An option on n assets, m observation times, the volatility of the ith asset is sigma, the correlation between the ith and jth asset is corr[i, j], where i, j = 0, 1, ... , n - 1what is the covariance matrix?My method is: assum the matrix is C( s * s) based index 0, where s = n * mif |i - j| % n == 0, then C[i, j] = sigma * sigmaelsethen C[i, j] = sigma[i % n] * sigma[j % n] * corr[i % n, j % n]Is that correct?

it always works as simple asC[i,j] = sigma * sigma[j] * corr[i,j]since {corr(i,i) = 1}

If I want to price an option (multi-assets), and assume the volatility sigma of all assets is the same, the correlation corr among all assets is the same, then the covariance matrix can not be applied Cholesky Decomposition, because it is not positive

QuoteOriginally posted by: fmanIf I want to price an option (multi-assets), and assume the volatility sigma of all assets is the same, the correlation corr among all assets is the same, then the covariance matrix can not be applied Cholesky Decomposition, because it is not positiveyes, you can not do Cholesky, so? plus, what is the meaning of such an assumption? sigma and correlation being equal for all assets.if you want simply a method to overcome non-positive covariance matrix problem, search"The most general methodology to create a valid correlation matrix for risk management and option pricing purposes".