Derivatives: Instruments whose values are derived from the prices of underlying assets

Derivatives Underlying Assets

Forward contracts Stocks

Futures contracts Stock indexes

Options Treasury bonds

Calls Currencies

Puts Commodities

Swaps Wheat, Pork Bellies

Gold, Silver

Electricity, snowfall

Denizens of derivatives markets

Arbitrageurs: Buy low – Sell HIGH … all at once– If you can buy one thing at a low price and sell

it or its equivalent at high price, do so until the prices are driven to equality

Can’t lose propositions

Hedgers: enter contracts whose winnings offset losses you would otherwise suffer

Speculators: place bets on expected price changes of underlying assets– Leverage your bets

Forward and Futures Contracts

Contract to buy (long position) or sell (short position) some amount of an underlying asset (stock,…) at a specified forward/future price on a specified delivery date.

Forward contracts: customized

Futures contracts: standard amounts and standard delivery (expiration) dates– Clearing corporations … back futures contracts

Margin account

Initial margin

Mark-to-market

Pricing Forward/Futures Contracts

PPFutures ↔ ↔ PPForward– Arbitrage makes it so: if you could sell a bundle of a

stock at a future price of $100 K and cover yourself by buying the same bundle forward at a price of $99 K … you and others would sell so much of the futures contract that you would drive PPFutures down to down to PPForward

PPFutures ↔ ↔ PPSpot

Seller of futures contract could put funds out to interest (R) or buy the bundle now at PPSpot and sell and sell it it at at PPFutures, locking in gross return of PPFuture/P/PSpot.

For Parity: (1+R) = PPFuture/P/PSpot or

PPFuture= (1+R) P= (1+R) PSpot.– The daily price of a futures contract is linked to

the price of the underlying asset.

Options: Calls and Puts

You buy an option … you pay the seller a premium up frontCall optionCall option: the right to : the right to buy a standard bundle a standard bundle of an underlying asset (stock, bond, …) at a of an underlying asset (stock, bond, …) at a specified specified strike price on (or before) a standard on (or before) a standard expiration date.Put option: right to right to sellsell a standard bundle of a standard bundle of an underlying asset (stock, bond, …) at a an underlying asset (stock, bond, …) at a specified specified strike price on (or before) a standard on (or before) a standard expiration date.– If an option is “in the money,” you’d exercise it.– If it is “out of the money,” you’d let it expire.

Pricing Options

Option Price

= Intrinsic Value + Option Premium

Intrinsic value: the extent to which an option is in the money or out of the money when it’s bought.

Option premium: An option is worth more the greater the chance it will be in the money big time– the longer it has to run– the more volatile the price of the underlying

asset