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Suppose you are managing a stock portfolio that is currently valued at $2,000,000.




Q1. Suppose you are managing a stock portfolio that is currently valued at $2,000,000. You expect the stock market will be bullish in the next 3 months. But you are also aware of a small chance of stock market crash and you want to insure that your portfolio value will be at least $1,800,000 in 3 months no matter what happens to the market. In other words, you don?t want to suffer more than 10% loss in the next 3 months. Assume your stock portfolio has a beta of 1.0 and the current S&P500 level is 2,000.;How would you hedge against your portfolio value dropping below $1.8M in 3 months? Be as specific with the strategy but no calculation is needed.;Part B.;On 11/21/2014, The Dow Jones Industrial Average (DJIA) closed at 17,810. The DJ index option is on 1/100th of DJIA level, so S0 = 178.10. The put option with K = $175 expiring on 3/20/2015 was $4.29.;Assume the risk-free rate is 0.50%, the dividend yield is 1.50%.;^DJX&date=1426809600;Q2. Use Derivagem to calculate the implied volatility of the put option. Please include DG output.;Q3. Use put-call parity for European index options to find the arbitrage-free price of a March2015 175 call. Hint: pg 340.;Q4. Given the call price answered in Q3, use Derivagem to find the implied volatility of the call option.;Q5. Confirm that the implied volatilities in Q2 and Q4 are the same. What do you conclude about put-call parity and the implied volatility of European call and put options?;Additional Requirements;Min Pages: 1;Max Pages: 3;Level of Detail: Show all work


Paper#21778 | Written in 18-Jul-2015

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