Hello,
I have a portfolio composed of 1 EUR zero-coupon bond and 1 EUR stock. I want to calculate its VaR using the standard variance-covariance method. Say my bond is sensitive to only 1 curves point so that my portfolio is sensitive to 2 risk factors (the curve point and the stock price). How would you calibrate the 2x2 covariance matrix ? It is standard to use basis-point volatility for rates and log-returns volatility for stocks, but how do you merge both approaches into a single covariance matrix ? Do you necessarily have to use the same kind of volatility for all risk factors when dealing with covariance matrices ? If not, how do you adapt the VaR formula to cope with these different approaches (with log-normal vol, VaR(95%) = 1-exp(-Vol * 1.645), whereas with normal vol, VaR(95%) = Vol * 1.645) ?
Regards,
Anatole