# Questions tagged [probability]

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### Lévy alpha-stable distribution and modelling of stock prices.

Since Mandelbrot, Fama and others have performed seminal work on the topic, it has been suspected that stock price fluctuations can be more appropriately modeled using Lévy alpha-stable distrbutions ...
2answers
12k views

### 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 ...
5answers
5k views

### 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 ...
10answers
12k views

### Probability of touching

For a vanilla option, I know that the probability of the option expiring in the money is simply the delta of the option... but how would I calculate the probability, without doing monte carlo, of the ...
3answers
2k views

### How are distributions for tail risk measures estimated in practice?

Let's say you want to calculate a VaR for a portfolio of 1000 stocks. You're really only interested in the left tail, so do you use the whole set of returns to estimate mean, variance, skew, and shape ...
5answers
2k views

### 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 / ...
2answers
842 views

### 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 ...
2answers
6k views

### 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?
1answer
5k views

### 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 ...
6answers
31k views

### How to calculate stock move probability based on option implied volatility and time to expiration? (Monte Carlo simulation)

I am looking for one line formula ideally in Excel to calculate stock move probability based on option implied volatility and time to expiration? I have already found a few complex samples which took ...
1answer
498 views

### Do people use unbounded interest rate models, and what alternatives exist?

A simple interest rate model in discrete time is the autoregressive model, $$I_{n+1} = \alpha I_n+w_n$$ where $\alpha\in [0,1)$ and $w_n\geq 0$ are i.i.d. random variables. When working with ruin ...
2answers
3k views

### What are some examples of Compound Poisson processes in insurance?

I'm writing the Bachelor thesis but I need some information. I need to find some practical examples and applications of the Compound Poisson Process in insurance. Does anyone have any good examples?
1answer
873 views

### Quantum Mechanics and Economics… What

I was reading this paper: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2002698&download=yes The author has the model presented here: http://modelingcommons.org/browse/one_model/3443#...
1answer
486 views

### 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 ...
2answers
952 views

2answers
586 views

### 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 ...
1answer
229 views

### pdf of simple equation, compound Poisson noise

I would like to find the probability density function (at stationarity) of the random variable $X_t$, where: \begin{equation*} dX_t = -aX_t dt + d N_t, \end{equation*} $a$ is a constant and $N_t$ is a ...
5answers
2k views

### 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 ...
1answer
1k views

### Arbitragefree Pricing: Q vs. P

I read that the Fundamental Theorem of Asset Pricing states, that a market is arbitrage-free if and only if there exists an equivalent martingale measure Q, under which the discounted asset price ...
1answer
786 views

### Modeling Call Price w.r.t. Strike w Models that Capture Vol Smile

I am trying to model $C(K)$, the price of the call $C$ as a function of strike $K$. Because this is tied to Prob ITM - and in fact the probability density function of that particular expiration (https:...
1answer
2k views

### open problems in mathematical finance

What are open problems in mathematical finance that use fundamental concepts of mathematics (functional analysis, geometry and topology, algebra and number theory etc.) and not data-driven. I have ...
2answers
435 views

### How can we have negative probabilities in finance? Can we have negative payments in bonds? If not, how else can we have negative probabilities?

In Half of a Coin: Negative Probabilities, the author mentions bond duration. Suppose we have payments at times $t = 1,2,...,n$ denoted respectively by $R_1, R_2, ..., R_n$ and the discount factor is ...
3answers
1k views

### Difference betweem martingale property and adapted filteration

What is the difference between a random process that is adapted to a filteration and one that had the martingale property. It seems the two notions are quite similar and would be helpful to construct ...
2answers
755 views

### on “recovering probability distributions from option prices” - how to subtract influence of stochastic volatility?

This is based on a 1995 paper by Rubinstein/Jackwerth by the above title where the authors produces a distribution of stock prices inferred from option prices. But their approach only produces a joint ...
2answers
1k views

### 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 ...
0answers
258 views

### Transition densities in the Heston model

Knowing the Characteristic function $\Phi_{T,t} = \mathbb{E} [ e^{i u S_T} | S_t, V_t]$ (or equivalently, the Laplace transform) of an affine process, it's possible to know the distribution of the ...
2answers
7k views

### 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 ...
2answers
272 views

### Can the concept of negative probabilities be used to price a call option?

Edit: I'm a dumbass. The thing below is supposed to be just the motivation of asking. I want to ask for below and in general, hehe. Assume that we have a general one-period market model consisting of ...
2answers
415 views

### Do futures follow physical or risk-neutral distributions

I've spent a while looking for an answer to this question and while I feel it is a simple question I have not found an answer. I know prices of option contracts follow an implied, risk-neutral ...
2answers
1k views

### How do you synthesize a probability density function (pdf) from equally weighted price data?

What I'm working with: I have a collection of prices that has very few to no repeating values (depending on the look back period) ie each price value is unique, some prices are clustered and some can ...
2answers
516 views

### Pricing when arbitrage is possible through Negative Probabilities or something else

Assume that we have a general one-period market model consisting of $d+1$ assets and $N$ states. Using a replicating portfolio $\phi$, determine $\Pi(0;X)$, the price of a European call option, with ...
2answers
128 views

### Importance of filtrations that are NOT natural filtrations

I know the natural filtration intuitively represents the history of the process as the process evolves over time, and hence can be used to talk about conditional probabilities and conditional ...
1answer
751 views

### 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 ...
1answer
174 views

### pricing of heat rate-linked derivative

It's a simplified model. Suppose $U_t$ is a random variables subject to Lognormal($x_1$, $z_1^2$)distribution. $V_t$ is a random variables subject to Lognormal($x_2$, $z_2^2$)distribution. Suppose ...
2answers
337 views

### Brexit implied probability

It is possible to bet on the Brexit e.g. on this page: https://sports.ladbrokes.com/en-gb/betting/politics/british/eu-referendum/uk-european-referendum/220800266/ The quotes are 8/15 for remain, and ...
1answer
585 views

### Coin Toss System

Coin Toss Runs Calculator The expected number of runs for two consecutive heads or tails is 3. Is there an edge if we place a progressive constant size bet(limited to 3 times)for consecutive ...
1answer
345 views

### Radon-Nikodym: Changing Distribution vs Changing Random Variable

Let $X \sim \mathcal{N}(\mu,\sigma^2)$ under the probability measure $P$ on the measurable space $(\Omega, \mathcal{F})$. We may define a Radon-Nikodym derivative $Z$, also defined on \$(\Omega, \...