You purchased an American up-and-out barrier put option some time ago in an over the counter market to hedge an underlying equity position. You have been assigned the job of determining its value. The option is on TTT with a strike price of $52, however, if the value of TTT ever exceeds $54 the option ceases to exist. The remaining term to maturity of the option is 3 months, the risk-free rate is 10% p.a. (continuously compounded) and TTT has a volatility of 40%. The TTT share price is currently $50 per share. TTT has just paid a full year dividend and is not expected to pay another dividend in the next 3 months. To calculate the value of the option you think it is prudent to use a number of different techniques to ensure that you get a reasonable answer. Calculate the value of the option using the following techniques: (a) Analytically assuming that the option is European rather than American. Clearly state the formula and the calculations. Hint: You may want to research for the analytical expression of such an option