hi,I have a question concerning the spreadsheet implementation of the HJM-model in Wilmott's 'on quantitative finance':How did he choose the volatility factors? I understand that it is reasonable to choose two, one of them constant and the other linear. But I don't understand how he's choosing the constants.I appreciate every answer and help!thx

You can do a PCA on past data to figure out the volatility. Say you have daily data on 10 different maturities for the past year. You first find the daily changes for each maturity. since you have 10 maturites you will end up having 10 daily change data set. next you will calculate the covariance matrix for those daily change vectors, and then find the eigenvalue/eigenvectors of the covariance matrix.the volatility from data is eigenvector * sqrt(associated eigenvalue). Plot the volatility with respect to maturity, you can figure out what's the relation between maturity and volatility. (constant, linear, quadratic, etc. do a regression to figure out the coefficients)you pick enough volatility terms that you could explain 95%+ movement. so sum(eigenvalue you picked)/sum(all eigenvalue)>95%.

thanks, I tried it and it seems to work!

unfortunately I got negative eigenvalues. what can I do?

what data did you use? actually, see this for more help:http://www2.gsu.edu/~mkteer/npdmatri.html

thx, I detected the error.HJM works now perfect

Hi,I have done the same implementation. I did the eigenvalue decomposition and estimated the volatility factors (I will use 3). So far, so good.My big problem now is, how do I get the drift term? Unfortunately, the 'Paul Wilmott on Quant Finance' doesn't give any hints here. Since I have estimated the volatility factors for each maturity directly through the PCA, I dont have a functions for the volatility factors...Any advise is highly appreciated!Thanks!

QuoteOriginally posted by: accelasYou can do a PCA on past data to figure out the volatility. Say you have daily data on 10 different maturities for the past year. You first find the daily changes for each maturity. since you have 10 maturites you will end up having 10 daily change data set. next you will calculate the covariance matrix for those daily change vectors, and then find the eigenvalue/eigenvectors of the covariance matrix.the volatility from data is eigenvector * sqrt(associated eigenvalue). Plot the volatility with respect to maturity, you can figure out what's the relation between maturity and volatility. (constant, linear, quadratic, etc. do a regression to figure out the coefficients)you pick enough volatility terms that you could explain 95%+ movement. so sum(eigenvalue you picked)/sum(all eigenvalue)>95%.

How do we determine the volatility from variance/covariance matrix ?

is this how we get vol ? http://www.risklatte.com/Articles/Quant ... /QF145.php