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2

Your formula for $p$ is $$p = \frac{e^{{(\alpha - \delta})h} - d}{u - d},$$ where $\alpha$ is not expected return on stock but continuous risk free rate, i.e. 1%. If you use $\alpha$ as 1%, you will get $p=0.009125828$ which is within $[0,1]$ EDIT: With the information given in the question, it must satisfy following equality: S_0e^{\alpha - ...

1

you need a positive dividend rate or a negative interest rate. Without these, it is a model-free result that early exercise is never optimal for a call option.

2

I think they have expanded the third term on the LHS and simplified.

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