Greeks for Caps and Floors

greghm · July 8th, 2003, 11:53 am

My pricer says that my 5-year Cap on 6-month Euribor with a 4% STRIKE is worth 1.66 %.The delta is -0.161 how is this delta calculated ? is it the summed delta of the Caplets ?2 What is the underlying that I have to monitor If I want to press my client to trade ? is it the BOBL Future ?

FDAXJihad · July 8th, 2003, 12:08 pm

Greghm: [is it the BOBL Future.... LOL, no it's not the BOBL future.... it's the EURIBOR Futures complex.this delta is the aggregate delta for a parallel shift. In that sense, it's the sum of the caplets, where each caplet would be hedged with a particular futures expiration (6 months apart).

greghm · July 9th, 2003, 7:12 am

Yeah but 6m euribor Futures (Eurex or Liffe) cannot go really far in term of liquidity and traded dates, If i have a 10 year cap I cannot hedge toward this date, can I ? Moreover, my most valuable caplets are the one over the strike so they are generally the closest to maturity ?

FDAXHunter · July 9th, 2003, 7:18 am

No, but you can use FRAs

greghm · July 9th, 2003, 7:24 am

okay I got it.and my next question is: how can I know as a sales if I can improve the price to the client ? For example, If I sell a 10 year swap payer, If the Bund, increase by 8 tics (which is the duration of the 10-year) , I can improve my price on the swap by 1bp.

FDAXHunter · July 9th, 2003, 7:37 am

Yeah, that's a rough guideline. Ticks(FGBL)/Duration(10y swap) = bps(Swap).

greghm · July 9th, 2003, 7:42 am

QuoteOriginally posted by: FDAXHunterYeah, that's a rough guideline. Ticks(FGBL)/Duration(10y swap) = bps(Swap).Sales just need to be convincing enough!and so what is the reference for an Interest Rate Cap ?

FDAXHunter · July 9th, 2003, 8:56 am

Well, if you wanted to be exact, it for a 10 year 6 month cap, it would be 20 6 month FRAs. But, you could substitute with a swap rate.

necro · April 22nd, 2005, 11:59 am

Quotethis delta is the aggregate delta for a parallel shift. In that sense, it's the sum of the caplets, where each caplet would be hedged with a particular futures expiration (6 months apart). does this mean that since the delta of a cap is a sum of deltas of some N options/caplets, it could be greater than 1?

Optron · April 23rd, 2005, 5:04 am

Yes why not. After all, a cap is a portfolio of call options on LIBOR. If you have N Eurpean vanilla options with say EACH of USD 1, then delta of each option would be less than mod(1). However, 0 <= total delta of N Options <= USD mod(N), and thus delta of a cap can be more than USD 1.mod - modulus