Risk Management Applications of Swaps Flashcards
Duration of a pay-fixed receive-floating swap
= duration of a floating-rate bond - duration of a fixed-rate bond with equivalent cash flows
Duration of a fixed-rate bond
Approximately 75% of the maturity
Duration of a floating-rate bond
- Approximately equal to the time remaining until the next coupon payment
- Example: Time between payments is approximately 0.25 for a bond with quarterly payments → The average duration is approximately 0.125
Swaption
- An option giving the right to enter into a swap
- Payer swaption (put) - enter as the fixed rate payer
- Receiver swaption (call) - enter as the fixed rate receiver
Swaption versus options on bonds
- A receiver swaption is analogous to a call option on a bond
- A payer swaption is analogous to an put option on a bond
- To synthetically add a call feature to a bond (call feature held by the issuer)
- To synthetically remove a call feature on a bond (call feature previously held by the issuer)
- Purchase a receiver swaption
- Sell a receiver swaption
- To synthetically add a put feature to a bond (put feature held by the bondholder)
- To synthetically remove a put feature on a bond (put feature previously held by the bondholder)
- Sell a payer swaption
- Purchase a payer swaption
The notional principal of a swap necessary to change the duration of a bond portfolio worth B from MDURB to a target duration MDURT
Converting foreign cash flows into domestic currency
- Foreign notional amount = foreign currency cash flows / (foreign currency swap rate / n)
- Domestic notional amount = foreign notional amount * current fx rate
- Domestic currency cash flows = domestic notional amount * (domestic currency swap rate / n)
Delta hedge at expiration
At expiration, at-the-money call options move very rapidly to a delta of 1 or 0. At this point, the gamma is the highest and it is very difficult to maintain a delta-hedged position
- Economic exposure
- Transaction exposure
- Translation exposure
- Arises when overseas sales of a manufacturer decline in the face of a stronger or weaker currency
- Arises when overseas sales denominated in a foreign currency must be converted to the domestic currency
- Arises when the financial statements of an overseas subsidiary must be converted to the domestic currency
Annualized VaR
Effective rate on a loan with a collar
Loan balance × (Actual days in period/360) × [Libort-1 + Spread – max(0, Libort–1 – Cap rate) + max(0, Floor rate – Libort–1)]
Swap rate quotation
The quote is the rate that the swap pays or receives
- Ex. If the swap rate is 4.9% in the US and 5.3% in the UK, it is possible to enter a swap that pays 4.9% on the USD notional and and receives 5.3% on the GBP notional.
Credit risk of swaps as a function of their maturity
- Credit risk is highest for interest rate swaps near the middle of their life because as the swap ages, the counterparties’ credit worthiness may have changed. As the swap nears its maturity and the number of remaining settlement payments decreases, credit risk decreases.
- Credit risk is highest for currency swaps between the middle of their life and their maturity due to the exchange of principal on the maturity date.