Normal Law

Hi there
will be very greatfull if anyone can help:
If X represent the daily yield of the S&P500(US Stock indices) and Y represent the daily yield of the DAX(German Stock Indice). Let assume that X and Y are Following a Normal Law and are independent.
X~N(M1,S1) M1 mean of X and S1 its standard deviation
Y~N(M2,S2) M2 mean of Y and S2 its standard deviation
Looking to calculate the probability:
P(X>Y and X>0)

Thanks in advance


TS Contributor
In this question you need to invoke the bivariate normal joint CDF, which in turns has no closed form solution unless for special cases.

You may use, e.g. R and search for packages to calculate the joint probability numerically, if the parameters are provided.


TS Contributor
Assumig independence would be rather questionable, unless this is an exercise,BTW.

In real life I would just simulate the two series and estimate the probability.

thx very much , I was hoping that we can have an analytic solution to this problem.
Seems like simulating historically with a large number of occurrence could give me a good estimation.