Question

Consider a variable that is not an interest rate: (a) In what world is the futures price of the variable a martingale? (b) In what world is the forward price of the variable a martingale? (c) Defining variables as necessary, derive an expression for the difference between the drift of the futures price and the drift of the forward price in the traditional riskneutral world. (d) Show that your result is consistent with the points made in Section 5.8 about the circumstances when the futures price is above the forward price.

   Consider a variable that is not an interest rate:
(a) In what world is the futures price of the variable a martingale?
(b) In what world is the forward price of the variable a martingale?
(c) Defining variables as necessary, derive an expression for the difference between the drift of the futures price and the drift of the forward price in the traditional riskneutral world.
(d) Show that your result is consistent with the points made in Section 5.8 about the circumstances when the futures price is above the forward price.

Options, Futures, and Other Derivatives

John C. Hull 10th Edition

Chapter 28, Problem 17

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In this world, the expected future value of the futures price is equal to the current value of the futures price, discounted at the risk-free rate. This implies that there is no drift in the futures price, and any changes in the futures price are solely due to Show more…

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Consider a variable that is not an interest rate: (a) In what world is the futures price of the variable a martingale? (b) In what world is the forward price of the variable a martingale? (c) Defining variables as necessary, derive an expression for the difference between the drift of the futures price and the drift of the forward price in the traditional riskneutral world. (d) Show that your result is consistent with the points made in Section 5.8 about the circumstances when the futures price is above the forward price.

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