For the single-period evolution given in the preceding figure, consider an American call option with maturity 1

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For the single-period evolution given in the preceding figure, consider an American call option with maturity 1 and strike price k = $0.92 on the three-period zero-coupon bond. What is the arbitrage-free price of this call option? Is early exercise (at time 0) optimal?
Strike Price
In finance, the strike price of an option is the fixed price at which the owner of the option can buy, or sell, the underlying security or commodity.
Maturity
Maturity is the date on which the life of a transaction or financial instrument ends, after which it must either be renewed, or it will cease to exist. The term is commonly used for deposits, foreign exchange spot, and forward transactions, interest...
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