An investor buys a put and a call on a stock. Currently the stock is trading at $50 and the volatility of stock is 25%. The strike price of the both the put and call is $50. The options expire in 3 months and the risk free rate is 1%.
N(0.0825)= 0.532875
N(-0.0825)= 0.467125
N(-0.0175)= 0.493019
N(0.0175)= 0.506981
N(0.1825)= 0.572405
N(0.1825)= 0.427595
N(-0.0425)= 0.48305
N(0.0425)= 0.51695
N(-0.1425)= 0.443343
N(0.1425)= 0.556657
N(0.0575)= 0.522927
N(-0.0575)= 0.477073
N(0.3963)= 0.654045
N(-0.3963)= 0.345955
N(0.2963)= 0.616486
N(-0.2963)= 0.383514
N(0.4963)= 0.690147
N(-0.4963)= 0.309853
N(0.2713) 0.606907
N(-0.2713)= 0.393093
N(0.1713) 0.567993
N(-0.1713)= 0.432007
N(0.3713) 0.64478
N(-0.3713)= 0.35522
a. What is the delta of the portfolio?
b. What is the gain or loss on the portfolio is the stock price increases by $2?
c. Is delta hedging sufficient to hedge the portfolio in (a)? Explain your answer