The probability tag has no wiki summary.
6
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1answer
113 views
characterization of coherent risk measures
Suppose we are given a coherent risk measure $\rho:L^0\to\mathbb{R}$. Our probability space is taken finite, i.e. $\Omega:=\{\omega_1,\dots,\omega_n\}$ and carrying a probability measure $P$. With ...
4
votes
1answer
79 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 ...
2
votes
1answer
105 views
t-statistics for the mean return, using Newey-West standard errors
I have seen that in several papers, where the aim was to evaluate the performance of a certain investment strategy, they use t-statistics to test for significance in the results. However, this seems a ...
5
votes
3answers
230 views
Calculate the expectation of a shift CDF
Suppose $X$ is a normal random variable with mean 0, and variance $\sigma^2$. $F(x)$ is the CDF(cumulative distribution function) of a standard normal random variable(mean 0 and variable 1), how to ...
2
votes
1answer
196 views
What are $d_1$ and $d_2$ for Laplace?
What are the formulae for d1 & d2 using a Laplace distribution?
3
votes
4answers
712 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 ...
4
votes
1answer
137 views
Certain probability statement in discrete mathematical finance
Le'ts suppose the following setting:
We have a filtred probability space $(\Omega,\mathcal{F},P,\{\mathcal{F}\}_{k=0,1})$ and an adapted $\mathbb{R}^d$ valued process $S=(S^1,\dots,S^d)$. Let ...
1
vote
1answer
269 views
Probability of trade's exit orders being triggered in random-walk market
When placing a trade with Stop Loss and Take Profit orders in a hypothetical random market (i.e. 0.5 probability of up tick and 0.5 probability of down tick), assuming:
x is the distance in ticks of ...
3
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0answers
183 views
Monty Hall Model
Given a fixed time period,say 3 days, the stock/market can go up,down or stay sideways. A hedge fund can long, short or use rangebound(options strategy) to bet for that 3 days closing level.
Hedge ...
0
votes
3answers
199 views
Profit estimation with a dice: 10 dollars for 6, -1 dollar for anything else
I recently found the following question: What is your profit estimate throwing a dice in the long run if you get 10 dollars for each time you hit 6 and lose 1 dollar for any other number?
I tried to ...
1
vote
4answers
283 views
Proof that the number of trades done (successfully) matters for whether or not a strategy was lucky
Me and a friend is trying to settle and argument in relation to the following quote by Nassim Nicholas Taleb:
I don’t want to spend too much time on Buffett. George Soros has 2 million times more ...
4
votes
2answers
380 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 ...
4
votes
1answer
380 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 ...
2
votes
0answers
77 views
Probability Density of Returns of Bonus Certificates
Could anyone please help me with the following?
I need to generate a histogram (resp. probability density) of returns of a bonus-certificate.
A bonus-certificate can be replicated by an underlying ...
2
votes
1answer
345 views
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 ...
1
vote
0answers
111 views
Modeling asset performance to Bitcoin revenue
I'm attempting to model asset performance to Bitcoin revenue, which is a driving force in the Bitcoin community.
Question
Is there any model, or research being done that tracks "hashes per second" ...
6
votes
1answer
301 views
What distribution should I apply to estimate the likelihood of extreme returns?
Say I have a limited sample, a month of daily returns, and I want to estimate the 99.5th percentile of the distribution of absolute daily returns.
Because the estimate will require extrapolation, I ...
7
votes
1answer
310 views
Simulating the joint dynamics of a stock and an option
I want to know the joint dynamics of a stock and it's option for a finite number of moments between now and $T$ the expiration date of the option for a number of possible paths.
Let $r_{\mathrm{s}}$ ...
5
votes
5answers
529 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 ...
0
votes
1answer
485 views
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 ...
6
votes
1answer
1k 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 ...
13
votes
2answers
564 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 ...
8
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2answers
758 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?
7
votes
1answer
331 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 ...
9
votes
1answer
347 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 ...
7
votes
3answers
751 views
How do I estimate the joint probability of stock B moving, if stock A moves?
I have two stocks, A and B, that are correlated in some way.
If I know (hypothetically) that stock A has a 60% chance of rising tomorrow, and I know the joint probability between stocks A and B, how ...
6
votes
1answer
518 views
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 ...
3
votes
2answers
616 views
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!
...
4
votes
2answers
436 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 ...
21
votes
4answers
2k 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 ...
11
votes
2answers
2k 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?
3
votes
2answers
462 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 ...
1
vote
3answers
813 views
Probability - Generating fair outcome using unfair coin
I have been thinking a lot about the following puzzle. But, could not arrive at a solution.
Can someone explain me how can you get a fair (equal probability) outcome using only an unfair coin (where ...
13
votes
5answers
895 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 / ...
11
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6answers
2k 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 ...
17
votes
2answers
476 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 ...
29
votes
5answers
1k views
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 ...
21
votes
2answers
2k 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 ...
