Suppose you are a portfolio manager and you are going to use derivatives to construct certain...

     

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Suppose you are a portfolio manager and you are going to use derivatives to construct certain portfolio. The current stock price for AAPL is $171.01 per share, at 10 am, March 8, 2019. You want to sell 1 unit of European Call on AAPL, with strike of $180 and maturity of 1 year. Suppose the annualized interest rate is 3%, the annualized drift for AAPL is 5%, no dividend, and the annualized volatility is 10%. In order to hedge the potential risk of your option, you are going to calculate several Greeks based on Black Merton-Scholes model. Suppose you are doing a monthly Delta-Hedge, that is, you re-hedge per month. After one month, at 10 am, April 8, 2019, the stock price is $180.2, and you want to re-hedge right now. Calculate the additional amount of shares of AAPL you should buy (positive for buying, negative for selling) at 10 am, April 8, 2019, in order to re-hedge. Think about why you are selling or buying stocks when the stock price goes up from the meaning of Delta Hedging. In your calculation, all results should round to four digits, and you should use the convention that 0.00005 will be rounded up to 0.0001. Calculate the change of your portfolio value (i.e. the net cashflow). Note that your answer should be in $ with new portfolio value minus previous value, in present value at 10 am, April 8, 2019. In your calculation, all results should round to four digits, and you should use the convention that 0.00005 will be rounded up to 0.0001. D. Suppose the market actually has a volatility skew: a(K) min{1, 18K-¹} Calculate your portfolio V again, at 10 am, March 8, 2019. Think about why the portfolio value goes higher or lower after we assume the volatility skew in the market. In your calculation, all results should round to four digits, and you should use the convention that 0.00005 will be rounded up to 0.0001. Suppose you are constructing another portfolio by buying a digital European Call on AAPL with strike 180 and selling a digital European Call on AAPL with strike 185. Calculate your portfolio value W, at 10 am, March 8, 2019. In your calculation, all results should round to four digits, and you should use the convention that 0.00005 will be rounded up to 0.0001. Suppose you are a portfolio manager and you are going to use derivatives to construct certain portfolio. The current stock price for AAPL is $171.01 per share, at 10 am, March 8, 2019. You want to sell 1 unit of European Call on AAPL, with strike of $180 and maturity of 1 year. Suppose the annualized interest rate is 3%, the annualized drift for AAPL is 5%, no dividend, and the annualized volatility is 10%. In order to hedge the potential risk of your option, you are going to calculate several Greeks based on Black Merton-Scholes model. Suppose you are doing a monthly Delta-Hedge, that is, you re-hedge per month. After one month, at 10 am, April 8, 2019, the stock price is $180.2, and you want to re-hedge right now. Calculate the additional amount of shares of AAPL you should buy (positive for buying, negative for selling) at 10 am, April 8, 2019, in order to re-hedge. Think about why you are selling or buying stocks when the stock price goes up from the meaning of Delta Hedging. In your calculation, all results should round to four digits, and you should use the convention that 0.00005 will be rounded up to 0.0001. Calculate the change of your portfolio value (i.e. the net cashflow). Note that your answer should be in $ with new portfolio value minus previous value, in present value at 10 am, April 8, 2019. In your calculation, all results should round to four digits, and you should use the convention that 0.00005 will be rounded up to 0.0001. D. Suppose the market actually has a volatility skew: a(K) min{1, 18K-¹} Calculate your portfolio V again, at 10 am, March 8, 2019. Think about why the portfolio value goes higher or lower after we assume the volatility skew in the market. In your calculation, all results should round to four digits, and you should use the convention that 0.00005 will be rounded up to 0.0001. Suppose you are constructing another portfolio by buying a digital European Call on AAPL with strike 180 and selling a digital European Call on AAPL with strike 185. Calculate your portfolio value W, at 10 am, March 8, 2019. In your calculation, all results should round to four digits, and you should use the convention that 0.00005 will be rounded up to 0.0001.

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1To calculate the additional amount of shares of AAPL you should buy at 10 am April 8 2019 in order to rehedge we need to calculate the delta of the European Call option The delta represents the chang... View the full answer