Options Introduction

1

• Options Introduction

Call and put option contracts Notation Defini
tions Graphical representations (payoff
diagrams)
Finance 30233, Fall 2007 Advanced Investments S.
Mann The Neeley School at TCU
2

• Options

Right, but not the obligation, to either buy or
sell at a fixed price over a time period
(t,T) Call option - right to buy at fixed
price Put option - right to sell at fixed
price fixed price (K) strike price, exercise
price (K X in BKM) selling an option write
the option
Notation call value (stock price, time
remaining, strike price) c ( S(t) , T-t,
K) at expiration (T) c (S(T),0,K)
0 if S(T) lt K S(T) - K if S(T) ?
K or c(S(T),0,K) max (0,S(T) - K)
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• "Moneyness"

Call moneyness
Call value
0
K asset price (S)
Out of the money in the money (S lt
K) (S gt K)
Put moneyness
Put value
0
K asset price (S)
in the money out of the money (S lt K) (S gtK)
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• Call value at maturity

c (S(T),0,K) 0 S(T) lt K
S(T) - K S(T) ? K
Value 5 0
Call value max (0, S(T) - K)
K (K5) S(T)
5

• Short position in Call value at maturity

c (S(T),0,K) 0 S(T) lt K
S(T) - K S(T) ? K short is opposite -c(S(T),0
,K) 0 S(T) lt K -S(T)-K
S(T) ? K
Value 0 -5
Short call value min (0, K -S(T))
K (K5) S(T)
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• Call profit at maturity

Call value at T c(S(T),0,K) max(0,S(T)-K)
Value 0
Call profit
Profit c(S(T),0,K) - c(S(t),T-t,K)
Breakeven point
K S(T)
Profit is value at maturity less initial price
paid.
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8

• Put value at maturity

p(S(T),0,K) K - S(T) S(T) ? K
0 S(T) gt K
Value 5 0
Put value max (0, K - S(T))
(K-5) K S(T)
9

• Short put position value at maturity

p(S(T),0,K) K - S(T) S(T) ? K
0 S(T) gt K short is opposite -p(S(T),0,K)
S(T) - K S(T) ? K 0 S(T) gt K
Value 0 -5
Short put value min (0, S(T)-K)
(K-5) K S(T)
10

• Put profit at maturity

Value 0
Put value at T p(S(T),0,K) max(0,K-S(T))
put profit
Profit p(S(T),0,K) - p(S(t),T-t,K)
Breakeven point
K S(T)
Profit is value at maturity less initial price
paid.
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Option values at maturity (payoffs)
long put
long call
0
0
K
K
short call
short put
0
0
K
K
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• European Put-Call parity Asset plus Put

Asset
K
K
K
K S(T)
Put
Asset plus European put S(0) pS(0),TK
K
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• European Put-Call parity Bond plus Call

Bond
K
K
K
K S(T)
Call
0
Bond European Call cS(0),TK KB(0,T)
K
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• European Put-Call parity

Value at expiration Position cos
t now S(T) ? K S(T) gt K Portfolio A Stock
S(0) S(T) S(T) put pS(0),TK K -
S(T) 0 total A S P K S (T)
Portfolio B Call cS(0),TK 0 S(T) -
K Bill KB(0,T) K K total B C
KB(0,T) K S(T)
European Put-Call parity S(0) pS(0),TK
cS(0),TK KB(0,T)
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Bull Spread value at maturity
S(0) 50 value at maturity position S(T)?
45 45 ? S(T)? 50 S(T) gt 50 Long call with
strike at 45 0 S(T) - 45 S(T) -45 Short
call w/ strike at 50 0 0 - S(T) -
50 net 0 S(T) -45 5
10 5 0
Position value at T
40 45 50 55 60 S(T)
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Bear Spread value at maturity
S(0) 30 value at maturity position S(T)
? 25 25 ? S(T) ? 35 S(T) gt35 Long call with
strike at 35 0 0 S(T) -35 Short call w/
strike at 25 0 -S(T) - 25 - S(T)
-25 net 0 25 - S(T) -10
0 - 5 -10
Position value at T
20 25 30 35 40 S(T)
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Butterfly Spread value at maturity
S(0) 50 value at maturity position
S(T)? 45 45 ? S(T ? 50 50 ? S(T) ? 55
S(T) gt 55 Long call , K 45 0 S(T) -
45 S(T) - 45 S(T) - 45 Short 2 calls, K
50 0 0 -2 S(T) - 50 -2S(T) - 50 Long call
, K 55 0 0 0 S(T) -
55 net 0 S(T) -45 55 - S(T)
0
10 5 0
Position value at T
40 45 50 55 60 S(T)
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Straddle value at maturity
S(0) 25 value at maturity position S(T)
? 25 S(T) gt 25 Long call, K 25
0 S(T) - 45 Long put , K 25 25 - S(T)
0 net 25 - S(T) S(T) - 25
10 5 0
straddle
Position value at T
Bottom straddle
15 20 25 30 35 S(T)
Bottom straddle call strike gt put strike put
K 23 call K 27