- CFA Exams
- 2023 Level I
- Topic 7. Derivatives
- Learning Module 52. Pricing and Valuation of Forward Contracts and for an Underlying with Varying Maturities
- Subject 2. Pricing and Valuation of Forward Contracts

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##### Subject 2. Pricing and Valuation of Forward Contracts PDF Download

**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)

where S

_{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

The forward price at initiation is:

_{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}

**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).

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**User Contributed Comments**
10

User |
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 |

Katek |
I still don't get why the benefits have been subtracted, can anyone explain? |

breh |
benefits need to be subtracted because a forward contract implies owning the underlying stock in the future date for the long side, thus any benefits before the expiration date are missed, and any cost in between is avoided. The missed benefits therefore devalue the contract and avoided cost increases the value on the opposite. |

I used your notes and passed ... highly recommended!