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At what stock price at maturity will you break even

Problem 1. Currently, a stock price is $47. Over each of the next 2 6-month periods it is expected to go up by 15% or down by 15%. The risk-free rate is 6% per annum with continuous compounding. What is the value of a 1-year European call option with a strike price of $50?

Problem 2. Suppose that put options on a stock with strike prices $35 and $45 cost $1 and $5, respectively. Use these options to create a bear spread. At what stock price at maturity will you break even?

Problem 3. A stock price is currently $70. Over each of the next two three-month periods it is expected to go up by 8% or down by 6%. The risk-free rate is 4% per annum with continuous compounding. What is the value of a six-month European put option with a strike price of $72?

Problem 4. Currently, a stock price is $100. It is known that at the end of 3 months it will be either $95 or $120. The risk-free rate is 13% per annum with continuous compounding. What is the value of a 3-month European put option with a strike price of $107?

Problem 5. A manager in charge of a portfolio worth $500,000 is concerned that the market might decline rapidly during the next 3 months. He would like to use index options as a hedge such that his hedged value is constant if S&P 500 falls below 1000. The S&P 500 is standing at 1200 and his portfolio beta is 1.2. The risk-free rate is 8% per annum and the dividend yield on both the index and the portfolio is 2% per annum. His choice of option is put option on S&P 500 with a strike price of 1000. How many put option contracts does he have to buy and what is the lowest hedged value that the manager can expect in 3 months?

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## Q : Determine present value of the future amount

Given some amount to be received several years in the future, if the interest rate increases, the present value of the future amount will be