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Options Introduction

Options Introduction. Call and put option contracts Notation Definitions Graphical representations (payoff diagrams). Finance 30233, Fall 2010 Advanced Investments S. Mann The Neeley School at TCU.

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Options Introduction

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  1. Options Introduction Call and put option contracts Notation Definitions Graphical representations (payoff diagrams) Finance 30233, Fall 2010 Advanced Investments S. Mann The Neeley School at TCU

  2. 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) : strikeprice, exercise price (K = X in BKM) selling an option: write the option Options 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)

  3. Call “moneyness” Call value "Moneyness" 0 K asset price (S) Out of the money in the money (S < K) (S > K) Put “moneyness” Put value 0 K asset price (S) in the money out of the money (S < K) (S >K)

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

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

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

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

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

  9. Value 0 Put profit at maturity 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.

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

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

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

  13. Value at expiration Position cost now S(T)  KS(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 European Put-Call parity: S(0) + p[S(0),T;K] = c[S(0),T;K] + KB(0,T)

  14. 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 0 Position value at T 40 45 50 55 60 S(T)

  15. 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 0 - 5 -10 Position value at T 20 25 30 35 40 S(T)

  16. 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 0 Position value at T 40 45 50 55 60 S(T)

  17. 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 0 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

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