Practice Quiz 4 — Option Pricing & the Greeks
A stock trades at $100. A 1-year European call option with strike $100 is priced at $12 using Black-Scholes. The risk-free rate is 5% and the stock’s volatility is 30%.
(a) Using put-call parity, what is the price of a 1-year European put option with the same $100 strike? Show your work.
(b) Without recalculating, state whether each of the following changes (holding all else equal) would increase or decrease the call price. Answer with just the direction and one short reason.
- Volatility rises from 30% to 40%:
- Stock price drops from $100 to $90:
- Time to expiration shortens from 1 year to 6 months:
(c) A trader says: “Higher volatility is bad for option holders because it means more risk.” Is this true for the holder of a long call? Explain in one sentence.