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.
369
questions
0
votes
0
answers
46
views
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....
- 1
-1
votes
0
answers
32
views
how to use ratio spread?
If I sell more options, then my gamma risk will be more difficult to control, but if I sell too few options, then when I judge the wrong direction, I will leave the market with a loss. I try to ...
0
votes
0
answers
32
views
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 ...
-1
votes
1
answer
69
views
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 ...
- 3
0
votes
0
answers
22
views
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 ...
- 561
0
votes
4
answers
128
views
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?
- 1
9
votes
10
answers
5k
views
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 ...
- 172
0
votes
0
answers
43
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 ...
0
votes
0
answers
24
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 ...
- 11
1
vote
0
answers
58
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 ...
- 11
0
votes
1
answer
45
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 ...
- 21
0
votes
0
answers
36
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 ...
- 21
1
vote
0
answers
519
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 ...
- 111
0
votes
0
answers
26
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 ...
2
votes
1
answer
163
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 ...
- 23
2
votes
1
answer
92
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 ...
- 121
0
votes
1
answer
94
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, ...
- 37
1
vote
1
answer
157
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 ...
- 45
1
vote
1
answer
124
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 ...
- 41
0
votes
0
answers
54
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 (...
- 127
0
votes
0
answers
63
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 ...
- 101
1
vote
0
answers
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 ...
- 1,398
0
votes
0
answers
103
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. ...
- 243
1
vote
0
answers
56
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 ...
- 11
1
vote
1
answer
158
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
0
answers
177
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 :
...
- 11
2
votes
0
answers
79
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 ...
user34971
0
votes
1
answer
68
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 ...
- 21
1
vote
1
answer
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 ...
- 111
0
votes
1
answer
53
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 ...
0
votes
0
answers
53
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 ...
0
votes
0
answers
244
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 (...
- 113
1
vote
0
answers
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([1],[2],[3]), and although several works stated that it is centralised ...
- 11
2
votes
0
answers
167
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 ...
- 83
0
votes
0
answers
108
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)}...
2
votes
1
answer
194
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 ...
- 71
0
votes
0
answers
139
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, $\mu$ ...
- 128
2
votes
2
answers
321
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 ...
- 93
1
vote
0
answers
77
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 ...
- 63
0
votes
0
answers
59
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 ...
- 548
0
votes
0
answers
46
views
How to compute the combined probability of loss for 2 time series (consisting of historical stock prices)?
May I please ask the community's support with the following problem?
I have 2 time series, with approximately 1000 observations each (same number of observations for both). They represent the daily ...
2
votes
1
answer
141
views
Analytical evaluation of the following caplet-type product under lognormal assumptions
Let $n \geq 2$, and consider a tenor discretization: $0 = T_{0} < T_{1} < ... < T_{n}$ and associated forward rates evaluated at time $t$, as $L_{i}(t):=L(T_{i},T_{i+1};t)$ for any $i = 0,...,...
- 83
0
votes
0
answers
115
views
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
1
vote
1
answer
286
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 ...
0
votes
0
answers
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
1
vote
1
answer
240
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
1
answer
155
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 ...
- 128
-1
votes
2
answers
427
views
Why can’t delta’s be used to price double no touch options?
Here is the link to a MATLAB one touch option pricing calculator I used:OT
I tried several inputs and I noticed that the one touch option price is approximately twice the delta of an equivalent ...
0
votes
0
answers
105
views
Performance of dollar cost averaging
If we're investing money into a stock $S$ at a continuous rate, $C$, what is the probability distribution of the amount we have invested?
For example, modelling a stock as GBM without contributions, $ ...
- 101
1
vote
1
answer
786
views
Alternatives to Kelly Criterion
I am preparing for Quantitative Trading interviews and I know that they basically require you to solve problems on the probability of winning in a given game and then they would ask you:
How much ...
- 165