# Questions tagged [probability]

A probability expresses quantitatively how likely an event is to occur. We often encounter probabilities as conditional probabilities which express how likely an event is to occur in light of certain (given) information.

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### Why do cumulative returns have a bimodal distribution?

Regular returns (log-differenced prices) have statistical distributions that are bell-shaped and unimodal (one mode/peak) despite being non-normal and fat-tailed. Cumulative returns, on the other hand,...
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### A model for probability of credit rating change for a single issuer

I am looking to model the probability of a single issuer upgrading or downgrading it's credit rating at some time using historical data. I have done research and everything I have found so far are for ...
1answer
117 views

### Bayesian analysis in R for low default portfolios

I want to apply the knowledge of this paper (Bayesian estimation of probabilities of default for low default portfolios, by Dirk Tasche) in R, but I can't find the right bayesian package and functions ...
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### Interpreting Autocorrelation as probability

I was recently asked: Given a random time series of 1s and -1s. Eg of a sample = [1, 1, 1, -1, -1, 1, -1,..]. The autocorrelation of this series is Z. What can you say about the probability of a 1(or ...
0answers
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### Probability and random walk

Let's says i have 10 years of daily prices on a stock ABC. I do some analysis and I realise that, for example, if the stock increases 5 days in a row (close > open), 75% of the time, the 6th day will ...
1answer
160 views

### What is the probability of a lookback option ending in the money (CRR-model)

I would like to compute the probability that a certain lookback option ends in the money, let's say that the option has the following payoff $h_N=\max\left\{0,K-\min\{S_1,...,S_N\}\right\}$ where $K$ ...
1answer
294 views

### Throwing a dice and risk neutral probability

Consider the game of throwing a "fair" dice. Not sure if the answer is obvious but is there any proof (e.g. replication argument) that under the risk neutral measure the probability of any outcome is ...
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### How to derive the CDF and the probability density function [closed]

Is there something missing in this question i dont seem to understand, can anyone help explaining what is required?
2answers
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### Produce the random variable for an asset from a uniformly distributed random varible

I'm working on a quant interview question from the book called Quant Job Interview Questions And Answers (by Mark Joshi and other authors). I cannot understand the following question(not the answer, ...
0answers
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### Introducting a new probability measure

I'm trying to understand what means : $$\frac {d \mathbb {\tilde{P}} }{d \mathbb P } \bigg\rvert_{\mathcal F_t }$$where $\mathcal F_t$ is a filtration I guess (not explicitely mentionned). they ...
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233 views

### Excel formula for Laplace distribution

I am trying to create a forecast model, projecting the number of passengers through an airport over a period of time (daily, weekly, and monthly). I've already used Excel's FORECAST and POISSON ...
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486 views

### Probability Density Function of a Wiener Process Minimum

Let $W_t$ be a standard Wiener process. Find the probability density function of $m_T = min_{t\in [0,T ]}W_t$. I know that it is based of the concept of the reflection principle, but I wasn't too ...
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299 views

### Arithmetic Brownian Motion in Market Making papers

We often consider high-frequency market maker and suppose that the reference price is the arithmetic Brownian Motion: $dS_{t} = \sigma d W_t$ What is the difference $t_n - t_{n-1}$ in this case? Is ...
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### Intuitive explanation of why ITM options have low Time/Extrinsic Values?

While brushing up on my knowledge about the Greeks, I have been struggling coming up with an intuitive, probability-based explanation behind why not only Out-of-the-Money (OTM), but also In-the-Money (...
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### Event Occurs Almost Surely

Consider an uncountably infinite space, an infinite coin-tossing. Let $(\Omega,\mathcal{F},\mathbb{P})$ be the probability space. If a set $A\in\mathcal{F}$ satisfies $\mathbb{P(A)=1},$ then we say ...
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