Notes on convexity and quanto adjustments for interest rates and related options

We collect simple and pragmatic exact formulae for the convexityadjustment of irregular interest rate cash flows as Libor-in-arrears orpayments of a swap rate (CMS rate) at an irregular date. The resultsare compared with the results of an approximative approach availablein the popular literature.For options on Libor-in-arrears or CMS rates like caps or binarieswe derive an additional new convexity adjustment for the volatility tobe used in a standard Black & Scholes model. We study the qualityof the adjustments comparing the results of the approximative Black& Scholes formula with the results of an exact valuation formula.Further we investigate options to exchange interest rates which arepossibly set at different dates or admit different tenors.We collect general quanto adjustments formulae for variable interestrates to be paid in foreign currency and derive valuation formulaefor standard options on interest rates paid in foreign currency.