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5 Options 1. Total: 20 points. An investor just traded in the options markets of SP500. They constructed a portfolio with the following payout exactly one year from today. St denotes the price of one share of SP500 at that time. Payout at T $200,000 $100,000 $0 3000 3100 3200 3300 3400 ST -$100,000 (a) 10 points. How much did the investor spend on this portfolio? Current prices of options written on one share in the SP500 are listed below. Pay close attention to the units on the vertical axis of the payout graph! Strike K Call Price Put Price 2800 2900 3000 3100 3200 3300 3400 592.20 538.99 489.67 444.11 402.14 363.60 328.30 264.34 310.14 359.82 413.26 470.30 530.76 594.47 (b) 6 points. Suppose the dividend yield of the SP500 is zero and the continuously com- pounded risk-free interest rate is 1%. What must be the current value of the SP500? (c) 4 points. Six months after the investor entered the options portfolio market volatility has increased considerably. What, if anything, can you say about the value of the options portfolio relative to what it was initially? 5 Options 1. Total: 20 points. An investor just traded in the options markets of SP500. They constructed a portfolio with the following payout exactly one year from today. St denotes the price of one share of SP500 at that time. Payout at T $200,000 $100,000 $0 3000 3100 3200 3300 3400 ST -$100,000 (a) 10 points. How much did the investor spend on this portfolio? Current prices of options written on one share in the SP500 are listed below. Pay close attention to the units on the vertical axis of the payout graph! Strike K Call Price Put Price 2800 2900 3000 3100 3200 3300 3400 592.20 538.99 489.67 444.11 402.14 363.60 328.30 264.34 310.14 359.82 413.26 470.30 530.76 594.47 (b) 6 points. Suppose the dividend yield of the SP500 is zero and the continuously com- pounded risk-free interest rate is 1%. What must be the current value of the SP500? (c) 4 points. Six months after the investor entered the options portfolio market volatility has increased considerably. What, if anything, can you say about the value of the options portfolio relative to what it was initially