Pricing and Valuation of Forward Contracts

50 questions available

Principles of Forward Pricing and Valuation5 min
A forward contract locks in a price today for a transaction in the future. At the inception of the contract (t=0), the value to both parties is zero. The Forward Price (F0) is set such that no upfront payment is required. This price essentially represents the future value of the spot price, compounded at the risk-free rate. If the underlying asset incurs storage costs or provides income (like dividends), these must be factored into the price. Specifically, present value of benefits is subtracted from the spot price, and present value of costs is added, before compounding.

Key Points

  • Value at initiation (V0) is zero.
  • Forward Price F0(T) = S0(1+r)^T for assets with no cash flows.
  • Net Cost of Carry adjusts the Spot Price before compounding.
  • Benefits (I) reduce the Forward Price; Costs (C) increase it.
Mark-to-Market Valuation5 min
As time passes and market conditions change, the forward contract accumulates value. The value of a long forward position at any time t prior to maturity is the current spot price minus the present value of the original forward price. Alternatively, it can be viewed as the present value of the difference between the current market forward price and the original contract price. At expiration, the value is simply the difference between the spot price at maturity and the contract price (St - F0).

Key Points

  • Vt (Long) = St - PV(F0).
  • Value changes as Spot Price (St) and interest rates change.
  • At expiration, Payoff = St - F0.
  • If St > F0, the long position has a positive value.
Forward Rate Agreements (FRA)5 min
FRAs are derivatives where the underlying asset is an interest rate. They allow participants to lock in a future interest rate for borrowing or lending. A 'Long' position corresponds to the borrower (gains if rates rise), while a 'Short' position corresponds to the lender (gains if rates fall). The contract notation 'A x B' defines the timing: the contract expires in A months, and the underlying loan period ends at B months. The payoff is based on the difference between the market reference rate at expiration and the contract rate, adjusted for the loan period.

Key Points

  • Long FRA = Right/Obligation to borrow at fixed rate.
  • Short FRA = Right/Obligation to lend/invest at fixed rate.
  • Notation: A x B means contract expires in A, loan matures in B.
  • Payoffs are driven by the direction of interest rate movements.

Questions

Question 1

What is the value of a forward contract to the long position at the initiation of the contract?

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Question 2

Which formula correctly represents the basic forward price F0(T) for an asset with no costs or benefits?

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Question 3

If an investor holds a long forward position, how is the settlement amount at maturity calculated?

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Question 4

Which of the following best describes the 'Mark-to-Market' (MTM) value of a forward contract?

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Question 5

How do storage costs associated with holding an underlying asset affect the forward price?

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Question 6

In the context of forward pricing, what does 'I' represent in the formula involving (S0 - PV(I) + PV(C))?

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Question 7

Calculate the Forward Price for a 1-year contract given: Spot Price = 100, Risk-Free Rate = 5 percent, No other costs or benefits.

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Question 8

An investor enters a long forward contract with a forward price of 50. At expiration, the spot price is 45. What is the value of the contract to the investor?

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Question 9

What does a '2 x 5 FRA' imply about the timing of the underlying loan?

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Question 10

In a Forward Rate Agreement (FRA), who is the 'Long' position?

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Question 11

If interest rates increase, which party benefits in a Forward Rate Agreement (FRA)?

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Question 12

How is the value of a forward contract calculated during its life (at time t, before maturity T)?

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Question 13

A forward contract was initiated with a price of 110. The current spot price is 130. The remaining time to maturity is 0.4 years and the risk-free rate is 10 percent. What is the approximate value of the contract?

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Question 14

What is 'Bootstrapping' in the context of interest rate forwards?

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Question 15

Which formula represents the interest rate parity for pricing FX Forwards (using continuous compounding as per the provided text)?

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Question 16

What is the relationship between Forward Price (F0) and Spot Price (S0) if the Net Cost of Carry (Benefits - Costs) is positive?

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Question 17

What is the duration of the loan underlying a 3 x 6 FRA?

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Question 18

Given Spot Price = 200, PV of Dividends = 5, PV of Storage Costs = 2, Risk-Free Rate = 0 percent (for simplicity). What is the Forward Price?

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Question 19

What does the term 'Convenience Yield' refer to in forward pricing?

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Question 20

Which of the following describes a 'Synthetic FRA'?

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Question 21

For a Short Forward position, how is the value at expiration (VT) calculated?

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Question 22

If a forward contract is priced correctly at initiation, what should be its Net Present Value (NPV)?

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Question 23

Which factor effectively reduces the Forward Price of an equity index?

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Question 24

What is the primary underlying asset in an Interest Rate Forward?

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Question 25

How is the settlement amount of an FRA typically paid?

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Question 26

If the Spot Price is 150 and the Forward Price is 155, what is the implied relationship?

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Question 27

In the valuation formula Vt = St - F0 / (1+r)^(T-t), what does the term F0 / (1+r)^(T-t) represent?

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Question 28

Calculate the value of a long forward position if Spot = 105, Original Forward Price = 100, Remaining Time = 0 (Expiration).

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Question 29

What happens to the value of a Short Forward position if the spot price of the underlying asset decreases?

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Question 30

Why do FX Forwards use the formula involving e^(rf - rd)T?

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Question 31

What is the key difference between a Forward contract and a Futures contract regarding value realization?

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Question 32

Which instrument provides a hedge against rising interest rates for a borrower?

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Question 33

If a 1-year forward contract on a non-dividend paying stock is priced at 105 and the spot price is 100, what is the implied risk-free rate?

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Question 34

When calculating the value of a forward contract, why is the term (T-t) used in the discount factor?

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Question 35

A 'Short' FRA position is equivalent to:

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Question 36

If the forward price is currently 120 and the original forward price locked in was 110, is the value positive or negative for the long position?

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Question 37

What is the Discount Factor (DF) for a period i given spot rate zi?

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Question 38

In the FRA diagram for a '1 x 3 FRA', when does the borrowing effectively occur?

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Question 39

If a company expects to receive a foreign currency payment in 6 months, how can they hedge the currency risk using forwards?

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Question 40

What is the relationship between forward rates and spot rates used in Bootstrapping?

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Question 41

Which formula is used to convert forward pricing to a value Vt during the contract's life involving benefits (I) and costs (C)?

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Question 42

What is the value of a Forward Rate Agreement at initiation?

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Question 43

If a 2x5 FRA has a rate of 4 percent, and at expiration the 3-month market rate is 5 percent, what is the outcome for the Long position?

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Question 44

What does a negative value for a long forward contract indicate?

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Question 45

How can a synthetic 'Short' forward position be created?

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Question 46

In the pricing of an equity forward, how are dividends typically handled?

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Question 47

If the risk-free rate increases, what happens to the value of an existing Long forward contract (assuming spot price stays constant)?

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Question 48

What is the settlement price of a forward contract usually based on?

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Question 49

Which notation represents the Forward Rate implied between period A and period B?

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Question 50

If a forward contract has a value of 0 at initiation, what can be said about the Forward Price relative to the Spot Price if interest rates are positive and there are no benefits/costs?

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