# 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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### 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 ...
36 views

### 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 ...
22 views

### 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 ...
1 vote
50 views

### 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 ...
37 views

### 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 ...
34 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 ...
1 vote
239 views

### 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 ...
24 views

### 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 ...
87 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 ...
84 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, ...
1 vote
121 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 ...
1 vote
109 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 ...
44 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 (...
54 views

### Incorporating Market Prices into Betting Models

In betting models, the price offered by the market is often ignored until the end. However, it seems like the price is a valuable piece of information that cannot be overlooked. Consider a ...
1 vote
42 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 ...
89 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. ...
1 vote
53 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 ...
1 vote
146 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 ...
1 vote
146 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 : ...
78 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 ... 66 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 ...
1 vote
99 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 ...
47 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 ...
51 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 ...
210 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 (...
1 vote
62 views

### 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(,,), and although several works stated that it is centralised ...
166 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 ...
100 views

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### Probability the stock price (following geometric Brownian motion) hits the upper boundary U before there is a retracement from the max by amount R?

I am looking for the probability that the stock price/Geometric Brownian Motion hits the upper boundary U, before there is a retracement (from the maximum price) that exceeds amount R. In other words,...
1 vote
269 views

### Variance of the price from returns variance

Let's say that we have the variance of the daily return at $t_0$: $$\sigma_{r_{t_0}}^2=\text{Var}[r_{t_0}]=\text{Var}[\frac{S_{t_0}-S_{t_0-1}}{S_{t_0-1}}]$$ for price process $S_t$. Is there a way to ...
53 views

### Average probability of varying input data

New to the quant finance exchange. I am stuck with a question maybe someone could help me. In the table below I have calculated if price is up/down w.r.t to the open shown in the 2nd column with ...
1 vote
189 views

### Confidence in Sharpe ratio given performance

Suppose I have a strategy that I believe has a Sharpe ratio of X - not the Sharpe ratio of the backtest (this can be absolutely determined), but the ratio I expect it will actually take on over the ...
1 vote
143 views

### Ito's lemma for option pricing with Levy-alpha stable drift

Consider $$dS=\omega\left(\Lambda-S\right)dt+\sigma_S S dW_t,$$ such that such that $W_t$ is a Wiener process, $\sigma_S$ is constant, $\omega: t\rightarrow\mathbb{R}$ represents anticipated drift and ...