All Questions
Tagged with normal-distribution probability
13 questions
2
votes
0
answers
167
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Game Theory Brainteaser
Seeking help / thought process guidance on the following interview problem, which seems centred on game theory
Setup: there’s a number X which we can measure once with error following N(0, 1). We can ...
- 21
2
votes
0
answers
61
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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
5
votes
1
answer
436
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sub-Gaussian random variables in financial economics
Unlike financial time series that typically possess fat tails, sub-Gaussian random variables have strong decay in the tails of their distribution. do sub-Gaussian random variables or processes appear ...
- 3,090
0
votes
1
answer
109
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Two commodities which are normal distributed and perfectly correlated
The daily price change in commodity 1 is distributed $N(0,0.15^2)$ and the daily price change in commodity 2 is distributed $N(0,0.3^2)$. The two commodities are 100% correlated.
1) Does the relative ...
- 2,662
1
vote
1
answer
2k
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What is the Probability Distribution of Max-Drawdown?
How to obtain the probability distribution of Maximum Drawdown, starting from the probability distribution of Daily Returns? Here the details:
Suppose I have a time serie of N=1000 daily returns.
...
- 460
0
votes
1
answer
73
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Quantile with periodic investing
Short Version
Can I get a quantile of such an expression?
\begin{equation}
\sum_{k=1}^{n} A_k\exp(\mathcal{N}(t_k\mu-\sigma\sqrt{t_k}/2,\sigma)))
\end{equation}
I know I can do it for one part of ...
- 123
2
votes
1
answer
542
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Quantile normal and lognormal
Let's assume we have a normal distribution $X\sim \mathcal{N}(\mu,\sigma^2)$. In a normal distribution the quantile can be calculated as follows:
\begin{equation}
\Phi_X ^{-1}(p)=\mu +\sigma {\sqrt {...
- 123
2
votes
2
answers
8k
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Box-Muller Method Proof
Here we want to show that the Box-Muller method generates a pair of independent standard Gaussian random variables. But I don't understand why we use the determinant? For me when you have two ...
- 23
1
vote
1
answer
314
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$\mathbb{P}$ and $\mathbb{Q}$ probability measure/distribution interpretations
I'm trying to understand probability distributions implied from market prices and was reading through this reference explaining the interpretation of $N(d_1)$ and $N(d_2)$ in the log-normal vol Black-...
- 223
1
vote
1
answer
477
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Creating the histogram for the distribution of the portfolio returns
Given log returns for some stocks $A$ and $B$, which are the constituents of our hypothetical portfolio in equal weights, how does one actually come up with a distribution of the log returns of the ...
- 305
1
vote
2
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4k
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Confidence Intervals of Stock Following a Geometric Brownian Motion
In preparation for my Options, Future's and Risk Management examination next week, I have been presented with a series of questions and their answers. Unfortunately, my lecturer, one of the less ...
8
votes
2
answers
745
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Normally Distributed Returns Become Leptokurtic Due to Compounding
I was running a bunch of simple simulations in excel the other day in excel. Using the NORM.INV(RAND(),0,1) to simulate daily stock returns I noticed that the more compounded the returns, ie, the more ...
- 2,138
2
votes
1
answer
130
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Creditworthiness indicator for copula one-factor model
In this paper in equation 15 on page 261 dealing with one factor copula model, one is using creditworthiness indicator as one of a variables. It is defined as
\begin{equation}
Y_c = \sqrt{\rho_c} Z +...
- 319