Overnight Indexed Swaps and Floored Compounded Instrument in HJM One-Factor Model

Two types of financial instruments including (overnight) compounding are studied in this note. The first one is overnight compounded instruments in the case where the settlement is delayed with respect to the end of the compounding period (floating leg of the OIS). The second is options on the composition. In both cases we study both continuous and discrete composition. We provide explicit formulas within the HJM one-factor models with deterministic volatility together with hedging strategies.