Organized trading of standardized option contracts began in 1973 (prior to that had existed OTC)...immediately the CBOE was a big hit...OTC options still exist and are doing very well...more customizable, higher transaction costs but most options are now traded on organized exchanges or on the newer ECNs.

Call option -gives the buyer the right to buy at a prespecified price

purchase price is called the premium

call contract is for 100 shares

value at expiration is the starting point of any investigation

value at expiration = proceeds you could get = stock price-exercise price

Profit = proceeds - original investment

Here you are betting that the underlying asset price falls.

- asset that derives its value from the value of another asset

- an agreement between two parties for the delivery of some asset at some time for some price

- unique to each contract - nonnegotiable, nontransferable, and cannot be traded

- can be customized

- very illiquid, high transaction costs

- are rarely entered into except by companies that have good credit ratings because of the high risk of default

- payoff of a long position = underlying asset price - price agreed upon

Futures - Standardized

- much more liquid than forward contracts - very active market

- payoff looks the same as forward contracts

if long: spot-original futures price

if short: original futures-spot

- if the price of the product goes up then the payoff of the long position goes up

- every contract is made with a middleman called a clearinghouse

- marked-to-market daily

- the contracts used to be settled with delivery but now more people are settling with cash which allows easier speculation

- a call gives the purchaser of the option the right but not the obligation to buy the underlying asset at an agreed upon price at either any time before expiration ( American) or at expiration (European)

- you can always walk away from a long option position thus the loss is limited to the price that you paid. (the payoff is zero if you walk away).

- A put option gives the purchaser of the option the right but not the obligation to sell the underlying asset at an agreed upon price at any time as an American or an European

- if you buy a call you profit when the underlying asset price goes up

- if you buy a put when profit when the underlying asset price goes down.

- if you "long a call" you purchased the call option and if the stock price is above the strike price then you want to exercise the option

- if you "long a put option" you are betting the market price will go down and bought the option to sell - if the stock price is below the strike price then you exercise the option

- In the money-if exercise would be profitable

- at the money-the strike price equals the asset price

- out-of-the money-if exercise would NOT be profitable

-Naked position - an option position when the owner does not own the underlying asset.

-Covered position- an option position when the owner does own the underlying asset.

- Zero sum game – all derivatives are "zero-sum" games. That means your gains come from the losses of others.

- Index options- underlying asset is an index such as the S&P 500.

-Futures options-underlying asset is the futures contract

-Commodity options- underlying asset is a commodity (ex. Pork bellies)

long a call

call price = max ( 0, stock price - strike price)

short a call

call price = min ( 0, strike price - stock price)

long a put

call price = max ( 0, strike price - stock price)

short a put

call price = min ( 0, stock price - strike price)

Hedging is the use of risk management techniques to lower the risk of the firm.

Speculating is when you are trying to profit from price movements even though it may add to the overall risk of your firm.

You should be able to read options quotes, for example from the WSJ. Also be aware of the problem of stale prices. This is when the price quoted is "stale" or out-of-date. This is because the quote is based off the last trade, not a current quote. This can lead to some apparently strange results. For example it is not rare to see prices listed for longer options that are "cheaper" than those options that are closer to maturity.

Although options have been around for a long time, the pricing of options really has only taken off since the early 1970s. Black and Scholes (1973) determined how to price call options using differential equations. Their model is based on the idea of replicating portfolios.

The bounds on the price of a call are

The upper bound is the price of stock (in English you would never buy the call option when you could buy the stock for the same price).

The lower bound is the stock price less the present value of the strike price. That is stock-PV(X) The intuition behind this is that if the call were lower than this bound, then an arbitrage opportunity would exist. For example suppose the discount rate is zero so that PV(X)=X. Let S = $25.00 and X=$15. The lowest the call option could sell at is S-X or 25-15= 10. Why? Imagine the call were selling for $8.00. Then you could buy the call, exercise the option for $15, and end up owning the $25 stock for only $23 ($8 + $15).

The Black-Scholes formula uses differential equations and to solves for this price within these bounds.

The Black-Scholes formula looks much more difficult than it really is.

Call Price = S*N(d₁) – Xe^-rtN(d₂)

Where S = the price of the underlying asset

X= the exercise price

N(d) is the cumulative standard normal distribution function

d1 = [ln (S/X) + (Rf + std²/2)*T] /[std * sqr. root of T]

d2 = d1 - std * sqr. root of T

where std = standard deviation (sigma) of the underlying asset

Although very widely used, the Black-Scholes does have some problems. Many of these are the result of the assumptions made.

Assumptions of the Black-Scholes Option Pricing Model

1. Perfect markets: no transaction costs

2. No default risk premiums

3. Stock does not pay dividends.

4. Continuous trading exists

5. The asset follows stochastic diffusion process

To the extent that these assumptions are problems, other pricing models have been developed. The most common of which is the binomial option pricing model.

Once you know what to look for, Options tend to show up all over the place.

Examples:

equity as a call position

callable bonds

covertibles

jr debt

product of financial engineering

Lyons etc that we spoke of earlier

1st issued by ML in 1985. They are zero-coupon bonds

callable, convertible, and puttable

Waste Management was underlying firm.

put option is a protective floor

simpler "new" product is aw bull certificate. Issued by many banks....esp popular in Europe

ex 70% of mkt gain but no loss.

the 70% number is called a multiplier

an "at-the money option"

multiplier =[rf/(1+rf)]/[c/s]

price that the depositor pays is in forgone interest. This interest would be paid at the end of the period. Hence discounting by 1+rf.

Book example: rf=6%

6 month at the money call=$20

Index =400

$20/400=.05 per dollar of mkt value. (this is the denominator)

CD rate is 3% per 6 months.

So the multiplier = [.03/1.03]/.05=.582.

many variations. Can have limited loss, or even set a min gain. (ie above zero)

generically this option is being purchased in forgone interest.