Международные валютно-кредитные отношения

Notation

• The current spot price is 𝑆𝑆0.
• The spot price at maturity ̃𝑆𝑇 is random.
• The forward price 𝐹𝑇 is fixed at time zero so that the market value of the forward contract equals zero.
• Risk-free rate is constant. Denote continuously compounded interest rate by 𝑟.

Contract	Spot now	Spot at T	Forward
Price	S0	̃𝑆𝑇	FT

Payoff diagrams of forwards

Forwards are derivative securities.
Payoffs tied to prices of underlying assets/commodities; Payoffs are linear in underlying asset price: ̃𝑆𝑇−𝐹𝑇.

Forward prices are linked to spot prices.

Forward prices

Two ways to buy the underlying asset for date-𝑇delivery:

• Buy a forward contract with maturity date 𝑇,
• Buy the underlying asset today and hold it until 𝑇.

A model of payout
Forward price
Replicating a forward
Example: a forward on a stock index
Currency forwards

• A forward contract to exchange a unit of one currency for a specified number of units of another currency.
• Example: on 7/20/2020, a forward contract to exchange one Swiss Franc for 1.10 US Dollars in July of 2023.
• Forward prices differ among contracts with different settlement dates:

Data source: CME Globex.
Pricing of currency forwards
Replication of currency forwards
Futures contracts: main characteristics

• A futures contract is an exchange-traded, standardized, forward-like contract that is marked to market daily.
• Standardized contracts:
• Underlying commodity or asset,
• Quantity,
• Maturity.
• Settlement: physical delivery or cash.

Trading of futures contracts