# Questions tagged [probability]

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### 2-state HMM / ARMA process?

I have issues with this problem: Let $\{X_t, t\in \Bbb N\}$ be a 2-state stationary Markov chain, with transition $M$ (and $M(1,2)\neq 0 \neq M(2,1)$), let $\{W_t, t\in \Bbb N\}$ be a strong Gaussian ...
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### Random matrix theory (RMT) in finance

The new kid on the block in finance seems to be random matrix theory. Although RMT as a theory is not so new (about 50 years) and was first used in quantum mechanics it being used in finance is a ...
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### Effects of random-generator-choice on derivative's price

There is a plethora of pseudo-random-generators out there. Some of them are definetly better and some of them severily underperform. My standard tool is Mersenne Twister - when I need to generate ...
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### Definition of orthogonality and independence for a stochastic processes

Somehow I can't find the explicit definition of when two processes are supposed to be orthogonal or independent anywhere. I think orthogonality and independence should mean the same thing in this ...
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### How do I calculate probability distribution of stock prices given option prices?

I'd like to calculate a probability distribution for prices given the option prices for that stock? Any ideas how to do this? My desire is to do this daily and then see how the price PD changes over ...
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### Normally Distributed Returns Become Leptokurtic Due to Compounding

I was running a bunch of simple simulations in excel the other day in excel. Using the NORM.INV(RAND(),0,1) to simulate daily stock returns I noticed that the more compounded the returns, ie, the more ...
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### Summary statistic for the average probability of default?

I have the following scenario: Let $X_i$ denote the event where some institution $i$ 'defaults' (don't worry about the exact definition of a default here, it is not relevant to the question at hand). ...
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### Strategies for Liar's Poker

This question is only tangentially related to quantitative finance. Scott Patterson's book The Quants describes how a quant at Kidder Peabody figured out a strategy to playing Liar's Poker in the late ...
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### Expected payoff and weighted average price

Settings Let you're trading a security whose probability to be equal to $S_{T}$ at time $T$ follows a p.d.f. like the ones in the picture below. (That is just an example found with Google images, ...
236 views

### Random Brownian Simulation Startling Results

I was playing around in Excel the other day, simulating possible equity curve/P&L paths for a simple game I designed. The game is really trying to find an optimal risk managment strategy. I start ...
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### default probability

Suppose the hazard rate is $\lambda$ the default probability density function follow exponential $f(t) = \lambda e^{-\lambda t}$ and cumulative probability function is $F(t) = 1 - e^{-\lambda t}$ ...
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### Help with understanding a normal distribution/probability question

Could someone please help me translate what this is saying on page P15, section 4.2: http://www.ntuzov.com/Nik_Site/Niks_files/Research/papers/stat_arb/Ahmed_2009.pdf Specifically: When the order ...
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### Finding Probabilities Using The Binomial Model

I was not able to find a similar question when searching, but if I've missed one please feel free to point me to it. Unfortunately the closest example in the textbook was not terribly helpful either. ...
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### Physical Option Implied Distribuition

So I got risk neutral probabilities from stock option prices. How can I then map them to a physical measure?
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### How to fit probability density function from sample moments?

If I have calculated the sample mean, variance, skew and kurtosis of a set of data, how would I go about fitting a probability distribution to match these moments (i.e. choosing a probability ...
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### what is the best way to calculate the probability of an equity option ending in the money?

Given historical implied volatility and all other know variables (stock price, option strike price, option expiration date, dividend rate, interest rate) what is the best way to calculate the ...
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### Fixed income modeling

I am currently working on my research paper and trying to explain a two-dimensional variable: volume and instrument of corporate debt financing. Independent variables that I believe must be included ...
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### How to estimate probability of default from bond prices?

How do you use bond prices/yields to infer probabilities of default? I would think of it as follows: Create a relationship between default free (e.g., Germany) and defaultable (e.g., Greece) bond ...
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### How do you distinguish “significant” moves from noise?

How do you distinguish between losses that are within the normal range for day-to-day shifts and situations with a real potential for loss? The specific application I have in mind is pattern ...
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### How does left tail risk differ from right tail risk?

How does left tail risk differ from right tail risk? In what context would an analyst use these metrics?
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### How useful is Markov chain Monte Carlo for quantitative finance?

Naively, it seems that Bayesian modeling, structural models particularly, would be quite useful in finance because of their ability to incorporate market idiosyncrasies and produce accurate ...
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### If stock A has a 60% chance of rising, and stocks A and B have 80% correlation, what is the chance of stock B rising?

As in the subject, I'm interested in a math puzzle of sorts: If stock A has a 60% chance of rising, and stocks A and B have an 80% correlation, what is the chance of stock B rising? Would it be ...
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### Risk neutral probability in binomial lattice option coming greater than 1…what's wrong?

I am substituting reasonable values in the below fomula (like r=0.12, T=20, nColumn=16, sigma=0.004)...why is probability coming out to be greater than 1? Any help? Thanks! ...
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### Heuristics for calculating theoretical probabilities of being ITM at time T for listed options

I'm looking for a heuristic way to calculate the probabilities of being in the money at expiry for non-defined risk options combinations (listed options). I use delta as a proxy for this probability ...
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### How to estimate the probability of drawdown / ruin?

A fairly naive approach to estimate the probability of drawdown / ruin is to calculate the probabilities of all the permutations of your sample returns, keeping track of those that hit your drawdown / ...