Assume the Black-Scholes framework. You are given: (i) The current price of a nondividend-paying stock is 50.
Question:
Assume the Black-Scholes framework. You are given:
(i) The current price of a nondividend-paying stock is 50.
(ii) The stock’s volatility is 30%.
(iii) The continuously compounded risk-free interest rate is 8%.
(iv) The following information about two European call options on the stock:
In each of the following cases, calculate the amount of the net investment you make today (including the sale of the 1,000 options in the first place):
(a) You have just sold 1,000 units of Call A. You immediately delta-hedge your position with shares of the stock.
(b) You have just sold 1,000 units of Call A. You immediately delta-hedge and gamma-hedge your position with shares of the stock and Call B.
(c) You are now further given that Call A is 50-strike and Call B is 60-strike, and both of them are 18-month call options. You have just sold 1,000 units of a 50-strike put otherwise identical to Call A. You immediately delta-hedge and theta-hedge your position with Call A and Call B.
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