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# 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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### Bayesian trade probability with factors

I have a strategy Y which is influenced by some factors X1, ..., Xn (for example asset volatility, distribution of macroeconomic factors). At moment t0 I have historical distribution(prior) of X1, ...,...
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### Expectation of the product of two Brownian motions [closed]

Could you please let me know the steps to follow to get to the solution?
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### Hedging Value-Financial Mathematics

EXERCISE We consider a free from arbitrage financial market $(Ω,F,P,S_0,S_1)$ with $α<S_0^{1}\cdot(1+r)<β$,where $$0<α:=min_{ω \in Ω} S_1^{1}(ω), β:=max_{ω \in Ω}S_1^{1}, α<β$$ Let C be a ...
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Exercise : We consider a market of one period $(\Omega, \mathcal{F}, \mathbb P, S^0, S^1)$, where the sample space $\Omega$ has a finite number of elements and the $\sigma-$algebra $\mathcal{F} = 2^\... • 193 1 vote 1 answer 1k views ### What is the Probability Distribution of Max-Drawdown? How to obtain the probability distribution of Maximum Drawdown, starting from the probability distribution of Daily Returns? Here the details: Suppose I have a time serie of N=1000 daily returns. ... • 450 2 votes 1 answer 146 views ### The duality of the free energy and relative entropy used to deduce deduce the stochastic game between an agent and the market I am reading the article Pricing via utility maximization and entropy by Richard Rouge and Nicole El Karoui. They talk about the relative entropy of a probability measure$Q$with respect to the ... • 123 3 votes 1 answer 438 views ### Conditional Probability - Geometric Brownian Motion Background I am trying to find a way to price a variant of a gap option by using closed-end expressions. What makes this option a bit tricky is that it can be exercised at four predetermined dates (t=... • 61 0 votes 1 answer 67 views ### How skew in vertical put spreads change the payoff? An spx four strikes wide Put Spread from at the money has a payoff ratio of 1 to 2 meaning if the Premium on the spread is \$10 your reward is \$20; yet the corresponding Call Spread with the same ... 2 votes 3 answers 902 views ### From Butterfly Price to Probability of$S_T$Falling within a Range If a butterfly in the limit represents a probability (by the Breeden-Litzenberger result), what can be said about the relative likelihood of a random variable$S_0$from the price of a vanilla-option ... • 695 1 vote 0 answers 161 views ### Probability of Implied Volatility Move [closed] I want to see the probability of Implied Volatility of an underlying moving up or down from its current position. Would it just be 50% probability of going up and 50% of it going down? Because I've ... • 11 2 votes 0 answers 785 views ### Detecting butterfly spread arbitrage for American options through European option prices It's easy to demonstrate that if European option prices are concave with strike, then an arbitrage exists. For example, the risk-neutral probability density is the second derivative of European put ... • 121 1 vote 0 answers 71 views ### How to determine the default probability of a county in a bond that is not in its native currency? Disclaimer: This post is cross posted in here also. Consider the following case: Country P uses the currency Euro and gives p percent interest on a one year bond issued in Euro. Country Q uses the ... • 111 1 vote 0 answers 53 views ### Prove that$F(s,x_0)=0$,$F(t,x)=1$and$\frac{\partial F}{\partial t}+\frac{1}{2}\frac{\partial^2 F}{\partial x^2}=0$Using the Dynkin's formula, prove that$F(s,x_0)=0$,$F(t,x)=1$and$\frac{\partial F}{\partial t}+\frac{1}{2}\frac{\partial^2 F}{\partial x^2}=0$where$F(s,t)=2\int_{x-x_0}^{\infty}\frac{1}{\sqrt{2\...
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Ref to my previous question here: Physical trading spot transaction analysis-Quantified I have been able to narrow down my aim to defining a physical trading strategy P&L. My question is, how ...
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### Binary probit model: relevant which outcome is 1?

I'm currently working on predicting bear and bull phases with a dynamic probit model in the form of $y_t=\beta_1X_t+\gamma_1y_{t-1}+\epsilon_t$. So far I've written all my code in matlab and it works ...
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### Expectation of N(d2)?

I am trying to find out the Pricing Equation for certain type of Options under Risk-Neutral pricing. This is the equation I am getting, but I am not sure if this can be solved or not. Any help is ...
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