The price of a stock today is $95 and its volatility is 20%. The risk-free rate is 3%.
1. Compute the price of a European call option with a strike of $100 and a maturity of 3 months using the BSM model.
2. Compute the price of a European put option with a strike of $100 and a maturity of 3 months.
3. Using the Vega, what is the new price of the call if the volatility decreases by 2%.
4. Using the Vega, what will be the price of a put if the volatility increases by 3%.
5. Using the delta, what will be the new call price if the underlying price increases by $1.5.
6. Using the delta, what will be the price of the put is the underlying price decreases by $2.3.