08-forward-future-swap.Rmd

# 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)