10. (Repeat for puts) On December 1, the S&P 500 index (SPX) is trading at 1396.71. The prices of put options on the index expiring on March 16 (i.e., a little over three months) are as follows:
| Strike K | Put Prices |
| 1300 | 11.20 |
| 1350 | 17.30 |
| 1400 | 30.50 |
Assuming the interest rate for that period is 4.88%, and the annual dividend rate on the SPX is 1.5%, compute the implied volatility for each of the options using the Black-Scholes formula. Are these volatilities the same? Explain. Also, are these volatilities the same as that obtained from the previous question? Should they be? Explain.
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