The current stock price of a non-dividend-paying stock is $80. The exercise (or strike) price is $85, the risk-free rate is 5 percent per year with continuous compounding, the volatility (or standard deviation) is 40 percent per year, and the time to maturity is 9 months. Assume that the call and put options have the same underlying asset, the same exercise price, and the same expiration date.

a) Find the value of the European call option on the stock. Also, find the value of the European put option on the stock.

b) Find the delta, theta (per calendar day and per trading day), gamma, vega, and rho of the European call option on the stock.

c) Find the delta, theta (per calendar day and per trading day), gamma, vega, and rho of the European put option on the stock