(Pricing a complex derivative) A prominent securities firm recently introduced a new financial product. This product, called “The Best of Both Worlds” (BOBOW for short), costs $10. It matures in 5 years, at which point it repays the investor the $10 cost plus 120% of any positive return in the S&P 500 index. There are no payments before maturity. (For example: If the S&P 500 is currently at 1,500, and if it is at 1,800 in 5 years, a BOBOW owner will receive back $12.40 = $10*[1 + 1.2*(1,800/1,500-1)]. If the S&P is at or below 1,500 in 5 years, the BOBOW owner will receive back $10).

Suppose that the annual interest rate on a 5-year, continuously compounded, pure-discount bond is 6%. Suppose further that the S&P 500 is currently at 1,500 and that you believe that in 5 years it will be at either 2,500 or 1,200. Use the binomial option pricing model to show that BOBOWs are worth more than their current price of $10.