# Lecture13 - Fundamentals of Options

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Basics Buy Call at Expiration Inputs Buy or Sell: 1 = Buy, -1 = Sell 1 Option Type: 1=Call, 2=Put 1 Exercise (Strike) Price \$40.00 Option Price (Premium) \$5.00 red line - option profit blue line - option payof Outputs Stock Price At Maturity \$0.00 \$8.00 \$16.00 \$24.00 \$32.00 \$40.00 \$48.00 \$56.00 \$64.00 \$72.00 \$80.00 Option Payoff \$0.00 \$0.00 \$0.00 \$0.00 \$0.00 \$0.00 \$8.00 \$16.00 \$24.00 \$32.00 \$40.00 Option Profit -\$5.00 -\$5.00 -\$5.00 -\$5.00 -\$5.00 -\$5.00 \$3.00 \$11.00 \$19.00 \$27.00 \$35.00 Key points 1. Observe profit patterns for buyer and seller of a call 2. Observe profit patterns for buyer and seller of a put 3. Find breakeven price for the buyer of call or put option 4. Change option price, observe changes in payoff and profit and break even price O PTION P AYOFFS AND P ROFITS \$0 \$10 \$20 \$30 \$40 \$50 \$60 \$70 \$80 -\$40 -\$20 \$0 \$20 \$40 Option Payoffs and Profits Stock Price At Maturity Payoff and Profit Suppose an option to buy o sell a single share costs \$5 And the exercise price in th option contract is \$40. Wha are the option's payoffs and profit if it is held to maturity For option bought: Option Profit = Option P For option sold (written Option Profit = Option P
ff <--see formula <-see formula or 5.00. he at d Payoff - premium n): Payoff + premium
Call Option Payoff Patterns Time 0 Time T Put Option Payoff Patterns Time 0 Time T Purchase call option, cash flow < 0 Terminal call payoff, Max[S T - K,0] > 0 Between times 0 and T: Cash flow = 0 for European option Cash flow > 0 for American option Write (I.e., issue) call option, cash flow > 0 Pay terminal call payoff = - Max[S T - K, 0] < 0 Between times 0 and T: Cash flow = 0 for European option Cash flow < 0 for American option Purchase put option, cash flow < 0 Terminal put payoff, Max[K - S T ,0] > 0 Between times 0 and T: Cash flow = 0 for European option Cash flow > 0 for American option Write (i.e., sell) call option, cash flow > 0 Pay terminal call payoff = - Max[K - S T , 0] < 0 Between times 0 and T: Cash flow = 0 for European option Cash flow < 0 for American option