Debt OPTIONS Options on Treasury Securities T-Bill

Debt OPTIONS

Options on Treasury Securities: T-Bill Options • Options on T-Bills give the holder the right to buy a T-Bill with a face value of $1 M and maturity of 91 days. • Exercise price is quoted in terms of the IMM index and the following formula can be used to determine X: • The option premium is quoted in terms of annual discount points (PT). The actual premium is

Options on Treasury Securities: T- Bond Options • Options on T-Bonds give the holder the right to buy a specified T-Bond with a face value of $100, 000. • Exercise price is quoted as a percentage of par (e. g. IN = 90). If the holder exercises, she pays the exercise price plus the accrued interest: • The option premium is quoted in terms of points (PT). The actual premium is

Fundamental Strategies • There are six fundamental strategies: – Call Purchase – Naked Call Write – Covered Call Write – Put Purchase – Naked Put Write – Covered Put Write

Profit Graph • Option Strategies can be evaluated in terms of a profit graph. • A profit graph is a plot of the option position’s profit and security price relation at expiration or when the option is exercised.

Figure 17. 3 -1: Call Purchase • Buy T-Bond call: X = $100, 000, C = $1000

Figure 17. 3 -2: Naked Call Write • Sell T-Bond call for: X= 100, 000, C=1000.

Figure 17. 3 -3: Covered Call Write • Long T-Bond at 100, 000, short 100 T-Bond call at 1.

Figure 17. 3 -4: Put Purchase • Buy T-Bond put: X=100, 000, P = 1000

Figure 17. 3 -5: Naked Put Write • Sell T-Bond put: X =100, 000, P = 1000

Figure 17. 3 -6: Covered Put Write • Short T-Bond at 100, 000, short 100 T-Bond put at 1.

Other Strategies

Figure 17. 4 -1: Straddle Purchase • Buy 100 T-Bond put for 1 and buy 100 T-Bond call for 1:

Figure 17. 4 -2: Bull Spread • Buy 100 T-Bond call for 1 and sell 101 T-Bond call for. 75:

Hedging

Table 17. 8 -4: Hedging the Cost of a September T-Bill Purchase with a T-Bill Call

Table 17. 8 -5: Hedging a Future T-Bond Sale with a T-Bond Put

Futures Options on Treasury Securities • Futures options give the holder the right to take a futures position: – Futures Call Option gives the holder the right to go long. When the holder exercises, she obtains a long position in the futures at the current price, ft, and the assigned writer takes the short position and pays the holder ft - X. – Futures Put Option gives the holder the right to go short. When the holder exercises, she obtains a short position at the current futures price, ft, and the assigned writer takes the long position and pays put holder X - ft. • Futures option on Treasuries: Options on T-Bill Futures, T-Bond Futures, and T-Note Futures.

Exhibit 17. 9 -1: Futures Options on Treasury Securities Call on T-Bill Futures: • X = IMM 90 or X = $975, 000 • PT =. 5 or C = $1, 250 • Futures and options futures have same expiration.

Exhibit 17. 9 -2: Futures Options on Treasury Securities Put on T-Bill Futures: • X = IMM 90 or X = $975, 000 • PT =. 5 or P = $1, 250 • Futures and options futures have same expiration.

Table 17. 9 -1: Put-Call-Futures Parity

Hedging Cases

Exhibit 18. 2 -2: Hedging $5 M CF in June with June T-Bill Futures Call

Managing the Maturity Gap with T-Bill Put • Case: In June, a bank makes a $1 M loan for 180 days which it plans to finance by selling a 90 -day CD now at the LIBOR of 8. 258% and a 90 -day CD ninety days later (in September) at the LIBOR prevailing at that time. To minimize its exposure to market risk, the bank buys a T-Bill put at X = IMM = 90 for $$1250.

Maturity Gap Hedged with T-Bill Puts

Hedging future T-Bond Sale With T-Bond Puts • Case: Three months from the present (. 25 of year), a bond manager plans to sell a T-Bond with maturity of 15. 25 years, F = $100, 000, and coupon rate = 10%. • Manager hedges the sale against interest rate increases by buying one put option on a T-Bond with a current maturity of 15. 25 years and face value of $100, 000. The put has an expiration of T =. 25 years, exercise price of X = IN = 95 or X = $95, 000, and is trading at P = 1 - 5 or P = [1. 15625/100]($100, 000) = $1156.

Hedging future T-Bond Sale With T-Bond Puts • Hedge T-Bond Sale:

Hedging Future Bond Portfolio Sale With T-Bond Puts • Case: Three months from the present (. 25 of year), a bond manager plans to liquidate a bond portfolio consisting of AAA, and A bonds. The portfolio currently has a WAM of 15. 25 years, F = $10 M, WAC = 10%, and has tended to yield a rate 1% above TBond rates. • Manager hedges the sale against interest rate increases by buying put options on a T-Bond with a current maturity of 15. 25 years and face value of $100, 000. The put has an expiration of T =. 25 years, exercise price of X = IN = 95 or X = $95, 000, and is trading at P = 1 - 5 or P = [1. 15625/100]($100, 000) = $1156. • To hedge, the manager buys 105. 26316 T-Bond puts for $121, 684:

Hedging Future Bond Portfolio Sale With T-Bond Puts • Hedge Bond Portfolio Sale:

Interest Rate Options

Interest Rate Options • Interest rate call option gives the holder the right to a payoff if an interest rate (e. g. , LIBOR) exceeds a specified exercise rate; interest rate put option gives the holder the right to a payoff if an interest rate is less than the exercise rate. • Interest rate options are written by commercial banks in conjunction with a future loan or CD investment.

Interest Rate Call Option Case: • A company plans to borrow $10 M in sixty days from Sun Bank. The loan is for 90 days with the rate equal to LIBOR in 60 days plus 100 BP. • Worried that rates could increase in the next 60 days, the company buys an interest rate call from the bank for $20, 000. • Terms: Exercise Rate = 7%; call premium plus interest will be paid at the maturity of the loan; any interest rate payoff will be paid at the loan’s maturity. • See Chapter 17.

Interest Rate Put Option Case: • A company plans to invest $10 M in sixty days in a Sun Bank 90 -day CD. The CD will pay the LIBBER. • Worried that rates could decrease in the next 60 days, the company buys an interest rate put from the bank for $15, 000. • Terms: Exercise Rate = 7%; put premium plus interest will be paid at the maturity of the CD; any interest rate payoff will be paid at the CD’s maturity. • See Chapter 17

Caps: Series of Interest Rate Call Options • A Cap is a series of interest rate calls that expire at or near the interest rate payment dates on a loan. They are written by financial institutions in conjunction with a variable rate loan. Case: • A company borrow $50 M from Commerce Bank to finance its yearly construction projects. The loan starts on March 1 at 8% and is reset every three months at the prevailing LIBOR. • Cap: In order to obtain a maximum rate while still being able to obtain lower rates if the LIBOR falls, the company buys a Cap from the bank for $100, 000 with exercise Rate = 8%. • See Chapter 17

Floor: Series of Interest Rate Put Options • A floor is a series of interest rate puts that expire at or near the payment dates on a loan. They are purchased by financial institutions in conjunction with a variable rate loan they are providing. Case: • Commerce Bank purchases a floor with an exercise rate of 8% for $70, 000 from another institution to protect the variable rate loan it made. • See Chapter 17

Table 17. 8 -1: Profit and Interest Rate Relation from Closing a Long 94 T-Bill Call Purchased at 1

Table 17. 8 -3: Profit and Interest Rate Relation from Closing a Long 94 T-Bond Put Purchased at $1000

Table 17. 8 -2: Profit and Interest Rate Relation from Closing a Long 94 T-Bill Put Purchased at 1