1. Explain carefully why a distribution with a heavier left tail and less heavy right tail than the lognormal distribution gives rise to a downward sloping volatility smile.
2. The market price of a European call is $3.00 and its price given by Black-Scholes- Merton model with a volatility of 30% is $3.50. The price given by this Black-Scholes- Merton model for a European put option with the same strike price and time to maturityis $1.00.
What should the market price of the put option be? Explain the reasons for your answer.