Chapter 8 Forward, Future and Swap

Forward: an agreement to enter into a transaction at a pre-specified time and price

  • Underlying asset: the asset on which the agreement is based

  • Expiration date: date on which transaction will take place

  • Forward price: price at which the transaction will take place

    • Non-dividend-paying stock \(F_{0,T}=S_0e^{rT}\)

    • Stock with discrete dividends \(F_{0,T}=S_0-PV(dividends)\)

    • Stock with continuous dividends \(F_{0,T}=S_0e^{(r-\delta)T}\)

  • Forward price is set such that no up-front payment or premium need be paid by either party to the other

  • Positions in a forward contract

    • Long: party which is obligated to buy the underlying asset

    • Short: party which is obligated to sell the underlying asset

  • Payoffs to forward contract positions

    • Long-forward payoff = \(S_T-F\)

    • Short-forward payoff = \(F-S_T\)

Long position of stock

  • Outright purchase

  • Borrow to pay for stock

  • Prepaid forward contract

  • Forward contract

Synthetic forward contract

  • Long forward = Stock - Bond

  • Short forward = Bond - Stock

Arbitrage strategy

  • Forward price is too low: short forward + stock - bond (cash-and-carry)

  • Forward price is too high: long forward - stock + bond (reverse cash-and-carry)

Futures contracts

  • Traded on an exchange

  • Relatively standardized

  • More liquid

  • Marked-to-market and settled daily

Swap contracts: covers a stream of cash flows over a period of time

  • A forward is like a single-payment swap

  • The possible types of swaps are:

    • Commodity swaps

    • Foreign exchange rate swaps

    • Interest rate swaps: Parties exchange fixed and floating interest

  • Typically, the price of a swap involves a level payment. This level payment is generally calculated such that the swap initially has some specified market value (generally zero, as with a forward)