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Homework 5 Q1. Put-call parity a. Does put-call parity mean the put and the call option (of the same stock, with same expiration, with same strike price) have the same value/price? b. If not, for put and call to have the same prices, what must be the relationship between the strike price and the current stock price? Hint: Find the Apple option page from Yahoo Finance and look for the strike price where the call and put price are similar. Q2.A European call option and a European put option on a stock both have the same strike price of $45 and expire in 6 months. Currently, the market call price is $10 and the put price is $6. The risk-free rate is 2% per annum, and the current stock price is $49. Identify the arbitrage opportunity open to the trader. All the interest rates are with continuous compounding. Hint: Arbitrage table from the class example. Q3. Suppose the price of a non-dividend-paying stock is currently $60, its volatility is 30%, and the risk-free rate for all maturities is 2% per annum. Use Derivagem (see Session 5) and price the following 3 European \"put\" options expiring in 3 months (=3/12 years). In Derivagem, choose \"Black-Scholes - European\" for Option Type in D17 cell. a. a put with $50 exercise price b. a put with $55 exercise price c. a put with $60 exercise price Your submission must include all 3 Derivagem screenshots or the outputs. Hint: If you price a \"call\" with $55 exercise price, the price is $6.6906. See the Derivagem output below. Q4: Graph the relationship between the stock prices at expiration and the profits of a butterfly spread using 3 \"put\" options in Q3. Hint: To graph, use the same method in Homework 4 spreadsheet. Use stock prices ranging between $45 and $65 with $1 increment. Your final graphs should look similar to Figure 11.7 in the textbook. Arbitrage Opportunity Requirements 1. no negative net cash flows 2. at least 1 postive net cash flows 10.4 Put-Call Parity c + K *exp(-r*T) = p + S0 (Eq 10.6) Objective: Check the put-call parity, and find strategy with arbitrage opportunity. Table 10.3 S0 (current stock price) r (risk-free rate) K (exercise price) T (expiration) c (call price) p (put price) c + K *exp(-r*T) = p + S0 $31.00 10% $30.00 0.25 $3.00 $1.00 (Eq 10.6) Q1. Calculate the left hand side (LHS) of put-call parity Q2. Calculate the RHS Q3. Is put-call parity violated? Q4. Which side to buy and which side to sell? t=0 Actions Net CF Q5. Calculate the arbitrage free put price using put call parity (Eq 10.6) CASH FLOWS t = 0.25 if S >= 30 if S = 30 if S = 30 if S