L19 - Interest Rate Options Flashcards
1
Q
What is a cap?
A
- With a varing interest rate over the life of a instrument say a variable rate mortgage, leasing etc we may be able to benefit from the upsides of interest changes and reduce the downsides of interest rate changes using options
- This option will usually have less time to expiry than the underlying with the strike price being the cap –> gives you the obligation to pay the fixed rate when reference rate is higher than cap but pay the market rate when it is lower
- When the rate is above the cap we exercise it when its below we do nothing –> protecting us from a high rate but allowing us to benefit from cheaper repayments when the IR is lower than the cap
- Issue with these options is they are long thus have a higher time value and therefore higher premium
- Also don’t pay continuously it will be on certain dates of the month made up of the rate and the premium of the option –> do you exercise the option on month 1? well what about the rest of the payment periods –> Based on a normal European option
- Thus the cap is actually made up of a portfolio of options and every option per payment period is called a caplet
2
Q
What is a floor?
A
- Say you are trading a coupon bond where the coupon is based on some underlying rate e.g. the T-bill rate
- What happens if the rate is negative (pay more for the bond than you will receive at the end)?
- In this case, we buy an option with a strike that we use as a floor
- This will define the lowest rate you can receive on the coupon, and higher you will receive the market rate and below you exercise and you receive the floor rate minus the premium for the floor option
- Each option for each payment periods are called floorlets
3
Q
What do writers of caps and floors base their estimate of the future interest rate on?
A
- Most likely the market expectation of expected forward rates
- Due to the upward sloping nature of the par yield curve, it means that the cap in the long term will have a higher premium
4
Q
How can you reduce the price of a cap?
A
Creating a bull spread by long a cap option and shorting a floor option –> This structured contract is called a collar
- intuitive this is cheaper than paying for the cap option as you are receiving the premium of the short floor
- The implication of this however is that:
- Above the cap –> you exercise the cap as it above the rate you want to pay but you are OTM on the floor so that isn’t exercises
- between floor and cap –> nothing happens both are out the money
- Below the floor –> Cap is OTM so not exercised by the buying of the floor will exercise their option –> you will have to pay 1% to the buyer of the cap
- IF you also have a mortgage you have to pay your 1% to the bank too so technically you are paying double what you would normally pay
- Therefore the maximum you pay is the strike of the cap, the minimum you pay is the strike of the floor and when in between the rates we pay the market rate (spot rate) which will fluctuated between the two rates
5
Q
What happens if the collar is 0?
A
- cap - floor is 0 –> so you bought and sold them at the same strike price
- The rate is then fixed at the strike –> so this will completely hedge the interest rate volatility –> transform a floating rate into a fixed –> created an Interest Rate Swap
- Although no one would do this as it is more complicated than simply buying a IRS
- THERE IS NO PREMIUM OF THE SWAP –> there is no option to swap from floating to fixed and vice versa
- Cap-floor parity –> floor and cap are in parity when they are at the same strike as they are equal to a Swap which has NO PREMIUM –> if this is not the case there is an arbitrage opportunity
- Therefore a portfolio of interest rate options (Caps or floors) equals a swap which equals/can be derived from forwards or bonds –> arbitrageurs are checking all the links and if one does not apply they will take advantage of the arbitrage opportunity that arises
