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# Questions tagged [probability]

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91 views

### 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, ...
70 views

### 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 ...
51 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 ...
186 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 ...
157 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 ...
59 views

### 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 (...
79 views

### 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 ...
99 views

112 views

### Reference material (EV/ betting game questions) for Quant Hedge Funds Interviews [closed]

I need material to practice EV games questions.But I lack practice in betting questions where a set-up of a game is given and one has to respond to the best strategy or best bet to take. A good book ...
130 views

### Importance of filtrations that are NOT natural filtrations

I know the natural filtration intuitively represents the history of the process as the process evolves over time, and hence can be used to talk about conditional probabilities and conditional ...
40 views

### Is every filtration a natural filtration of some stochastic process?

We have a notion of natural filtrations, which intuitively represents the history of the process as the process evolves over time. We also have a notion of filtrations in general, which are ...
103 views

### Compare two distributions for forecasting returns

Let's imagine that we have two separate models, both used to forecast the return for the next period. Both models are estimated everyday, and both models outputs a probability distribution. How can we ...
230 views

### Probability and statistics in Quantitative Finance

Certain types of traders attempt to repeatedly buy and sell the same asset for a profit over a short time period, such as high-frequency “market makers”. For example, if you can repeatedly sell a ...
68 views

400 views

### 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. ...
112 views

### The duality of the free energy and relative entropy used to deduce deduce the stochastic game between an agent and the market

I am reading the article Pricing via utility maximization and entropy by Richard Rouge and Nicole El Karoui. They talk about the relative entropy of a probability measure $Q$ with respect to the ...
212 views

### Conditional Probability - Geometric Brownian Motion

Background I am trying to find a way to price a variant of a gap option by using closed-end expressions. What makes this option a bit tricky is that it can be exercised at four predetermined dates (t=...
44 views

### How skew in vertical put spreads change the payoff?

An spx four strikes wide Put Spread from at the money has a payoff ratio of 1 to 2 meaning if the Premium on the spread is \$10 your reward is \$20; yet the corresponding Call Spread with the same ...
343 views

### From Butterfly Price to Probability of $S_T$ Falling within a Range

If a butterfly in the limit represents a probability (by the Breeden-Litzenberger result), what can be said about the relative likelihood of a random variable $S_0$ from the price of a vanilla-option ...
127 views

### Probability of Implied Volatility Move [closed]

I want to see the probability of Implied Volatility of an underlying moving up or down from its current position. Would it just be 50% probability of going up and 50% of it going down? Because I've ...
245 views

### Detecting butterfly spread arbitrage for American options through European option prices

It's easy to demonstrate that if European option prices are concave with strike, then an arbitrage exists. For example, the risk-neutral probability density is the second derivative of European put ...