Problem 1.2. A stock is trading at $50. An investor wants you to design her a portfolio whose value after six months will depend on the price of the stock at that time as shown in the figure below. The portfolio value varies linearly between circular markers and continues linearly to the right of the figure's bounds. How can you structure such a portfolio for her? How much will it cost her? Assume option prices are given by Black-Scholes formulas. Assume that the stock does not pay dividend and its volatility is 45%. The risk-free rate is 3% per annum with continuous compounding. Ignore transaction costs and any other fees. Assume each option is written on one stock and you can buy and sell fractional stocks, bonds, and options. To ensure that your answer is correct, check the value of the portfolio at maturity for a few values of stock price after six months. You don't need to report these checks. 1,000 900 800 700 600 Portfolio Value After Six Months 500 400 300 200 100 10 20 30 40 50 60 70 80 90 100 Stock Price After Six Months Problem 1.2. A stock is trading at $50. An investor wants you to design her a portfolio whose value after six months will depend on the price of the stock at that time as shown in the figure below. The portfolio value varies linearly between circular markers and continues linearly to the right of the figure's bounds. How can you structure such a portfolio for her? How much will it cost her? Assume option prices are given by Black-Scholes formulas. Assume that the stock does not pay dividend and its volatility is 45%. The risk-free rate is 3% per annum with continuous compounding. Ignore transaction costs and any other fees. Assume each option is written on one stock and you can buy and sell fractional stocks, bonds, and options. To ensure that your answer is correct, check the value of the portfolio at maturity for a few values of stock price after six months. You don't need to report these checks. 1,000 900 800 700 600 Portfolio Value After Six Months 500 400 300 200 100 10 20 30 40 50 60 70 80 90 100 Stock Price After Six Months