Share on Facebook Share on Twitter Email
Answers.com

Forward price

 
Investment Dictionary: Forward Price
Home > Library > Business & Finance > Investment Dictionary

The predetermined delivery price for an underlying commodity, currency or financial asset decided upon by the long (the buyer) and the short (the seller) to be paid at predetermined date in the future.

At the inception of a forward contract, the forward price makes the value of the contract zero.

The Forward Price can be determined by the following formula:



where:
represents the current spot price of the asset
represents the forward price of the asset at time T
represents a mathematical exponential function

Investopedia Says:
Taking positions in a forward contract is a zero-sum game. For example, if Joe takes a long position in a pork belly forward agreement and Jane takes a short position in a forward agreement, any gains that Joe makes in the long position equal the losses that Jane incurs from the short position. By initially setting the value of the contract's value to zero, both parties are on equal ground at inception of the contract.

Related Links:
For those who are new to futures but want a solid understanding of them, this tutorial explains what futures contracts are, how they work and why investors use them. Futures Fundamentals
Learn how these futures are used for hedging and speculating, and how they are different from traditional futures. Getting Started in Foreign Exchange Futures


Search unanswered questions...

Enter a question here...
Search: All sources Community Q&A Reference topics

Wikipedia: Forward price
Top
Home > Library > Miscellaneous > Wikipedia
Question book-new.svg
 This article does not cite any references or sources. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. (June 2007)

The forward price (or sometimes forward rate) is the agreed upon price of an asset in a forward contract. Using the rational pricing assumption, we can express the forward price in terms of the spot price and any dividends etc., so that there is no possibility for arbitrage.

Contents

Forward Price Formula

The forward price is given by:

F = S_0 e^{(r+q)T} - \sum_{i=1}^N D_i e^{r(T-t_i)} \,

where

F is the forward price to be paid at time T
ex is the exponential function (used for calculating compounding interests)
r is the risk-free interest rate
q is the cost-of-carry
S0 is the spot price of the asset (i.e. what it would sell for at time 0)
Di is a dividend which is guaranteed to be paid at time ti where 0 < ti < T.

Proof of the forward price formula

The two questions here are what price the short position (the seller of the asset) should offer to maximize his gain, and what price the long position (the buyer of the asset) should accept to maximize his gain?

At the very least we know that both do not want to lose any money in the deal.

The short position knows as much as the long position knows: the short/long positions are both aware of any schemes that they could partake on to gain a profit given some forward price.

So of course they will have to settle on a fair price or else the transaction cannot occur.

An economic articulation would be:

(fair price + future value of asset's dividends) - spot price of asset = cost of capital

Forward price = Spot Price + cost of carry

The future value of that asset's dividends (this could also be coupons from bonds, monthly rent from a house, fruit from a crop, etc.) is calculated using the risk-free force of interest. This is because we are in a risk-free situation (the whole point of the forward contract is to get rid of risk or to at least reduce it) so why would the owner of the asset take any chances? He would reinvest at the risk-free rate (i.e. U.S. T-bills which are considered risk-free). The spot price of the asset is simply the market value at the instant in time when the forward contract is entered into. So OUT - IN = NET GAIN and his net gain can only come from the opportunity cost of keeping the asset for that time period (he could have sold it and invested the money at the risk-free rate).

let:

K = fair price
C = cost of capital
S = spot price of asset
F = future value of asset's dividend
I = present value of F (discounted using r )
r = risk-free interest rate compounded continuously
T = length of time from when the contract was entered into

Solving for fair price and substituting mathematics we get:

K = C + S - F \,

where:

C = S(e^{rT} - 1) \,

(since e^{rT} = 1 + j \, where j is the effective rate of interest per time period of T )

F = c_1 e^{r(T - t_1)} + \cdots + c_n e^{r(T - t_n)}

where ci is the i th dividend paid at time t i.

Doing some reduction we end up with:

K = (S - I)e^{rT}. \,

Forward versus Futures prices

There is a difference between forward and futures prices when interest rates are stochastic. This difference disappears when interest rates are deterministic.

In the language of stochastic processes, the forward price is a martingale under the forward measure, whereas the futures price is a martingale under the risk neutral measure. The forward measure and the risk neutral measure are the same when interest rates are deterministic.

See Musiela and Rutkowski's book on Martingale Methods in Financial Markets for a continuous time proof of this result. See van der Hoek and Elliott's book on Binomial Models in Finance for the discrete time version of this result.

See also


This entry is from Wikipedia, the leading user-contributed encyclopedia. It may not have been reviewed by professional editors (see full disclaimer)

 
 

 

Copyrights:

Investment Dictionary. Copyright ©2000, Investopedia.com - Owned and Operated by Investopedia Inc. All rights reserved.  Read more
Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Forward price".  Read more