(a) Given the standard Brownian Motion variable W. Evaluate E[5W+-s + W Wt-s), where t>s [8] (b) Three 3-month European put options with strike prices of $40, $60, and $80 cost $2, $4, and $7, respectively. (i) What is the maximum gain when a butterfly spread is created from the put options? (ii) What is the maximum loss when a butterfly spread is created from the put options? (iii) For what two values of St does the holder of the butterfly spread breakeven with a profit of zero, where Spis the final stock price in three months? (a) Given the standard Brownian Motion variable W. Evaluate E[5W+-s + W Wt-s), where t>s [8] (b) Three 3-month European put options with strike prices of $40, $60, and $80 cost $2, $4, and $7, respectively. (i) What is the maximum gain when a butterfly spread is created from the put options? (ii) What is the maximum loss when a butterfly spread is created from the put options? (iii) For what two values of St does the holder of the butterfly spread breakeven with a profit of zero, where Spis the final stock price in three months