2. (8 marks For this question, you may assume that interest rates are zero. Consider a butterfly position, constructed from a put options struck at $55, $60, and $65. The market prices are $3, $5, and $8, respectively. (a) Why would a trader buy this position? (b) Discuss whether the buyer of the position could be said to be long or short in the volatility of the underlying asset if the current value of the stock is $150. (e) Describe how you might construct another position with the same Profit (P/L) diagram using call options, forward contracts and (zero-coupon) bonds. (f) Sketch the profit diagram, P/L, for the position, as functions of the value (ST) of the underlying asset at the expiry time T