A European put option provides the right to sell a stock at a pre-specified strike price at maturity date
− . The Black-Scholes equation for pricing a put option is given as follows:
= (− 2
− ( − ) − (− 1
) + ( +
) ( − )]
2 = 1 − √ −
a) You want to know the correct price for a put option with 26 weeks until expiration (assume 52
weeks in a year). The current stock price is = $20.50, and the strike price on the put option is
= $19. The stock has an annualized volatility of = 0.20 and the corresponding annual riskfree
rate is = 0.03. What is the correct price for this put option?
b) What is the price of a call option on the same underlying stock with the same maturity and
strike price? Why is the call option more expensive than the put option?
c) Suppose that you own 900 put option contracts, where each contract represents 100 shares.
What is your delta position? How many shares do you need to buy or sell to achieve delta
neutrality? For this question, you will first need to calculate the delta of a put option, which is
given as follows:
Δ = − (− 1)
d) Assume the option position and delta-neutral share position from part (c). Following an earnings
announcement on that day, uncertainty in the stock price skyrockets to = 0.40. The stock
price, however, remains unchanged ( = $20.50). Calculate the new delta position following
this change in uncertainty. How many shares do you need to buy or sell (relative to your share
position from part (c)) to achieve delta neutrality?