Problem 2 (20 marks)

The following information is given about options on the stock of a certain company:

S₀ = $20, X =$20, r % (c.c.), T = 0.5 year, s= 0.20

No dividends are expected. One option contract is for 100 shares of the stock. All notations are used in the same way as in the Black-Scholes-Merton Model.

• Whatwillbethepayoffandprofitoftheprotectiveputifthestockpriceonmaturityis$16,$18,$20,$22,or$24?
• Inordertosolvethisproblemyoumustusefollowingcomments:

Problem 2 Part 4:

At T=$16

Exercise Put and sell at strike price, receive $20

Cost of Protective Put = -$20.88

Payoff = -$0.88

Use similar reasoning to complete the table at the other St values.

Problem 2 (20 marks) The following information is given about options on the stock of a certain company: S0 = $20, X =$20, r =5% (c.c.), T = 0.5 year, = 0.20 No dividends are expected. One option contract is for 100 shares of the stock. All notations are used in the same way as in the Black-Scholes-Merton Model. Answer the following questions: 1. What is the European call option price and European put option price, according to the Black-Scholes model? Input Data Stock Price now (P) Exercise Price of Option (EX) Number of periods to Exercise in years (t) Compounded Risk-Free Interest Rate (rf) Standard Deviation (annualized 20 20 0,5 5,00% 20,00% Output Data Bank Loan N(d2)*PV(EX) 19,506 2 0,1414 0,2475 0,1061 0,5977 10,576 9 Value of Call Value of Put 1,3777 0,8839 Present Value of Exercise Price (PV(EX)) *t^.5 d1 d2 Delta N(d1) Normal Cumulative Density Function Protective Put: Short Position in Stock and Long position in Put Covered Call: Long position in Stock and Short position in Call 2. What is the cost of buying a protective put? Buying a protective put: Buying a share of the stock: pay 20 Buying a put: pay 0.8839 Cost of protective put = -20 +( -0.8839) = -20.8839 3. What is the cost of writing a covered call? Writing a covered call: Writing a call: receive premium1.3777 Buying a share of the stock: pay 20 Cost of writing a covered call = -20 + 1.3777 = -18,6223 4. What will be the payoff and profit of the protective put if the stock price on maturity is $16, $18, $20, $22, or $24? Problem 2 Part 4: At T=$16 Exercise Put and sell at strike price, receive $20 Cost of Protective Put = -$20.88 Payoff = -$0.88 Use similar reasoning to complete the table at the other St values