Questions tagged [normal-distribution]
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98
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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 ...
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1
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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
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2
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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
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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
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1
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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 ...
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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 ...
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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 ...
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1
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532
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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 ...
- 21
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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 ...
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expression on page 90 of shreve's stochastic calculus for finance II
Hi: In the middle of page 90, Shreve has an expression which implies that (I'm using $t$ where he uses $u$ only because I find it confusing to use $u$ and $\mu$ in the same expressions):
$ E[\exp(\...
- 1,160
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Why is the price of an ATM straddle not the same as the "dollar move" from implied volatility?
Knowing that implied volatility represents an annualized +/-1 Standard Deviation range of the stock price, why does the price of an ATM straddle differ from this? Also for simplicity, no rates, no ...
user46424
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Significance of annualized volatility over 100% on the normal distribution? [closed]
Assume stock is 50 dollars. From what I understand, an annualized vol of 20% means there is a ~68% chance the stock will be between 40 and 60 a year from now; a ~95% chance it will be between 30 and ...
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A question in information strucutres and probability measures - How are they connected?
Suppose that $\mathcal{I}=(X,\sigma^{\mathcal{X}},\mu)$ is an information strucutre, which is a probability space, where
$X=X^1\times X^2$ is the cartesian product of the individual finite sets of ...
- 193
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Showing that the shortfall-to-quantile ratio of a normal distribution goes to one
I dont get why $$\lim_{x \to \infty}
\frac{\mu \{1 - \Phi(x)\} + \sigma \phi(x)}{(\mu + \sigma x) \{1 - \Phi(x)\} }
= \lim_{x \to \infty}
\frac{1}{1 - \sigma \frac{1 - \Phi(x)}{(\mu + \...
- 123
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Is there a closed-form solution for the following integral?
The integral under consideration is as follows:
$$
F=\int_{a}^{1} \exp\Big\{c\Phi^{-1}(x+b) + d\Big\}\; \mathrm dx,
$$
where $0<a, b<1$, and $c>0, d\in\mathbb{R}$ are constants, and the ...
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