Footnote 1 shows that the correct discount rate to use for the real-world expected payoff in the case of the call option considered in Figure 12.1 is \(42.6 \%\). Show that if the option is a put rather than a call the discount rate is \(-52.5 \%\). Explain why the two real-world discount rates are so different.

Figure 12.1

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Stock price = $20 Stock price = $22 Option price = $1 Stock price = $18 Option price = $0