Consider a stock currently trading at $81. You are looking at European options traded on this stock with a strike price of $90 and 60 days to expiration. The underlying stock volatility is 50%, and the continuously compounded risk free rate is 3%.
1. What is the value of a call option on this stock?
2. What is the value of a put option on this stock?
3. What happens to the call option price if the stock price increases to $82?
4. What is the put option delta?