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For the following questions, use the data on Microsoft call options in the table below...

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Finance

For the following questions, use the data on Microsoft call options in the table below and assume that the repo (risk-free) rate is 4.9% per year, the maturity is in 40 calendar days (40/365 = T), and you are long 20 contracts (on 2000 shares) with strike price 130 (each costing 100* the price listed below and paying 100*max[S - 130, 0] ):

  1. What are the sigma, delta, gamma, vega, and rho of the 130 option?
  2. What transaction(s) would you need to undertake to make your total position delta-neutral (without selling the contracts)? Just use the underlying asset for this hedge.
  3. If you have the delta hedge in (b) set and the price jumps from 142.1875 down to 112.5, what will the new option price be? What will be your gain or loss on the options position? What will be your gain or loss on your position in the underlying shares? What does the difference in these two values represent?
  4. What transaction(s) would you need to undertake to make your total position delta and gamma-neutral (again without selling the calls)?
Close Strike Maturity Price
142.1875 130 40 days 16.5
142.1875 140 40 days 10.25

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