Question 5

ABC is currently trading at $78 per share. Your previous calculation of the historical volatility for ABC indicated an annual standard deviation of return of 27 percent, but examining the implied volatility of several ABC options reveals an increase in annual volatility to 32 percent.

There are two traded options series that expire in 245 days as show in the following table:

	Call	Put	Call	Put
DELTA	0.6674	-0.3326	0.574	-0.426
GAMMA	0.0176	0.0176	0.019	0.019

The options have $75 and $80 strike prices respectively. The current 245-day risk-free interest rate is 4.75 percent per annum, and you hold 2,000 shares of ABC.

Construct a portfolio that is DELTA- and GAMMA- neutral using the call options written on ABC. Show all calculations.