You are attempting to formulate an investment strategy. In particular, you short a put option with strike price X₁ equals to $95 and you long another put option with strike price X₂ equals to $115. Both put options have the same underlying stock and will expire at time T.

(a) Plot the payoff structure of this investment strategy as a function of S_T, which stands for the price of the underlying stock at maturity. The X-axis for S_t and the Y-axis is the total payoff. [hint: you can first calculate the total payoff in the three scenarios: S_T < 100, 100 S_T 115 and S_T > 115.]

(b) given the following information:

Stock price right now S₀ = $100, X₁ = $95, X₂ = $115; the annualised risk free rate at 2%; volatility of the stock = 0.18; T equals to 5 years. The stock has a policy of not paying out any dividends. BAsed on these information, calculate the cost of establishing the above investment strategy based on the Black-Sholes model.