chapter 11. trading strategies with options

© Paul Koch 1-1

Chapter 11. Trading Strategies with Options

I. Basic Combinations. A. Calls & Puts can be combined with other building blocks (Stocks & Bonds) to give any payoff pattern desired.

1. Assume European options with same exp. (T), K, & underlying.

2. Already know payoff patterns for buying & selling calls & puts:

a. Calls. _______│_______S _______│________S__________K K

b. Puts. _______│_______S _______│________S K___________ K

3. Consider payoffs for long & short positions on:

a. Stocks. _______│_______S _______│________S K K

b. Bonds. _______│_______S _______│________S K _ _ _ _ _ _ K _ _ _ _ _ _ _

+c -c

+p -p

+S -S

+B-B

© Paul Koch 1-2

I.B. Protective Put (S+P)

B. Buy Stock (+S) and Buy Put (+P)Value

S

+S

+P

S+P

© Paul Koch 1-3

I.C. Principal - Protected Note* (B+C)

C. Buy Bond (+B) and Buy Call (+C)

* If you buy a zero-coupon, deep discount bond, the initial outlay (B) is small (esp. if r is high); If volatility of S is low, call (C) is cheap; Then the initial cost (B+C) may be set ≈ K (PPN). Then your principal is protected (worst outcome; S < K, call OTM, get to keep Bond payoff (K).

Value

S

+B

+C

B+C

© Paul Koch 1-4

I.D. Put-Call Parity (S+P = B+C)

D. B & C give same payoff pattern (S+P = B+C)Value

S

+B

+C

B+C

+S

+P

S+P

© Paul Koch 1-5

I.E. Writing a Covered Call (+S - C)

E. Buy Stock (+S) and Sell Call (-C)Value

S

+S

-C

S - C

S+P = B+C ↓+S-C -B = -P

© Paul Koch 1-6

I.F. Buying a Straddle (+C+P)

F. Buy Call (+C) and Buy Put (+P), with same KValue

S

+C

+P

C+P

© Paul Koch 1-7

I.G. Selling a Straddle (-C-P)

G. Sell a Call (-C) and Sell a Put (-P), with same KValue

S

-C

-P

-C - P

© Paul Koch 1-8

I.H. Buying a Strangle (+C+P) – with Different K’s

H. Buy Call with K2; Buy Put with K1, with different K (K1 < K2)Value

S

+C2

+P1

C2+P1

K2K1

© Paul Koch 1-9

II. How to Plot Payoff Pattern for Any Combination

Problem: Given any Combination of shares, bonds, & options, graph the Payoff Pattern for the Intrinsic Value; show slopes of line segments; & show break-even points.

Three Steps:

1. Compute the initial cost / revenue of the Combination, and get values of S where all options are worth zero (ATM or OTM). For these values of S, Combination is worth the initial cost / revenue.

2. Get values of S where one option is ITM. For these values of S, Combination Value = initial cost / revenue + intrinsic value of this option.

3. Get values of S where next option is ITM. For these values of S, Combination Value = old value + intrinsic value of this option.

Continue until you examine all values of S, for all options in combination.

© Paul Koch 1-10


Example 1: Strip; Buy 1 Call & 2 Puts with same K = $50; C = $5; P = $6.

1. Initial Cost = (-1) x ($5) + (-2) x ($6) = -$17. At S = K = $50, both options ATM, Combination Value = -$17.

2. If S > $50, Call ITM, Combination Value = -$17 + 1(S - K). (coeff. of S = +1)

3. If S < $50, Puts ITM, Combination Value = -$17 + 2(K - S). (coeff. of S = -2)

K = $50

____________________________________________________________ S $41.50 │ $67

│ │ │

slope = -2 │ slope = +1

│ │ │ │

-17 │ │

© Paul Koch 1-11


Example 2: Buy 1 Call with K1 = $40 (C1 = $8); Sell 2 Calls with K2 = $45 (C2 = $5).

1. Initial Cost = (-1) x ($8) + (+2) x ($5) = +$2. If S < K1 = $40, both options OTM, Combination Value = +$2. (coeff of S = 0)

2. If 40 < S < $45, C1 is ITM, Value = +$2 + 1(S - K1). (coeff = +1)

3. If S > $45, C1 & C2 are ITM, Value = +$2 + 1(S - K1) - 2(S - K2). (coeff = -1)

K = $40 K = $45

│7│ │ │ slope = +1

│ │ slope = -1

2│ slope = 0 │

_____________________________________________________ S

│ $45 $52

│

© Paul Koch 1-12

II.A. Bull Spread with Calls (C1 - C2)

A. Buy Call with K1 (pay C1); Sell Call with K2 (receive C2)

(K1 < K2); Thus (C1 > C2); So (-C1 +C2) < 0; initial outflow (left)Value

SK2K1(-C1 +C2)

+C2

-C1

© Paul Koch 1-13

II.B. Bull Spread with Puts (P1 - P2)

B. Buy Put with K1 (pay P1); Sell Put with K2 (receive P2)

(K1 < K2); Thus (P1 < P2); So (-P1 +P2) > 0; initial inflow (right)Value

SK2

K1 -P1

+P2

(-P1 +P2 )

© Paul Koch 1-14

II.C. Bear Spread with Calls (C2 - C1)

C. Sell Call with K1 (receive C1); Buy Call with K2 (pay C2)

(K1 < K2); Thus (C1 > C2); So (+C1 -C2) > 0; initial inflow (left)Value

SK2K1 C2

C1(+C1 -C2)

© Paul Koch 1-15

II.D. Bear Spread with Puts (P2 - P1)

D. Sell Put with K1 (receive P1); Buy Put with K2 (pay P2)

(K1 < K2); Thus (P1 < P2); So (+P1 -P2) < 0; initial outflow (right)Value

SK2K1

P1

P2 (+P1 -P2)

© Paul Koch 1-16

II.E. Butterfly Spread with Calls (C1 - 2C2 + C3)

E. Buy 1 Call with K1; Sell 2 Calls with K2; Buy 1 Call with K3

(K1 < K2 < K3); Thus, (C1 > C2 > C3); initial outflow (left).

© Paul Koch 1-17

II.F. Butterfly Spread with Puts (P1 - 2P2 + P3)

F. Buy 1 Put with K1; Sell 2 Puts with K2; Buy 1 Put with K3

(K1 < K2 < K3); Thus, (P1 < P2 < P3); initial outflow (right).

© Paul Koch 1-18

III.A. Graphing Total, Intrinsic, and Extrinsic Value

Total Value

Intrinsic Value

Extrinsic Value

S

S

S

K

K

K

© Paul Koch 1-19

III.B. Buy Calendar Spread using Calls (+C2 - C1)

B. Buy Call with maturity, T2 ; Sell Call with maturity, T1 ;

(T2 > T1); Thus, (C2 > C1); initial outflow (left).

© Paul Koch 1-20

III.C. Buy Calendar Spread using Puts (+P2 - P1)

C. Buy Put with maturity, T2 ; Sell Put with maturity, T1 ;

(T2 > T1); Thus, (P2 > P1); initial outflow (right).

© Paul Koch 1-21

IV. Interest Rate Option Combinations (Hull Chap 21)

A. Using Options on Eurodollar Futures.

1. ED Futures Contract Characteristics : (Review)

a. Underlying Asset - ED deposit with 3-month maturity.

b. ED rates are quoted on an interest-bearing basis, assuming a 360-day year.

c. Each ED futures contract represents $1MM of face value ED deposits maturing 3 months after contract expiration.

d. 40 different contracts trade at any point in time; contracts mature in Mar, Je, Sept, and Dec, 10 years out.

e. Settlement is in cash; price is established by a survey of current ED rates.

f. ED futures trade according to an index; Q = 100 - R = 100 - (futures rate); e.g., If futures rate = 8.50%, Q = 91.50, and interest outlay promised would be

(.0850) x ($1,000,000) x (90 / 360) = $21,250.

g. Each basis point in the futures rate means a $25 change in value of contract:[ (.0001) x ($1,000,000) x (90 / 360) ] = $25 ]

h. The ED futures is truly a futures on an interest rate. (The T.Bill futures is a futures on a 90-day T.Bill.)

© Paul Koch 1-22

IV.A. Using Options on ED Futures

2. Example: Long Hedge with ED futures for a Bank. (more Review)

Jan. 6: Bank expects $1 MM payment on May 11 (4 months). Anticipates investing funds in 3-month ED deposits.

Cash Market risk exposure:

Bank would like to invest @ today’s ED rate, but won’t have funds for 4 mo.If ED rate , bank will realize opportunity loss(will have to invest the $1 MM at lower ED rates).

Long Hedge: Buy ED futures today (promise to deposit later @ R).

Then if cash rates , futures rates (R) will & futures prices (Q) will .So long futures position will to offset opportunity loss in cash mkt.

The best ED futures to buy is June contract; expires soonest after May 11.

Jan. 6 May 11 June 14 |__________________________________________|_____________|

$1 MM receivable due May 11. Cash: Plan to invest $1MM on May 11Invest the $1 MM in ED deposits. Futures: Buy 1 ED futures. Sell futures contract.

© Paul Koch 1-23


3. Data for example – (more Review)Jan. 6: Cash market ED rate (LIBOR) = RS = 3.38% (S1 = 96.62)

June ED futures rate (LIBOR) = RF = 3.85% (F1 = 96.15) ; Basis = (S1 - F1) = .47%

May 11: Cash market ED rate = 3.03% (S2 = 96.97)

June ED futures rate = 3.60% (F2 = 96.40) ; Basis = (S2 - F2) = .57% _______________________________________________________________________________

Date Cash Market Futures Market Basis

1 / 6 bank plans to invest $1MM bank buys 1 Je ED futures at cash rate = S0 = 3.38% at futures rate = R0 = 3.85% .47%

5 / 11 bank invests $1MM in 3-mo ED bank sells 1 June ED futuresat cash rate = S1 = 3.03% at futures rate = R1 = 3.60% .57%

Net opport. loss = 3.38 - 3.03 = .35% futures gain = 3.85 - 3.60 = .25% change

Effect (35) x ($25) = $875 (25) x ($25) = $625 .10% .

Cumulative Investment Income: Interest @ 3.03% = $1,000,000 (.0303) (90/360) = $7,575 Profit from futures trades: = $625 Total: $8,200

Effective Return = [ $8,200 / $1,000,000 ] x (360 / 90) = 3.28% (10 bp worse than spot market = change in basis). This is basis risk.

© Paul Koch 1-24


4. Using Options on ED futures to build Floors, Caps, & Collars.

a. ED futures contract: Buy ; Promise to buy ED ( lend @ forward ED rate); Sell ; Promise to sell ED (borrow @ forward ED rate). [ Lock in R. ]

b. Call option on ED futures: Right to buy ED futures (lend @ forward ED rate).

c. Put option on ED futures: Right to sell ED futures (borrow @ fwd ED rate).

d. Lender? Want to buy ED in future. To hedge risk of loss with falling rates:

i. Buy ED futures. If rates , lock in min. lending rate. --(hedged) But if rates , opportunity loss (could have loaned at higher rates).

ii. Buy Call option on ED futures. If rates , lock in min. lending rate. NOW if rates , lend at higher rates! Call is OTM - interest rate Floor.

e. Borrower? Want to sell ED in future. To hedge risk of loss with rising rates:

i. Sell ED futures. If rates , lock in max. borrowing rate. --(hedged) But if rates , opportunity loss (could have borrowed at lower rates).

ii. Buy Put option on ED futures. If rates , lock in max. borrowing rate. NOW if rates , borrow at lower rates! Put is OTM - interest rate Cap.

f. Combining Call & Put on ED futures gives Collar.

© Paul Koch 1-25


5. Example: Building Interest Rate Collar for a bank. Cap: Buy a Put . Floor: Sell a Call . Both: Collar . Strike Option Strike Option Range of Net Price Premium Price Premium Borrowing Cost Premium . 96.00 .13 96.75 .02 3¼% - 4% .11 = $275 96.50 .40 96.75 .02 3¼% - 3½% .38 = $950 96.25 .23 96.50 .05 3½% - 3¾% .18 = $450 . Cap at 4%; Floor at 3¼ %; Collar: Net Cost = 11 basis points.

| | | 96.00 96.75 |> Futures Price (Q) |

| |

Loss a. CAP borrowing rates @ 4% by buying a Put with K = 96.00 (= 100 - 4). Must pay 13 bp for this Put (13 x $25 = $325). i. If ED rates above 4%, Q below 96.00, & Put is ITM – Cap at 4%.

ii. If ED rates below 4%, Q above 96.00, & Put is OTM – Borrow at < 4%.

b. If you don’t think ED rates will below, say, 3.25%, can recover some of cost by selling a Call with K = 96.75 (= 100 - 3.25). Receive 2 bp ($50). i. If ED rates below 3.25%, Q above 96.75%, & Call is ITM – Floor at 3.25%.

0.02

0.110.13 Buy put

Sell call

chapter 11. trading strategies with options

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