Question

Show that, if $C$ is the price of an American call option on a futures contract when the strike price is $K$ and the maturity is $T$, and $P$ is the price of an American put on the same futures contract with the same strike price and exercise date, then $$ F_0 e^{-r T}-K<C-P<F_0-K e^{-r T} $$ where $F_0$ is the futures price and $r$ is the risk-free rate. Assume that $r>0$ and that there is no difference between forward and futures contracts. (Hint: Use an analogous approach to that indicated for Problem 17.12.)

   Show that, if $C$ is the price of an American call option on a futures contract when the strike price is $K$ and the maturity is $T$, and $P$ is the price of an American put on the same futures contract with the same strike price and exercise date, then
$$
F_0 e^{-r T}-K<C-P<F_0-K e^{-r T}
$$
where $F_0$ is the futures price and $r$ is the risk-free rate. Assume that $r>0$ and that there is no difference between forward and futures contracts. (Hint: Use an analogous approach to that indicated for Problem 17.12.)

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 18, Problem 19

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Step 1

To prove this, we can use a similar approach as in Problem 17.12. We can create a portfolio that consists of a long position in the call option and a short position in the put option. The value of this portfolio at time $t$ is given by $V(t) = C(t) - P(t)$. At Show more…

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Show that, if $C$ is the price of an American call option on a futures contract when the strike price is $K$ and the maturity is $T$, and $P$ is the price of an American put on the same futures contract with the same strike price and exercise date, then $$ F_0 e^{-r T}-K<C-P<F_0-K e^{-r T} $$ where $F_0$ is the futures price and $r$ is the risk-free rate. Assume that $r>0$ and that there is no difference between forward and futures contracts. (Hint: Use an analogous approach to that indicated for Problem 17.12.)

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