You use the following information to construct a binomial forward tree for modeling the price movements of a stock:

(i) The length of each period is 1 year.

(ii) The current stock price is 200.

(iii) The stock’s volatility is 30%.

(iv) The stock pays dividends continuously at a rate proportional to its price. The dividend yield is 3%.

(v) The continuously compounded risk-free interest rate is 5%.

Consider a special 3-year geometric average price European 180-250 collar with the average calculated based on yearly closing stock prices and a double barrier feature. The collar is knocked out whenever either the upper barrier of 300 or the lower barrier of 150 is crossed over the life of the collar.

Calculate the price of this special collar.