# 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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### 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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### MC with transition kernels

I started to search for information about MC pricing with local volatility for European options and don't understand a possibly obvious problem. I have a call options surface (no arbitrage), discrete ...
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### 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 ...
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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 ...
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### 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 ... 62 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 ...
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### Probability of touching barrier and stochastic interest rates

I am trying to figure out the impact of the stochastic interest rates on the price of barrier option. I was reading the book "FX Barrier Options" by Zareer Dadachanji and in the section ...
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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 ...
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### 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 ...
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### 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 ...
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### 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 (...
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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(,,), and although several works stated that it is centralised ...
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### 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 ...
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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
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### 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 ...
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### 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
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### 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
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### 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 ...
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### 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 ...
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### Structuring and Customization

It seems complex derivatives in particular exotic options are not available at any retail broker. Can a regular retail trader get access to these instruments? Maybe through prop firms or banks? ... 112 views

### Does time remaining matter in NO Touch-ONE Touch probabilities?

I asked a question some days back and got an answer which I understand and make sense: Probability of touching short call strike and not touching touching short put strike of a short strangle? However,...  