PS3 - Vol Q's

Question 1

Suppose that the price of a call option with strike K increases, while the price of a put option on the same underlying with strike K remains unchanged. Assuming put-call parity is not violated, and that the risk-free rate hasn’t changed, what could explain this? Assume that the options are European.

Answer 1

An increase in volatility coupled with a drop in the stock price could explain this pattern.

Question 2

Define the volatility skew and give one possible explanation for its existence.

Answer 2

Skew represents the fact that low-strike options (typically puts) are overpriced according to B-S. One reason is excess retail demand.

Question 3

What is the difference between the risk neutral probability of a state, and the stochastic discount factor associated with that state? How are they related?

Answer 3

Risk neutral probability is Q. SDF is 1/Rf x Q/P.