Options Introduction Call and put option contracts Notation Definitions Graphical representations (payoff diagrams) Finance 30233, Fall 2006 Advanced Investments S. Mann The Neeley School at TCU S.Mann, 2006

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) < K S(T) - K if S(T)  K or: c(S(T),0,K) = max (0,S(T) - K) S.Mann, 2006

"Moneyness" Call “moneyness” Call value K asset price (S) Put K asset price (S) Out of the money in the money (S < K) (S > K) Put “moneyness” Put value K asset price (S) in the money out of the money (S < K) (S >K) S.Mann, 2006

Call value at maturity c (S(T),0,K) = 0 ; S(T) < K 5 Call value = max (0, S(T) - K) K (K+5) S(T) S.Mann, 2006

Short position in Call: value at maturity c (S(T),0,K) = 0 ; S(T) < K S(T) - K ; S(T)  K short is opposite: -c(S(T),0,K) = 0 ; S(T) < K -[S(T)-K] ; S(T)  K Value -5 Short call value = min (0, K -S(T)) K (K+5) S(T) S.Mann, 2006

Call profit at maturity Call value at T: c(S(T),0,K) = max(0,S(T)-K) Value 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. S.Mann, 2006

S.Mann, 2006

Put value at maturity p(S(T),0,K) = K - S(T) ; S(T)  K 5 Put value = max (0, K - S(T)) (K-5) K S(T) S.Mann, 2006

Short put position: value at maturity p(S(T),0,K) = K - S(T) ; S(T)  K 0 ; S(T) > K short is opposite: -p(S(T),0,K) = S(T) - K ; S(T)  K Value -5 Short put value = min (0, S(T)-K) (K-5) K S(T) S.Mann, 2006

Put profit at maturity Put value at T: p(S(T),0,K) = max(0,K-S(T)) put 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. S.Mann, 2006

Option values at maturity (payoffs) long put long call K K short call short put K K S.Mann, 2006

European Put-Call parity: Asset plus Put Asset plus European put: K K K K S(T) Put Asset plus European put: S(0) + p[S(0),T;K] K S.Mann, 2006

European Put-Call parity: Bond plus Call K K K K S(T) Call Bond + European Call: c[S(0),T;K] + KB(0,T) K S.Mann, 2006

European Put-Call parity: S(0) + p[S(0),T;K] = c[S(0),T;K] + KB(0,T) Value at expiration Position cost now S(T)  K S(T) > K Portfolio A: Stock S(0) S(T) S(T) put p[S(0),T;K] K - S(T) 0 total A: S + P K S (T) Portfolio B: Call c[S(0),T;K] 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) + p[S(0),T;K] = c[S(0),T;K] + KB(0,T) S.Mann, 2006

Bull Spread: value at maturity S(0) = $50 value at maturity position: S(T) 45 45  S(T) 50 S(T) > 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 Position value at T 40 45 50 55 60 S(T) S.Mann, 2006

Bear Spread: value at maturity S(0) = $30 value at maturity position: S(T)  25 25  S(T)  35 S(T) >35 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 - 5 -10 Position value at T 20 25 30 35 40 S(T) S.Mann, 2006

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) > 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] -2[S(T) - 50] Long call , K = $55 0 0 0 S(T) - 55 net: 0 S(T) -45 55 - S(T) 0 10 5 Position value at T 40 45 50 55 60 S(T) S.Mann, 2006

Straddle value at maturity S(0) = $25 value at maturity position: S(T)  25 S(T) > 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 straddle Position value at T Bottom straddle 15 20 25 30 35 S(T) Bottom straddle: call strike > put strike: put K = 23; call K = 27 S.Mann, 2006