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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What does expectations of a Random variable change with respect to an indicator function [closed]

What does E[Y 1A] mean where E is expectations, Y is a Random Variable, 1A is indicator function with respect to another function A. And how to prove the below property? E [Y 1A] = E [E[Y | Fn] 1A]
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Deferred mortality probabilities (mortality table)

My question has to do with drawing correct conclusions regarding deferred mortality probability from a mortality table. I am looking at the table below (source). In it, the $q_x$ (2nd columns) is ...
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What underlying distribution does one use while calculating the Stutzer Information Statistic?

Cramer's Theorem is used to derive this form for the Stutzer Information Statistic $I_p$: $$I_p=\max_\theta -\log(E[\text{e}^{\theta r_t}])$$ Here, $r_t$ is the portfolio's excess returns over some ...
1 vote
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Sum Over Min Die

You have been tasked to find the expected value of a die game in which you are rolling 2 dice at a time. Your first roll of the dice will all be summed up and will be your starting score. Your next, ...
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two guys flip fair coins until they obtain their first heads. it takes strictly fewer flips for one to get his first heads than the other

Alex and Blake each flip fair coins until they obtain their first heads, respectively. Given that it takes strictly fewer flips for Alex to get his first heads than Blake, compute the expected number ...
1 vote
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Probability Distribution of Stock Returns [closed]

Is there a modern theory for the probability distribution of stock returns? It is relatively easy to deduce that under idealized conditions stock returns follow a log normal distribution. One arrives ...
1 vote
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Comparing standard error asymptotics of standard deviation and mean absolute deviation estimators

I was reading Chapter 4 of Jean-Philippe Bouchaud's book "Theory of Financial Risk and Derivative Pricing: From Statistical Physics to Risk Management" and in section 4.2.2 author was ...
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1 vote
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Drawdown distribution mentioned in Expert Trading Systems (John Wolberg)

In equation 2.13 of Chapter 2 (pg. 41), in his book "Expert Trading Systems: modeling financial markets with kernel regression," John Wolberg writes the probability of drawdown of $P$ ...
1 vote
132 views

Validator for Risk-Neutral Distributions Derived from Option Prices

I've developed a validator for risk-neutral distributions. I did this for the purpose of testing the risk-neutral distributions generated by a Spectral Analysis risk-neutral density recovery method, ...
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1 vote
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Seeking Advice on Normalizing Implied Volatility Change for Options Modeling

I'm working with a substantial dataset spanning five years of weekly options data, with records down to the second. My goal is to develop a model that can accurately predict the probability mass ...
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Two-period binomial model probability question

I have started to work with given two period binomial model S(0)=100 u=1.25 d=0.8 r=0.05 and the market probability of stock going up each period is p=0.55. I am trying to calculate two probabilities; ...
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Colosseum Fight - A probability problem

Problem Statement : Alice and Bob are in Roman times and have 4 gladiators each. The strengths of each of Alice's gladiators are 1−4, while Bob's gladiators have strengths 4,5,9, and 12. The ...
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Validating an option-implied risk-neutral distribution by integrating it twice and comparing the resulting "prices" with the original ones

From Breeden-Litzenberger, we know that the second derivative of a European call option's price with respect to the strike price is equal to the risk-neutral probability density function of the ...
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On measurements of ambiguity and their shortcomings

Ambiguity in quant finance is defined as the uncertainty in the probabilities of the return distribution, whereas risk is defined as the uncertainty in the returns of the asset. There are various ...
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Average time it takes to test a strike?

My question can be confusing so it’s better I explain it with an example. Let’s say I sell a strangle. That is with call at +27 delta and put at -27 delta. With 30 days to expiration. Is it possible ...
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Probability of success given expected return and volatility [closed]

I am reading Taleb "Fooled By Randomness", and the author says that a 15% return with 10% volatility translates to 93% success in a year and 50.02% success in any given second. Could someone ...
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Taking a set of normally distributed random variables as the sample space to fitting an exponential distribution

Disclaimer, this is my first question/interaction in this forum. Let's assume I have random variables that are normally distributed. Then, say I take the observations that are greater than the mean, i....
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Estimating implied probability based on prediction betting odds

I am attempting to estimate prediction betting market efficiency for a project, and I am hoping for assistance with a couple of questions. The prediction market makers add a commission to the betting ...
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What is the probability of an asset trending or ranging

Some assets are know(or at-least assumed)to trend more than others. Is the probability of an asset trending equal to the probability of that same asset ranging(i.e 50-50)? Is there a mathematical ...
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State Price Densities vs PDF of Payoffs in Ait-Sahalia (1998)

At the start of section I in the paper, the authors talk about the difference between the SPD/risk-neutral PDF/equivalent martingale measure vs the PDF of payoffs. I understand that the SPD is used in ...
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Оptimal strategy when throwing dice [closed]

Given a dice, you can throw it no more than three times, and you can stop at any time. How should you act so that on average you get as many as possible in the last throw?
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Probability Puzzle from a Quant Interview

An urn contains 20 balls colored each of the 7 colors of the rainbow (140 total balls). We select balls one-by-one without replacement. Given that in the first 70 draws we selected 5 more red balls ...
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How to calculate VaR on loss distribution

I sorted simulated portfolio losses in ascending order (sorted_losses variable). X-axis is loss, Y-axis probability of loss. I want to calculate 95% Value at risk in R. I used the below code, but am I ...
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Credit value at risk

In my dataset I have probabilities of default for each borrower, loan amounts. I have calculated expected loss= EAD * PD * LGD. How would I calculate unexpected credit losses of a portfolio and in ...
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1 vote
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How to calculate expected return on a loan while having probability of default

I have data on loans including: initial loan taken by each borrower, their probability of default. Is there a way to calculate VaR that would show potential loss of that asset? First what I need is ...
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Curve optimization to predict monetary policy path (OIS Curve)

This is a question about a relatively undeveloped market (Chile) in which Camara the O/N rate is daily compounded (OIS Curve). The available instruments in the market are short term rates ie 1m 2m 3m ...
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Probability Theory: Maximizing the difference between distribution functions

Given a sample of observations $X$, by changing a parameter $p$ we can divide $X$ into two subsamples $X_1$ and $X_2$ (this division is done in a non-trivial way which is nonetheless irrelevant to ...
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Market Making Card Sum Game

I am preparing for an interview with a prop trading firm and wanted to discuss potential strategies for the classic market making games. I have seen similar posts on the forum, but a lot of the ...
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Design a bilateral price negotiation for assets swap

Person alpha owns asset A. Person beta owns asset B. Alpha and beta wish to swap their assets A and B and settle the net cash of agreed price of A and B. What's the best mechanism to agree on price A ...
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How to calculate the variance of this coin flip?

I am reading the article “Shannon’s Demon & How Returns Can Be Created Out of Thin Air” by Richmond Quantitative Advisors (2021). The main premise is a fair coin flip. If heads, you gain 50%. If ...
1 vote
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Find probability of stock reaching certain price in the future given current price today based on historical data [closed]

Say I have historical data of a ticker for the past 5 years. I look at the price on the current date for each of the five years (e.g. today is 20 Jul 2023 so I will look at 20 Jul 2022, etc.) and then ...
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Solving Equation for estimation risk averse parameter

Let the portfolio value follow the SDE: $$V_t=(\mu w+r(1-w))\cdot V_t\cdot dt +\sigma \cdot w\cdot V_t \cdot dB_t$$ where $\mu$ = drift of the portfolio, $\sigma$=standard deviation of the portfolio, ...
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1 vote
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Bloomberg FXFM: what is the point of knowing risk neutral probabilities?

Among other things, Bloomberg FXFM function allows you to check risk neutral probabilities for currencies. For instance, you can check the probability of the euro depreciating 5% vs the dollar in 6 ...
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1 vote
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Gaming strategy for "closest number" game [closed]

Suppose there are 3 people A, B, C and a referee. A, B, C individually takes one number from [0,1] with the order A->B->C. B could see the choice of A, C could see the choice of A and B. After ...
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Predicting Bank of Canada Future Rate Changes Based on 3-month CORRA Futures [duplicate]

Earlier I asked a general question about how probabilities are derived from futures prices for derivatives related to the Bank of Canada's policy rate. I have been advised the Overnight Index Swaps (...
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1 vote
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Implying a probability distribution from option prices [duplicate]

I was reading this article, when I came across this text: Without using a complex options pricing model, one can use intuition to translate option prices into implied probabilities. For instance, the ...
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Generalizing a hidden semi-Markov model for trading

Taken from Wikipedia: A hidden semi-Markov model (HSMM) is a statistical model with the same structure as a hidden Markov model except that the unobservable process is semi-Markov rather than Markov. ...
1 vote
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Determining Stock Price Distribution [closed]

I am trying to derive a Stock Price Distribution for a particular time frame. Meaning thereby, let's say Market is about to close in 30 minutes and I want to calculate Stock Price Distribution for the ...
1 vote
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How to fit KDE from existing probability density function values

I am working with options data, and I am using Breeden-Litzenberger formula to derive the risk-neutral terminal stock price PDF. After applying the formula, here is a scatter plot of strike price vs ...
1 vote
328 views

Call probability of a callable swap

For one call date, The call probability is just the probability that the swap rate for the remaining life of the swap is below the strike rate. This is easily obtainable in a normal vol model, it is : ...
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Default risk and stock price probability distributions [closed]

First of all, I realise this question might border on `meta-finance', so I'd be totally OK if it gets closed. Having said that, the question itself: Given a stock $S$, in the absence of default it is ...
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What is the meaning of the following mathematical equations? [closed]

Let's say that we have a discrete probability distribution, where $$x_i$$ represents each of the possible outcomes (discrete set of possible outcomes), and $$L$$ represents the expected value we ...
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Vol binomial tree

Suppose that we have a stock $X_t$ valued at 100 euros per share. At each time step the price can go up or down 1 euro with prob $1/2$. Assuming that interest rates are $0$ and the volatility of the ...