Implied volatilities of the AAPL American put option

Let's consider the option data of the stock Apple (AAPL), which was gathered at the end of the day on October 3, 2014. These details are provided in the following table. The option expires on December 20, 2014. The prices listed are the mid-points of the bid and ask prices:

Strike price Call price Put price
75 30 0.16
80 24.55 0.32
85 20.1 0.6
90 15.37 1.22
92.5 10.7 1.77
95 8.9 2.54
97.5 6.95 3.55
100 5.4 4.8
105 4.1 7.75
110 2.18 11.8
115 1.05 15.96
120 0.5 20.75
125 0.26 25.8

The last traded price of AAPL was 99.62, with an interest rate of 2.48 percent and a dividend yield of 1.82 percent. The American options expire in 78 days.

Using this information, ...

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