(a) Speculators typically have a negative public image, briefly explain how allowing speculators to trade on futures exchanges is beneficial for the market.

(b) Interpret the meaning of N(-d1) and N(-d2) in the put formula of BlackScholes model if N(-d1) = 0.5111 and N(-d1) = 0.3333.

(c) A portfolio consists of a short-covered call (i.e., short stock + long call) and a protective put. Assume the naked options in these trading strategies have the same underlying asset, strike, and maturity. Explain why the portfolio is equivalent to a long straddle?

(d) A portfolio consists of a long stock (i.e., the current stock price is $100) and a long European put option on the stock with a strike price of $105. Explain why the net payoff of the portfolio is equal to or greater than $5 at maturity? (Hint: ignore the premium)

(e) A stock price is currently $100. It is known that it will be either $110 or $90 at the end of two months. The risk-free interest rate is 10% per annum with continuous compounding. Calculate the value of a two-month European call option with a strike price of $95.Using the no-arbitrage approach of the binomial tree model. (Required: Show your work step by step)