Hey,has anybody given any thought to the convexity in OIS swaps introduced by the deferred payoff (t+1 for eonia swaps, t+2 for FF swaps - at least to my knowledge)?Let [$]r_i[$] be the overnigth rate between [$]t_i[$] and [$]t_{i+1}[$].Let [$]N(t_n) = \prod_{i=0}^{n-1} (1+r_i \cdot dcf)[$] be the discrete ois bank account with corresponding risk-neutral measure [$]Q_N[$].Then the PV of the float leg of a ois swap maturing in [$]t_n[$] and paying in [$]t_{n+1}[$] with spotDay [$]t_2[$] is given by[$]PV_{floatLeg} = E_t^{Q_N}[\frac{\prod_{i=2}^{n-1} (1+r_i \cdot dcf)-1}{N(t_{n+1})}] = E_t^{Q_N}[\frac{1}{N(t_2) \cdot (1+r_n \cdot dcf)}] - \underbrace{E_t^{Q_N}[\frac{1}{N(t_{n+1})}]}_{=DF^{ois}[t_{n+1}]}[$]I would like to introduce some simplifying assumptions to evaluate the first term. If everything were deterministic one would get[$]PV_{floatLeg} = DF^{ois}[t_2] \cdot \frac{DF^{ois}[t_{n+1}]}{DF^{ois}[t_n]} - DF^{ois}[t_{n+1}][$]But obviously this is too simplifying. Happy for any stimulating discussion.Bernd

QuoteOriginally posted by: BerndSchmitzHas anybody given any thought to the convexity in OIS swaps introduced by the deferred payoff (t+1 for eonia swaps, t+2 for FF swaps - at least to my knowledge)?Bernd,I look at this a long time ago (10 years now ). My notes on that questions where collected in Overnight Indexed Swaps and Floored Compounded Instrument in HJM One-Factor Model. Obviously this is single curve, but would still work with OIS valuation with overnight collateral. In the document there is also a analysis of the difference between continous compounding and periodic compounding (daily in this case). There are some numerical results using extended Vasicek model (Hull-White one factor). The impact of the convexity adjustment is tiny.I hope it helps.Marc

Great document. This is exactly what I was looking for.Many thanks