# Cap and Floor Position

Can anyone provide a clear/simple summary of the “Interpretation of a Cap and Floor Position” concept found in the CFAI books? Book 6, pg. 434. I understand the concept with the cap and floors (rate above cap equals payment…etc) but where I’m completely confused is when they talk about interest rate caps/floors being equivalent to a “package of interest rate options”. Hope someone can clarify this. Thank you.

I will try… Cap -> is a Call on an Interest Rate. Cap could be active (bought / sold) for multiple periods. Long Cap gains when the Reference Rate > Strike Rate on the Cap. In order to value the Cap - consider each period separately - evaluate the Cap at each of those periods, and then sum up the values of the individual Caps. It is thus equivalent to a package of interest rate options. (for the purposes of valuation). In the above - you were LONG a CAP. Now if you flip this around, and instead think in terms of a Fixed Income Bond instrument. When rate rises - Fixed Income Bond loses value. So you need to have bought a Put (Long Put) on a Fixed Income instrument to have the same pay off structure. If the rate rises, you have (as the holder of the put) the option to put the bond back. ==================================================== Long Cap on Interest Rate = Long Put on Fixed Income Instrument. ==================================================== Short Cap on Interest Rate When Interest rate goes up - and above the reference rate -> you pay When Interest rate goes up -> Fixed Income instrument falls in value. Sell a Put on Fixed Income instrument - it will be put to you, when Interest rates go up (since Put is at the behest of the option holder). So Short Cap on Interest Rate = Short Put on Fixed Income instrument. If you had a Short Call on Inter

Does the following make sense. Long a Floor on Int. Rates = Long a Call on Fixed Income Interest rates DECREASE. Long a Floor - I pay. Long a Call - I call and pay out the bond. Short a Floor on Int. Rates = Long a Put on Fixed Income Interest rates DECREASE Short a Floor - Get paid. Long a Put - Put and get paid out.

Know how to value EACH caplet then sum to get the value of the cap. Same goes for floors. Simply use the same process when calculating interest rate binomials ie 50% probability of up and down. (rate given - cap rate)X notional/1+one yr cap rate to get the ‘terminal’ value, the PV each back to the respective nodes. Cap a portfolio of call options, Floor a portfolio of put options Cap is also a portfolio of put options on bond PRICES an vice versa.