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
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Spot now
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Spot at T
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Forward
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Price
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S0
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̃𝑆𝑇
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FT
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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:
- Settlement: physical delivery or cash.
Trading of futures contracts
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