**Derivatives**

**Reading 49. Basics of Derivative Pricing and Valuation**

**Learning Outcome Statements**

c. explain how the value and price of a forward contract are determined at expiration, during the life of the contract, and at initiation;

d. describe monetary and nonmonetary benefits and costs associated with holding the underlying asset and explain how they affect the value and price of a forward contract;

*CFA Curriculum, 2020, Volume 6*

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### Subject 3. Pricing and Valuation of Forward Contracts

**Pricing and Valuation at Expiration**

At expiration T, the value of a forward contract to the long position is:

_{T}(T) = S

_{T}- F

_{0}(T)

_{T}is the spot price of the underlying at T and F

_{0}(T) is the forward price.

The forward price is the price that a long will pay the short at expiration and expect the short to deliver the asset.

**Pricing and Valuation at Initiation Date**

There is no cash exchange at the beginning of the contract and hence the value of the contract at initiation is zero.

_{0}(T) = 0

_{0}(T) = S

_{0}(1 + r)

^{T}

*Example*

Consider a forward contract on a non-dividend paying stock that matures in 6 months. The current stock price is $50 and the 6-month interest rate is 4% per annum. Compute the forward price, F. Solution: Assuming semi-annual compounding, F = 50 x 1.02 = 51.0.

If we add benefits ʇ (dividends, interest, and convenience yield), and costs θ the forward price of an asset at initiation becomes

_{0}(T) = S

_{0}(1 + r)

^{T}- (ʇ - θ) (1 + r)

^{T}

F = 1018.86 x 1.04

^{2}- 50 x 1.04 - 50 = $1,000

**Pricing and Valuation during the Life of the Contract**

The value of a forward contract after initiation and during the term of the contract change as the price of the underlying asset (S) changes. The value (profit/loss) of a forward contract between initiation and expiration is the current price of the asset less the present value of the forward price (at expiration).

###
**User Contributed Comments**
8

You need to log in first to add your comment. ###### lordcomas

Didn't understand the example part of the formula -50$

###### lordcomas

Never mind, got it.

###### ashish100

Can some one explain the second part of the example? Went 0 - 100 real quick.

###### grangermac

@ashish100 Yeah it did. This is just how I see it, doesn't mean I'm right haha. I assume you mean the coupon payments (-50x1.04-50). Since the bond pays semiannual coupons of $50 each, the first is payed out 6 months from the end of the contract. Therefore you must compute the forward price of this payment ( 6 months @ 8% pa. = 50x1.04). Since the last payment is made right before delivery there is no need to adjust for time value. Think a time line make it a bit more clear if that still doesn't make sense.

###### vik7868

@Grangemarc I did stuck upon this too. But you explained it really well.

###### cfashruti

In 2nd example, why the benefits have been subtracted? Aren't they supposed to be added?

###### cfashruti

Ok got it

###### TheCFAGuy

Long Position = Buy side

Short Position = Sell side