1
$\begingroup$

So I'm short a GBP denominated zero-coupon bond which has a face value of 1 million pounds and a remaining maturity of 6 months. Furthermore, I have to assume that the daily return of a 6-month zero GBP bond has a volatility of 0.06% (when its price is converted into Euro). The current exchange rate is 0.88 Pound Sterling per Euro and the 6-mont interest rate in GBP is 5% per annum with continuous compounding.

I now have to calculate the 10-day 99% relative normal VaR of this investment and as a hint, I have that I must start by defining the volatility of the P1L of my investment. However, I'm not sure how I can solve this particular exercise as I haven't really worked with the VaR with different currencies.

$\endgroup$
2
$\begingroup$

I would think that you would treat this as computing the VAR of a two asset case. In your case these assets would be 1/ your GBP bond and 2/ an FX position in EURGBP. You already have a vol measure for asset 1. Once you have a vol measure for the FX, you should be able to obtain the standard deviation of the combined asset via $$\sigma_{X+Y}=\sqrt{\sigma_X^2+\sigma_Y^2 +2\rho\sigma_X\sigma_Y}$$after making an estimate of $\rho$ (the correlation between the GBP bond and EURGBP), say via historical analysis.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.