Options & Swaps

Question 1

Delta Neutral Dealer Perspective

Answer 1

From the buyers perspective:

Buy Call. Delta between 0 and +1

Buy a Put. Delta between 0 and -1

From Dealer Perspective:

Dealer has sold call. Delta between 0 and -1

Dealer to buy stock to cover position

Dealer has sold put. Delta between 0 and 1+

Dealer to short stock to cover position

Calculating number of shares needed to get to delta neutral:

-(delta)(#options)

Question 2

Delta Neutral Observations

Answer 2

• Is done for a short period of time only - days or weeks
• Assumes normal market conditions
• Earns the risk free rate
• Delta is only an approximation
• Delta changes over time even without any other changes

Question 3

Delta Neutral Rebalancing

Answer 3

• Day 1 position:

-(delta)(#options)

• Day 2 position

-(delta)(#options)

• Buy or sell options based on the difference between Day 1 and Day 2
• If options are sold, the proceeds can be invested at risk free rate
• If options need to be bought, then borrow at risk free rate

Question 4

Swaps General

Answer 4

• Value of swap at initiation is zero
• A Swap’s Libor rate is paid in arrears e.g Libor rate on Day 0 is paid out on Day 180.
• Swaps not just used for speculation. They are used for risk management.

Question 5

Swap Duration General

Answer 5

• For a floating rate instrument the duration is half the reset period
  e. g. for a quarterly reset period duration = 0.25/2 = 0.125
• Dur_{pay floating} = Dur_{recieve fixed} - Dur_{pay floating} > 0 (Dur increases)
• Dur_{pay fixed} = Dur_{recieve floating} - Dur_{pay fixed} < 0 (Dur decreases)

Question 6

Fixed and floating rate liabilities and risks

Answer 6

• Floating rate liability:

Cash Flow Risk but no Market Value Risk

• Fixed rate liability:

No Cash Flow Risk but has Market Value Risk

Question 7

Using Swaps to adjust duration

Answer 7

NP = V (MDur_t - MDur_p) / (MDur_swap)

Question 8

Currency Swap

Answer 8

• Banks have advantage of borrowing in their local market, rather than borrowing from the foreign bank which would charge an unfavourable rate.
• Principle is exchanged. Interest rate payments will be subject to exchange rate. The principle is not as the rate is locked in.
• Counterparty will have to pay interest on the amount/currency they borrowed at the Interest Rate of the borrowed currency

E.G. A US bank borrows £2mil (principle) and will pay interest in £ at the £ Interest Rate. At the end of the swap the US bank will pay back the principle of 2mil plus the last interest payment.

Question 9

Converting Foreign Cash Receipts into Domestic Currency

Answer 9

• Determine notional principle in foreign currency:
• Foreign Currency / Swap Fixed Rate of Foreign currency (deannualise)*
• Translate notional principle in foreign currency into domestic currency:
• Foreign currency notional / current exchanage rate*
• Calculate interest in domestic currency
• Domestics currency x Swap Fixed Rate of Domestic currency (deannualise)*

Question 10

Swaptions

Answer 10

• When considering whether to exercise a swaption based on the interest rate movements - consider from the perspective of both the fixed rate and floating rate legs.
  e. g. in a 6% payer swaption if the rates increased you would exercise for two reasons. Firstly you would be recieving LIBOR (floating leg) at a higher rate. However entering a swap in the new interest rate environment would mean paying a fixed rate above 6 %.