hello,I have computed the greeks for each caplet/floorlet belonging to a given cap/floor.To compute the greeks for the whole cap/floor is it correct to make the simple sum of the greeks of respective caplets/floorlets ?any documentation on this topic is well appreciated!thanksJL

I assume you are talking about a vanilla cap/floor and I will ignore counterparty risk.The payoff of the cap/floor can be written as the sum of the payoffs of the caplets/floorlets, therefore you are dealing with a portfolio of options and the totalprice is the sum of the individual prices. Hence the sensitivities of the total price are the sum of the sensitivities of individual prices.

Hello,JohnLaw is right only for options' portofolio cases where all the trades have the same notional. Otherwise, the wight of each trade is to be taken into account.The Cap greek is compute as below:G = Sum[W(i) * G(i)] / Sum[W(i)]where G(i) is the greek of the caplet iW(i) is the weight of the caplet iW(i) = N(i) * Dc(i), N(i) is the Notional for the caplet i and Dc(i) is the time decount with Dc(i) = EndDate(i) - StartDate(i) / NbDaysPerYearHope that this can helpPs:Sorry for my english

QuoteOriginally posted by: JohnLawhello,I have computed the greeks for each caplet/floorlet belonging to a given cap/floor.To compute the greeks for the whole cap/floor is it correct to make the simple sum of the greeks of respective caplets/floorlets ?any documentation on this topic is well appreciated!thanksJLNo, for example the vega of each option is the sensitivity to change in implied vol. implied vol is affected by a whole series of factors: Supply demand for each cap maturity and strikeexpected realized voladjustment for model errors...etc.short term implied vols are much more volatile than long term implied vols (same holds actually for realized), vol of vol. There is very good logic behind this. So if you for example are long a lot of 1 year caps and short some 5 year caps, 5 years cap with very low notional 1 year (to make example more extreme but fully realistic) then it could look like you are vega neutral if just adding up vegas. . If studying realized vol be very careful to adjust for sampling error if comparing realized vols from different number of sampling points. The term structure of vol is not moving in parallel fashion and some of the statistical properties are highly deterministic. For example the vol of short term implied vols are much higher than vol of long term implied, these I have a large unpublished empirical research about with very good data (sorry can not post it here). Be careful if doing empirical research here, many traps to fall into. The correlation between imp vols for different maturities is highly unstable. 1. If you want to add up vegas for different caplets you would clearly be better off by giving short term caplets vegas more weight, I recommend doing large empirical work (as we did for own trading) to get an idea about weighting. In general I would recommend empirical study of the implied vols. Realized vol for vega less important, yes often they are somewhat correlated, but implied vol in real markets is far from just expected realized vol.2 even then be very careful by adding up in particular vegas for different maturities (holds for almost types of options), as vols of vols are unstable and correlations between implied with different maturity are highly unstable. Taking into account also options with different strikes this add to the complexity.Always be very very very careful by summing up greeks.Experience, empirical data, logic and simulations clearly shows that nothing can replace a good local hedge. That is hedging option with as close as possible to option you want to hedge is naturally the most robust hedge, but yes you also need to take into account costs of hedging and opportunities to hedge, and that if you want to hedge at all. If you for good reasons think implied vol will explode tomorrow why would you try to hedge away all your long vega exposure.

QuoteOriginally posted by: luke75 Hence the sensitivities of the total price are the sum of the sensitivities of individual prices.This only holds if you assume for example individual caplet vols among all caps for same underlying are moving parallel. This is far from reality. If the non-parallel behavior was purely stochastic (random) your best way to add Greeks would still simply be to add them up yes (naturally weighted by notional), but there are several quite deterministic statistical properties here (read my previous message). In other words if anyway wants to add up Greeks from different maturities you can do considerably better than simply add up (notional based).Not directly related to summing up caplet Greeks, but yes as late as in mid 1990s we did a few close to risk free arbs in world most liquid cap market: USD. A few banks did not got it right when they priced up caps when going from caplet vols to cap vols. This could have big effect if you asked for caps with strange notional structure. A new generation are now possibly becoming market makers? Time to look for cap/caplet arb again? I broke my professional option-virginity on USD caps and floors. My very first job was on market maker desk USD caps and floors, swaptions, hedging with Chicago products and laying off at other market makers. (But yes I had traded options before my first job, PA). We had direct lines down in the Chicago pit, I started thinking about the dynamic of the caplet vol structure, and it was a wonderful time. But it was after the wild 80's. I still remember a trader-women that told the story about the wild 80s when she on a corporate party had ordered her bathtub filled with champagne, and it was filled with up with champagne. The restrictions on such behavior she told me came after the crash of 87, when several banks blew up.I always wondered, but never asked (I was very junior and a bit shy) if she (they?) ever drank all that champagne? Or if most of it went down the drain?