Question

IBM stock currently sells for 64 dollars per share. The implied volatility equals 40.0. The risk-free rate of interest is 5.5 percent continuously compounded. If you shorted an option on 100 shares of IBM stock with strike price 69 and maturity 9 months, how many shares of stock would you have to buy (sell) to create a delta-neutral hedge

Answer 1

Answer:

53.19

Explanation:

$64 per share

Implied volatility = 40.0

risk-free rate of interest = 5.5%

number of shares shorted ( N ) = 100

strike price = 69

with maturity = 9 months

Calculate number of shares of stocks you have to be buy(sell) to create a delta-neutral hedge

we will apply the Black Scholes Formula

= N [ (ln(64/69) + (5.5%+(40%)^2 / 2) * (9/12)) / (40%* √(9/12)) ]

= N [ (ln(64/69) + (0.055+(0.40)^2 / 2) * (9/12)) / (0.40* √(9/12)) ]

= N * 0.5319

Number of shares to create a delta neutral hedge = 100 * 0.5319 =  53.19