1. Options - 2

2. CBOE lists 12 basic option strategies for investors. These are:
buying or selling naked calls, covered calls, buying or selling naked
puts, protective puts, bear spread, bull spread, straddle, butterfly spread, strangle, synthetic stock
The CBOE has a nice online tutorial that supplements most of what appears in my notes. They even have questions to test yourself. The link to that site was in the previous set of notes. This section pertains to the advanced strategies portion of their online course.

3. COVERED CALLS
Buy $ 75 Write 80 CALL for $ 1.5. Total Net Cost = = (recover this to break-even).
Stock Stock Call Total
Price Gain/Loss G/L G/L
Gains limited on the upside, essentially gains above 80 are given up for current income.
6.50
-8.50

4. COLLARS
ADD 70 PUT TO THE ABOVE COVERED CALL, New net Cost = =
This must be recovered to break even
Stock Stock Call Put Total
Price Gain/Loss G/L G/L G/L
3.375
-6.625

5. Bull Spread Expiration Cash flows S 90 95 97 98 100 102 103 105
Stock = Strike Price Call Price Costs
Buy 1 call at
Write 1call at Graph turns at the strikes
Total Cost =
Expiration Cash flows S
95 call (B)
100 call (W)
Total
- cost
Net CF +2 95
100 -3

6. BEAR SPREAD Stock = 100 Strike Price Call Price Costs
Stock = Strike Price Call Price Costs
Buy 1 call at
Write 1 calls at
Total Cost =
Expiration Cash flows S
105 call (B)
100 call (W)
Total
-Cost
Net C

7. BUY STRADDLE:
Stock Price = $ 60, Strike = $60, Call Price = $ 3, Put Price = $ 2, same exp.
Buy Put = - 2
Buy Call = - 3
Initial Cost = - 5
At expiration, the gains (G) or losses (L) are: 60 65 55

8. WHAT IF EXPECTATION IS OF PRICE MORE LIKELY TO INCREASE THAN TO FALL ?
Load up on the CALL side: BUY STRAP, i.e BUY 2 CALLS and BUY 1 PUT, FOR COST OF $ 8.
Now BREAK-EVEN => $ 8 movement on 1 put OR $ 4 movement in each call of 2. OR $8 movement
on 1 put So the prices are 52 AND 64.
Graph similar to straddle but skewed more to the left (break-even of 52 vs 55 for straddle)
WHAT IF EXPECTATION IS OF PRICE MORE LIKELY TO FALL THAN TO INCREASE ?
Load up on the PUT side: BUY STRIP, i.e BUY 1 CALL and BUY 2 PUTS, FOR COST OF $ 7.
Now BREAK-EVEN => $ 7.00 movement on 1 CALL, OR 3.50 movement on each PUT (of 2).
Break even prices are 56.5 or $ 67
WITH BOTH STRIPS AND STRAPS, LOSSES ARE IF THE STOCK PRICE DOES NOT MOVE.

9. STRANGLE: (changes the strike price).
Buy 60 Call = -3.00
Buy 55 put = (versus 60 put for $ 2.00)
Initial cost = -3.50
Break-evens: Above 60 call gains, S = 63.50
Below 55 put gains S = 51.50
Between 55 and 60, neither gains, and max loss = 3.50
51.5
63.5
-3.50 55 60

10. LONG BUTTERFLY
Stock = Strike Price Call Price Costs
Buy 1 call at
Write 2 calls at
Buy 1 call at
Total Cost =
Expiration Cash flows S
105 call (B)
100 call (2W
95 call (1B)
Total
- cost
Net CF

11. Comments on STRATEGIES
There is no reason to keep the number of options on each leg the same, they can be in a ratio.
There is no reason to keep the expirations on each leg the same, they can be along a calendar.
There are many more, think of them as a tool kit, from which you extract what seems appropriate for a given market situations.
Most traders don’t seem to do that- they learn one or two and implement them regularly.
Brokerage houses offer strategy finders for option beginners.

12. PUT-CALL-PARITY IMPLIES THAT S + P = C + PV(X)
Recall from earlier strategy discussion that a) buying stock and a put looks like a call; b) buying stock and selling calls => writing a put. So clearly the three are related. As proof:
Using S = 75, X = 75, P = 4, C = 4.74, rates are 1% to exp, think of two strategies.
I. a) Buy Put Buy Stock; b) Buy Call AND Invest PV (X) in T-Bills
a) Cost of (a) is = $79 ; Cost of (b) is /(1.01) = $ COST EQUAL
II. Evaluate at expiration. S= 60 S= 90
a) Stock
Put
PAYOFFS THE SAME!
b) Call
Bill
PUT-CALL-PARITY IMPLIES THAT S + P = C + PV(X)

13. This holds exactly for European options since the payoff above is at expiration. For American options, because of early exercise,put-call parity holds approximately. The main message is really of linkages between stock, option and interest rate markets.
Think in terms of arbitrage. Suppose the call is priced at $4. One side of PCP is greater than the other, but both payoff the same at expiration.
Buy Put Buy Stock = > Buy Call AND Invest PV (X) in T-Bills = 78.26
So, sell the expensive side, buy the cheap side, arbitrage profit is the difference. \
Sell the put
Short the stock
Buy the call
Invest in bills
  Keep in cash per unit.
At expiration, everything washes out !

14. Once again, the strategy was
SELL PUT
SHORT STOCK
BUY CALL
INVEST IN BILLS
Suppose at expiration, the stock is below 75 (the strike price).
Call is worthless
Put gets exercised, you buy the stock for 75, using the proceeds from the T-bill, whose FV is 75
And deliver against the short.
Suppose the stock closes above strike (say at 80).
Put expires worthless
You exercise the call, buying the stock at 75 using the proceeds from the T-Bill and delivering it against the short.

15. MOTIVATING BINOMIAL PRICING
1. START WITH COVERED CALLS, S = 100, C= 7, X = 100
Say stock price increases to 110 or drops to 95 (crude volatility)
a) Buy 1 Share + write 1 Call
Cost S = S = 95 S C
b) Buy 1 Share + write 2 Calls
Cost Exp S = 110 S = 95 S C

16. c) Buy 2 Shares + write 3 Calls
Cost S = 110 S = 95 S C
What happened here!
In (a) cash flow varied with stock price change (100 or 95)
In (b) cash flow varied with stock price change (90 or 95)
In (c) cash flow SAME with stock price change (190)
(IS RISKFREE).
So investment of 179 should earn risk-free rate. Thisis the notion of a risk-free
hedge created from purchasing two shares and writing 3 calls.
DELTA OR HEDGE RATIO

17. A: BINOMIAL PRICING MODEL (FORMULA VERSION)
S = 100, X = 100, risk-free rate r = 6% (over the period). Suppose price increases to 110 or decreases to 90 (volatility).
Stock Call
110=Su u= Cu
S= C u, d = up, down
90=Sd d= Cd
Step 1: Find Hedge ratio (h) = Cu - Cd = = 1
Su - Sd –
pCu + (1-p) Cd r -d
Value of call C = , p =
(1+r) u - d
p = ( – 0.9)/( ) = 0.8
C = [0.8 * * 0]/1.06 = 7.55.

18. REVISIT NOTION OF SYNTHETICS
BY REARRANGING P-C-P
DYNAMIC HEDGING
ISLAMIC FINANCE ANYONE.