The value of the future

Quantitative Finance Level 1

How does the price of a future change as interest rate increases?

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Increases. It is more expensive to borrow money Stays constant. Interest rate has no effect Decreases. More people want to place their money in the bank Increases. More people can borrow money to buy stocks Decreases. It is more expensive to borrow money

1 solution

Calvin Lin Staff
Feb 10, 2015

Since $F = S e ^ { rt }$ , we know that as the interest rate increases, the price of the future $F$ will increase.

The tricky part of this problem is explaining why this increase will happen. Recall that the future is priced through arbitrage . In particular, we needed to borrow money at the rate of $r$ to finance the buying of the future. As $r$ increases, it becomes more expensive to borrow money, and thus the price of the future increases to account for this.

Should it not be e^-rt?

Lawrence Mayne - 5 years, 8 months ago

You're thinking of discounting the current stock price from the value of the future.

If you have $1000 right now, it would be worth more later on due to interest earned. Hence we multiply by $e^{rt} > 1$ .

Calvin Lin Staff - 5 years, 8 months ago

Shouldn't the price of Futures decrease to account for an increased interest rate to finance the buying of Futures?

Yash Shekhar - 5 years ago

Unlike stocks, there is no upfront cost to buying a futures contract .

Your brokerage might require you to post margins, but those are considered transaction costs.

Calvin Lin Staff - 5 years ago

The value of the future

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