Questions tagged [joint-probability]
The joint-probability tag has no usage guidance.
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Seeking Advice on Normalizing Implied Volatility Change for Options Modeling
I'm working with a substantial dataset spanning five years of weekly options data, with records down to the second. My goal is to develop a model that can accurately predict the probability mass ...
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Finding a representation for Joint probability density function of dependent random variables
Suppose that $\underline{\mathbf{X}}=(X_1, X_2, ..., X_n)$ is a vector of independent random variables. Then, we know that the joint probability density function $f_{\underline{\mathbf{X}}}(x_1, x_2, ....
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How would I develop confidence bounds for a function of 3 random variables, 2 of which are correlated?
I am tasked with developing confidence intervals for the function x = 1 - |(a+b)/c|
where a, b and c are random variables. a and b are normally distributed, but c is heavily skewed left. further ...
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Portfolio - Default Probability
Suppose we want to identify the frequency of default on a portfolio with a 1000 loans. In the independence case, each firm’s default process follows a Bernoulli distribution with parameter $p = 0.01$. ...
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Does E[max(x, y)] equal to E[x|x>y]*P(x>y) + E[x|x<y]* P(x<y) when x and y are not independent?
Suppose x and y are discrete random variable, I can write them in summation. And it seems like they are equal. Any ideas?
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Alternatives to Elliptical and Archimedean copulas for modelling dependency structure between stocks
Except from the well-know and well-documented Elliptical (i.e. Gaussian, Student-t) and Archimedean (i.e. Frank, Clayton, Gumbel) copulas used to model the dependency structure between stock returns, ...
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NPV of a mortage loan
I need to model the expected NPV of a mortage loan over his whole life-time. Assume that only the prepayment and default risk matters and that these events can occour at only discrete time-points. I'm ...
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Get expected joint-payoff price of digital options from individual payoffs
I am trying to model a joint distribution $f(X_1,X_2)$
(where $X_1$ and $X_2$ are market prices of the options) and then find from it the value of joint payoff price:
$F(X_1, X_2; B_1, B_2) = E[ ...
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How to write time-varying functions in R? Applied example
Let's say I want to use a Gaussian copula
$$C_{R_t}(\eta_1, ..., \eta_n) = N_{R_t}(N^{-1}(\eta_1), ...,N^{-1}(\eta_n))$$
with a time-varying correlation matrix $R_t$. Through DCC we model the ...
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Marginal Distribution using GARCH model: How to do inverse probability transform?
I have $n$ return series. I fitted AR(1)-GARCH(1,1) to each return series. Then used probability integral transform, PIT(residuals), to transform the residuals to have a uniform distribution. Then I ...
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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 ...
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Where does this copula come from?
In a paper I encountered the following notation
$$P(Z\leq z,u\leq Y\leq v)=C(F_{Z}(z),F_{Y}(v)-F_{Y}(u))$$
However I don't see why this holds in relation to uniform random variables. Usually
$$P(Z\...
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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 $r_{\mathrm{s}}$ ...
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Tools in R for estimating time-varying copulas?
Are there libraries in R for estimating time-varying joint distributions via copulas?
Hedibert Lopes has an excellent paper on the topic here. I know there is an existing packaged called copula but ...
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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 ...
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