Questions tagged [normal-distribution]

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Distribution when positive values are rescaled?

Suppose I have a series of gross P&L values, which are normally distributed with mean $\mu$, variance $\sigma^2$. For positive P&L values, there is a $x\%$ commission. For example, $x=5\%$. So ...
49 views

Covariance matrix of Gaussian EM output

I have a project where i wanted to use Expectation Maximization to fill in missing logreturns. With regards to that I have a question I haven't been able to solve. Logically EM should decreese ...
• 3
154 views

Price Option B Knowing The Price of a Similar Option A

How do we find the implied volatility from the price in a call option and apply it to another option without a calculator? Or is there actually a better way? For example, given a 25-strike 1.0-expiry ...
• 123
66 views

Risk-Neutral Non-Linear Option Pricing Black Scholes Model

Looking for some help on this question. Suppose the Black-Scholes framework holds. The payoff function of a T-year European option written on the stock is $(\ln(S^3) - K)^+$ where $K > 0$ is a ...
• 123
248 views

Necessary conditions to ensure that stochastic integral is a normal variable

Let $\left(W_t\right)_{t\geq 0}$ be a Brownian motion with respect to filtration $\mathbb{F}=\left(\mathcal{F}_t\right)_{t\geq 0}$. Let $\left(\alpha_t\right)_{t\geq 0}$ be an $\mathbb{F}$-adapted ...
• 747
56 views

Distribution of discrete Geometric average and Stock Price

If we have $$S_t = S_0 e^{(r-\frac{1}{2} \sigma ^2) +\sigma W_t}$$ and a discrete geometric average of stock prices $$G_n = (\prod_{i=1}^{n} S_{t_i})^{\frac{1}{n}}$$ where the monitoring points are ...
85 views

Why don’t methods focus on constructing expected distributions and solving the integrals

Everyone knows assumptions of normality etc are bad and that the expected distributions of financial quantities (such as returns) change depending on the circumstances. We know that we can compute the ...
529 views

Kelly Criterion for cash game poker (normally distributed returns)

I'm trying to apply the Kelly Criterion to poker. Poker players have been stuck using outdated bankroll management techniques for decades, and I want to change that. My goal is to graph the log growth ...
1 vote
132 views

How can I estimate value-at-risk of a long/short portfolio without making simplifying assumptions?

I have had a couple of long-standing questions about the mathematics behind a simple "vanilla" parametric VaR calculation and I'm hoping someone could clear up my confusion. Most likely I am ...
77 views

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