Cap
FinPricing offers:
Four user interfaces:
- Data API.
- Excel Add-ins.
- Model Analytic API.
- GUI APP.
Cap/Floor Valuation
An interest rate cap is an OTC derivative where the buyer receives payments at the end of each period when the
interest rate exceeds the strike, whereas an interest rate floor is a similar contract where the buyer receives
payments at the end of each period when the interest rate is below the strike.
| 1. Interest Rate Caps and Floors Introduction |
An interest rate cap is an OTC derivative where the buyer receives payments at the end of each period when the
interest rate exceeds the strike. It actually consists of a series of European call options
(caplets) on interest rates. The buyer receives payments at the end of each period when the interest rate exceeds the
strike. In return, the buyer needs to pay an up-front premium to the seller.
Interest rate caps are frequently purchased by issuers of floating rate debt who wish to protect themselves from the
increased financing costs that would result from a rise in interest rates. Investors use caps to hedge against the risk
associated with floating interest rate and will benefit from any risk in interest rates above
the strike. The holder gets a payment when the underlying interest rate exceeds a specified strike rate.
An interest rate floor consists of a series of European put options (floorlets) on
interest rates. The buyer receives payments at the end of each period when the interest rate falls below the strike.
The payment frequency could be monthly, quarterly or semiannually. The exercise is done automatically that is different
from any types of options. For example, let the strike be 2.0%. The buyer would get paid if LIBOR fell below 2.0%;
otherwise, he would receive nothing if LIBOR rose above it.
Floors are frequently purchased by purchasers of floating rate debt who wish to protect themselves from the loss of
income that would result from a decline in interest rates. A floor is a guarantee of a future interest rate. Investors
use floor to hedge against the risk associated with floating interest rate. Investors will
benefit from any risk in interest rates below the strike.
| 2. Interest Rate Caps and Floors Valuation |
A cap consists of a series of cash flows, i.e., caplets. Each cash flow is a call option on a floating rate index level at a specified date in future. The price of a caplet is valued using the Back formula. Whereas, A floor consists of a series of cash flows, i.e., floorlets. Each cash flow is a put option on a floating rate index level at a specified date in future. The price of a flootlet is valued using the Back formula.
The present value of a cap is given by
The present value of a floor is given by
Practical Notes
- The pricing model for pricing caps/floors is the Black formula in the market.
- The forward rate is simply compounded.
- The first key is to generate the cash flows of a cap/floor. The cash flow generation is based on the start time, end time and payment frequency, plus calendar (holidays), business convention (e.g., modified following, following, etc.) and whether sticky month end.
- Then you need to construct yield curve by bootstrapping the most liquid interest rate instruments in the market. FinPricing provides useful tools to build various curves, such as swap curve, basis curve, OIS curve, bond curve, treasury curve, etc. Go to the list of the tools
- Another key for accurately pricing an outstanding cap/floor is to construct an arbitrage-free cap implied volatility surface. FinPricing is using SABR model to construct cap impliend volatility surface. Go to the list of volatility construction tools
- The accrual period is calculated according to the start date and end date of a cash flow plus day count convention
- Any compounded interest yield curve data can be used to compute discount factor, of course the formulas will be slightly different. The most common used one is continuously compounded zero rates.
- The formula above doesn’t contain the last live reset cash flow whose reset date is less than valuation date but
payment date is greater than valuation date. The reset value is
PVreset = max( r – K, 0)NτD for cap
PVreset = max (k – r, 0)NτD for floor
that should be added into the above present value.
| References |