Concepts Implementation Design Choose an exchange and fetch all the available options from it For each underlying asset Rebalance current options positions Look for new misp...

Table of Contents Contents Financial Mathematics Probability Etc Contents Financial Mathematics CIR model $(dX_t = \kappa(\theta - X_t)dt + \sigma\sqrt{X_t...

Statement Let $B(t)$ be Brownian motion and let $f \in C^2(\mathbb{R})$. Then for $a < b$, [f(B(b)) - f(B(a)) = \int_a^b f’(B(t))\, dB(t) + \frac{1}{2}\int_a^b f’‘(B(t))\, dt \quad \text{a.s}....

Statement Let $\lambda$ and $\mu$ be positive finite measures on $\mathfrak{M}$. There exists a unique decomposition of positive finite measures \(\lambda = \lambda_a + \lambda_s\) where ...

Statement [\frac{\partial V}{\partial t} + r S \frac{\partial V}{\partial S} + \frac{1}{2} \sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} - rV = 0.] Assumptions Stock price dynamics The underly...

Statement [n! \sim \sqrt{2 \pi n} \left( \frac{n}{e} \right)^{n}.] Proof Asymptotic behavior of $n!$ Using monotonicity of \(\log x\), we have \[\sum_{k=1}^{n-1} \log k \leq \int_1^n \...