# Options Introduction Finance 30233, Fall 2011 Advanced Investments S. Mann The Neeley School at TCU Call and put option contracts Notation Definitions.

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Options Introduction Finance 30233, Fall 2011 Advanced Investments S. Mann The Neeley School at TCU Call and put option contracts Notation Definitions Graphical representations (payoff diagrams)

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

"Moneyness" Kasset price (S) Call “moneyness” Out of the money in the money (S K) 0 Call value Put “moneyness” 0 in the moneyout of the money (S K) Kasset price (S) Put value

Call value at maturity Value 5 0 K(K+5)S(T) Call value = max (0, S(T) - K) c (S(T),0,K) = 0 ; S(T) < K S(T) - K ; S(T)  K

Short position in Call: value at maturity Value 0 -5 K(K+5)S(T) Short call value = min (0, K -S(T)) 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

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

Put value at maturity Value 5 0 (K-5) K S(T) Put value = max (0, K - S(T)) p(S(T),0,K) = K - S(T) ; S(T)  K 0 ; S(T) > K

Short put position: value at maturity Value 0 -5 (K-5) K S(T) Short put value = min (0, S(T)-K) 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 0 ; S(T) > K

Put profit at maturity Value 0 K S(T) 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 Profit is value at maturity less initial price paid.

Option values at maturity (payoffs) 0 K K K K 00 0 long call short put long put short call

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

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

European Put-Call parity European Put-Call parity: S(0) + p[S(0),T;K] = c[S(0),T;K] + KB(0,T) Value at expiration Positioncost nowS(T)  KS(T) > K Portfolio A: Stock S(0) S(T)S(T) putp[S(0),T;K]K - S(T)0 total A:S + PKS (T) Portfolio B: Callc[S(0),T;K]0S(T) - K BillKB(0,T)KK total B:C + KB(0,T)KS(T)

Bull Spread: value at maturity S(0) = \$50value at maturity position:S(T)  45 45  S(T)  50 S(T) > 50 Long call with strike at \$450S(T) - 45 S(T) -45 Short call w/ strike at \$5000- [ S(T) - 50] net:0S(T) -45 5 4045505560 S(T) Position value at T 10 5 0

Bear Spread: value at maturity S(0) = \$30value at maturity position:S(T)  25 25  S(T)  35 S(T) >35 Long call with strike at \$3500 S(T) -35 Short call w/ strike at \$250-[S(T) - 25]- [ S(T) -25] net:025 - S(T) -10 2025303540 S(T) Position value at T 0 - 5 -10

Butterfly Spread: value at maturity S(0) = \$50value at maturity position: S(T)  45 45  S(T  50 50  S(T)  55 S(T) > 55 Long call, K= \$450 S(T) - 45 S(T) - 45 S(T) - 45 Short 2 calls, K= \$500 0 -2 [S(T) - 50]-2[S(T) - 50] Long call, K = \$5500 0 S(T) - 55 net:0 S(T) -45 55 - S(T) 0 4045505560 S(T) Position value at T 10 5 0

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= \$2525 - S(T) 0 net:25 - S(T)S(T) - 25 1520253035 S(T) Position value at T 10 5 0 Bottom straddle: call strike > put strike: put K = 23; call K = 27 straddle Bottom straddle

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