things work, even if it is not clearly applicable to practice. Belal Ehsan Baaquie published several books on applications ...
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### How do you derive this Carr-Madan-like equation?

Equation (11) in Kammeyer and Kienitz' paper is a very well-known and popular option pricing formula. It goes back to the work from Lewis (2001), see Theorem 3.2 in Lewis' paper. Original Formula ...
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### Recommendations for books to understand the math in quantitative finance papers?

Paul Wilmott on Quantitative Finance.

### Book recommendation: math toolkit for quantitative finance and statistics

I would recommend the books from Steven Shreve. Here is a link to some one of his older online pdf's (1997 but nevertheless true) so you can check if that fits the bill. http://citeseerx.ist.psu.edu/...
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### Risk-Neutral Probabilities, Trinomial Model

Trinomial trees give incomplete markets so there is a range of possible risk neutral prices. So you have to find the possible probabilities that make the tree risk-neutral and see what prices you get. ...
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Use Dynkin's formula to write the expectation: $\mathbb{E}[e^{-r\tau} \phi(S_\tau)]= g(S_0)+\mathbb{E}[\int_ 0 ^ \tau (A g -rg) dt]$ where $\phi$ is the payoff. Use the infinitismal generator $A$ to ...