1
$\begingroup$

We are trying to analyze an algorithm (internal to our company) to calculate currency option pricing using the Garman and Kohlhagen model.

Our internal algorithm calls for CBS (Currency Basis Swaps) rates to be added to interest rates in the following manner.

Add to the USD interest rate the CBS rate for the non-USD currency.

Can anyone explain the logic for taking the CBS rate in the model? There is unfortunately no documentation in our code.

$\endgroup$
2
$\begingroup$

This is an issue that arises in the calculation of currency forward rates:

  • You could simply take the Forward Rate from the FX Forward market, as "the market is always right" ;)

  • You could calculate the Forward Rate from the Spot Rate and the Interest Rates in the 2 countries. This relies on the CIP Formula (Covered Interest Parity) which until 2008 was believed to be highly accurate... However you would get a Forward Rate different from the actual rate in the market and hence not accurate. The solution is as you indicated: by adding the CBS in this manner you correct for the malfunction in the CIP relation and recover the correct forward rate. The CBS is quoted in the market and measures the discrepancy between the CIP theory and the current state of the FX market.

There are many posts here and elsewhere as to the causes of the discrepancy between the CIP and real life. Which is a separate and more complicated subject.

$\endgroup$
3
  • 1
    $\begingroup$ If you have access to old code or old documentation you will probably see that this feature was not there in 2008/2009 but was added at a later date as a fix to a problem that only gradually became recognized and understood. Certainly Garman and Kohlhagen never envisioned this in their original paper. $\endgroup$
    – noob2
    May 8 '20 at 16:15
  • $\begingroup$ Thank you @noob2. May I assume that - reading between the lines of what you wrote -the same would apply to Option pricing as well as Forward pricing? $\endgroup$
    – gordon613
    May 10 '20 at 10:41
  • 1
    $\begingroup$ Yes, the Option price is (implicitly or explicitly) based on the forward price F. Especially in FX it makes sense to explicitly base it on F. $\endgroup$
    – noob2
    May 10 '20 at 10:43

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.