Question 20

The stock of Zebra Analytics is trading at $30. Six-month call options are available with a strike price of $27.50. The continuously compounded risk-free rate is 2.3%, and the annualized volatility of this stock is 13.5%. You own 75,000 shares of Zebra Analytics in a portfolio being managed for a pension fund. Assume each option contract is written on 100 shares. How many call options are necessary for a delta-neutral hedge, given the following abbreviated cumulative distribution table?

z	0	0.01	0.02	0.03	0.04	0.05	0.06	0.07	0.08
0.5	0.6915	0.6950	0.6985	0.7019	0.7054	0.7123	0.7157	0.7190	0.7224
0.6	0.7257	0.7291	0.7324	0.7357	0.7389	0.7422	0.7454	0.7486	0.7549
0.7	0.7580	0.7611	0.7642	0.7673	0.7704	0.7734	0.7764	0.7794	0.7823
0.8	0.7881	0.7910	0.7939	0.7967	0.7995	0.8023	0.8051	0.8078	0.8106
0.9	0.8159	0.8186	0.8212	0.8238	0.8264	0.8289	0.8315	0.8340	0.8365