9. A prominent securities firm recently introduced a new financial product. This product, called the Best of
Question:
9. 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 five years, at which point it repays the investor the $10 cost plus 120 percent 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 1500, and if it is at 1800 in five years, a BOBOW owner will receive back $12.40= $10*[1 + 1.2* (1800/1500 − 1)]. If the S&P is at or below 1500 in 5 years, the BOBOW owner will receive back $10.
Suppose that the annual interest rate on a five-year, continuously compounded, pure-discount bond is 6 percent. Suppose further that the S&P 500 is currently at 1500 and that you believe that in five years it will be at either 2500 or 1200. Use the binomial option-pricing model to show that BOBOWs are underpriced.
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