# Questions tagged [distribution]

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### Log normal price simulation

I'm trying to figure out a spreadsheet I have which simulates 50000 returns in excel using the following function: LOGNORM.INV(RAND(),0,0.35)-1 Question: How ...
59 views

### Quantile with periodic investing

Short Version Can I get a quantile of such an expression? $$\sum_{k=1}^{n} A_k\exp(\mathcal{N}(t_k\mu-\sigma\sqrt{t_k}/2,\sigma)))$$ I know I can do it for one part of ...
272 views

### 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: \Phi_X ^{-1}(p)=\mu +\sigma {\sqrt {...
146 views

### Why/When local volatility is preferred over implied distribution sampling?

Let's say we have an option whose payoff is path dependent (let's say it's asian option with observations every month). Then why these are usually priced with local vol instead of sampling from ...
257 views

### Distribution of realized volatility for stock prices from a GBM

If you generate random stock price paths according to a GBM with daily increments, what will be the distribution of the realized volatility? Assume that the realized volatility is measured over daily ...
74 views

### How to compute Pr(S>100) when S follows Geometric Brownian Motion?

I have been trying to resolve this problem, under (b), but I cannot find the correct answer. For i=1, my ultimate answer (P=1) deviates from the correct answer (P=0.7580). Please let me know whether ...
116 views

### Why do I get this error using ghyp-distribution function?

I want to fit multivariate GH distribution on my data, and then generate simulations for that distribution. Using the instructions given in ghyp package, I wrote following lines of code in R. ...
3k views

### Consensus on Cauchy distribution for stock prices

What is the general consensus for using a Cauchy distribution to model stock prices? I can't find much after researching online and wonder if it has been tried and discarded. My motivation is to find ...
185 views

### Question on implied vol (surface) and strikes

there have been loads of papers on skews ATM / OTM, volatility premium and such. Lots of explanations for why iv is different on same stock with different strikes focused on preference of informed ...
180 views

### Distribution of pay-off of an exotic option

Can any assumptions be made about the pay-off of an exotic option? For example, might we say the distribution of the pay-off a vanilla option would be Normal? I have built a valuation tool that ...
43 views

### How to simulate the exponential law over an interval of the form [0,T]?

How do you simulate an exponential random variable over an interval $[0, T]$ with $T > 0$?
1k views

### What the implied distribution really is?

From volatility surfaces we have a implied distribution of $S_T$. This distribution is the real world distribution or this is a risk neutral distribution?