The current price of a non-dividend paying stock is $100. Over each of the next two 3-month periods, the stock price is expected to either move up by 10% or move down by 10%. The risk-free rate is 12% per annum with continuous compounding. Now, what is the value today of a six-month American call option on the stock with a strike price of $100 if the holder has the additional option of selling this call back to its writer for $9 at the end of the first 3-month period?