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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Showing a basic market admits no arbitrage

I'm learning the fundamentals of financial mathematics and came across the following problem I cannot solve Setting We work in $\left(\Omega, \mathcal{F},\left(\mathcal{F}_t\right)_{t=0}^1, \mathbb{P}\...
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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 ...
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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 ...
pierce's user avatar
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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 $P$ ...
Woodpecker's user avatar
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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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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 ...
Manish Arora's user avatar
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63 views

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; ...
mva's user avatar
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2 votes
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230 views

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 ...
v.y.'s user avatar
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6 votes
2 answers
215 views

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 ...
KaiSqDist's user avatar
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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 ...
manish's user avatar
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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....
ak10's user avatar
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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 ...
FawaMop's user avatar
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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 ...
KaiSqDist's user avatar
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4 answers
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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?
User_001's user avatar
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10 answers
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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 ...
kaddy's user avatar
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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 ...
user69062's user avatar
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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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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 ...
Jone's user avatar
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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 ...
SwapperAtPar's user avatar
0 votes
1 answer
89 views

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 ...
bond-pricer's user avatar
2 votes
1 answer
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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 ...
Anon's user avatar
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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 ...
tellme_why's user avatar
2 votes
1 answer
197 views

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 ...
bernresearch's user avatar
1 vote
1 answer
114 views

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 ...
Haikal Yeo's user avatar
0 votes
1 answer
101 views

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, ...
XY0's user avatar
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1 vote
1 answer
246 views

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 ...
Peter's user avatar
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1 vote
1 answer
194 views

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 ...
Xu Shan's user avatar
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0 answers
61 views

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 (...
ixodid's user avatar
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1 vote
0 answers
45 views

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 ...
Homunculus Reticulli's user avatar
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0 answers
129 views

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. ...
SuperCodeBrah's user avatar
1 vote
0 answers
59 views

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 ...
Amit Gupta's user avatar
1 vote
1 answer
166 views

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 ...
Marco Di Bartolo's user avatar
1 vote
0 answers
259 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 : ...
Lrzo48's user avatar
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2 votes
0 answers
83 views

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 ...
user avatar
0 votes
1 answer
69 views

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 ...
Joquim's user avatar
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0 votes
1 answer
139 views

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 ...
Samantha Smith's user avatar
0 votes
1 answer
82 views

calculating probability of a return below a specific value [closed]

assume a probability distribution with a mean of %10 and standard deviation of %1.5. In wanting to solve the probability being lower than %5, the normal distribution is written down and integrated as ...
luccafmichael's user avatar
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0 answers
54 views

Probability distribution function for stock price given many parameters

First of all, I am not in the US market. I am trying to find out if I can do probabilistic analyses of stock price movements using the buy and sell summaries. Kindly let me then explain my problem. My ...
Aditya Tan's user avatar
0 votes
0 answers
332 views

Convert implied probability into real probability

In this article I have read that: A risk-neutral world is one where all investors are indifferent to risk and don’t require any extra risk premium for the risk they bear. In this world, all assets (...
Goo Gle's user avatar
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1 vote
0 answers
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Quantile function for fractional Brownian motion (fBm)

If anyone could help me to understand if it is possible calculate the quantile function for fBm? I’ve checked several papers([1],[2],[3]), and although several works stated that it is centralised ...
Serg Gini's user avatar
2 votes
0 answers
174 views

If $\Delta \log(V_{t})$ behaves like the increments of fractional Brownian motion, why do we model the rough volatility as follows

From Gatheral's paper, Volatility is rough and empirical evidence, it is clear that $\big\{\log(V_{t+1})-\log(V_{t})\big\}_{t}$ behaves like the increments of fractional Brownian motion $B^{H}$ with ...
user9078057's user avatar
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0 answers
113 views

Inconsistency between simulation and the probability of a "stock" hitting take profit before stop loss

Let's assume a stock at time $t$ is worth $X(t)$. If the returns of $X(t)$ are i.i.d. and normally distributed,the probability of $X(t)$ hitting a value $H>X(t)$ before $L<X(t)$ is $\frac{H-X(t)}...
Vanillihoot's user avatar
2 votes
1 answer
239 views

Are there optimal portfolio theories than instead of the expected value they were based on the Mode of distributions

Are there optimal portfolio theories than instead of the expected value they were based on the Mode of distributions? During my engineer student days I saw the Markowitz theory for portfolio selection ...
Joako's user avatar
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0 votes
0 answers
171 views

What is the Kurtosis of Returns in Geometric Brownian Motion?

Suppose that $dS_t=S_t(\mu\mathop{dt}+\sigma\mathop{dW_t})$ which has solution $$S_t=S_0\exp\left(t\left(\mu+\frac{\sigma^2}{2}\right)+\sigma W_t\right),$$ such that $W_t$ is a Wiener process, $\mu$ ...
UNOwen's user avatar
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2 votes
2 answers
426 views

Option implied risk neutral distribution vs BKM risk neutral moments

I am doing some research on the option implied risk neutral distribution and methods calculate it, and so far have come across two ways to do so. The first way is through the Breeden-Litzenberger ...
des224's user avatar
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1 vote
0 answers
80 views

How much compensation need to take on risk?

Quant Firm Interview Question We roll three, 8 sided dice. If same face appears 3 times we win 80 dollars. We have a bank of 10,000 dollars. How much are we willing to pay to play? What if we increase ...
MrChair549's user avatar
0 votes
0 answers
60 views

What is the P-probability of an unhedged call-arbitrage to lose money at expiration

Assume that the Risk Neutral Price (under the $\mathbb{Q}$-measure) of an European Call Option with expiration date $T$ has a price of $F(S_0,0)$ at time $t=0$ in the single asset Black-Scholes model ...
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