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Lecture notes on Option Markets
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This document is all lecture notes, regarding option markets, combined.
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Option marketsThe Option Contract
Call option Put option
Gives its holder the right to purchase an asset Gives its holder the right to sell an asset for a
for a specified price, called the exercise or specified exercise or strike price on or before
strike price, on or before some specified date. some expiration date.
Sellers are said to write calls. Sellers are said to write puts.
Call holder will exercise only if the price of the Put will only be exercised if the price of the
underlying asset is more than exercise price. under lying asset is less than the exercise price.
X = $105
S0 = $101.51
ST = ?
C0 = $1.45
P0 = $4.79
The purchase price of the option is called the
premium.
It represents the compensation the call holder
pays to the call writer that gives them the right
to exercise the option.
,Market and Exercise Price Relationships
• In the money occurs when exercise would produce positive cash flow
o Call option is in the money when the asset price is greater than the exercise price
ST > X
o Put option is in the money when the asset price is less than the exercise price ST < X
• Out the money – exercise would result in a negative cash flow, the payoff is less than 0.
• At the money-exercise and asset prices are equal, would make a loss once the premium is
taken into consideration.
Option trading
Traded on exchanges are standardized by allowable expiration dates and exercise prices.
Each stock price contract provides the right to buy or sell 100 shares of stock.
All market participants trade in a limited and uniform set of securities. Allows for lower trading costs
and increased market liquidity.
Both in-the-money and out-of-the-money options listed.
Value of a call is lower when the exercise price is higher.
Value of a put is higher when the exercise price is higher.
American and European Options
American options allow its holder to exercise the right to purchase (if a call) or sell (if a put) the
underlying asset on or before the expiration date.
• Generally more valuable than European options
, • Most traded options in the U.S. are American-style, except foreign currency and stock index
options.
European options allow for exercise of the option only on the expiration date.
The Option Clearing Corporation
The clearinghouse for options trading places itself between the two traders (buyer or seller).
All individuals deal only with OCC, which effectively guarantees contract performance.
When an option holder exercises an option, the OCC arranges for a member firm with clients who
have written that option to make good on the option obligation.
Because the OCC guarantees contract performance, it requires option writers to post margin to
guarantee that they in turn can fulfil their obligations. Option holders do not need to post margin
because the holder will exercise only if it is advantageous to do so.
The margin required is determined in part by the amount by which the option is in-the-money.
Values of Options at Expiration – Call Holder
The value of the option at expiration equals
Payoff to call holder
𝑆𝑇 − 𝑋 𝑖𝑓 𝑆𝑇 > 𝑋
The payoff cannot be negative.
0 𝑖𝑓 𝑆𝑇 ≤ 𝑋
Where:
𝑆𝑇 is the value of the stock at expiration
X is the exercise price
Call is exercised only if 𝑆𝑇 > 𝑋
Values of Options at Expiration – Call Writer
Call writer incurs losses if the stock price is high, in which case the writer will receive a call and will
be obligated to deliver a stock worth 𝑆𝑇 for only X dollars.
Payoff to call writer:
−(𝑆𝑇 − 𝑋) if 𝑆𝑇 > 𝑋
0 if 𝑆𝑇 ≤ 𝑋
, Payoff and Profit to Call Option at Expiration
Suppose you hold a call option on FinCorp with X=$100 and FinCorp is now selling at $110. You can
exercise your option to purchase the stock at $100 and simultaneously sell the shares at the market
price of $110, clearing $10 per share. Yet if the shares fall below $100, you can sit on the option and
do nothing, realizing no further gain or loss. The option’s value increases by $1 for each dollar
increase in the stock price. The solid line is the value of the call at expiration. The dashed line in the
profit to the call holder.
Breakeven point: (ST-X)-C0 = 0
The mirror image of payoff and profit to Call Holder.
The break-even point is also $114.
Values of Options at Expiration – Put holder
Holder will not exercise the option unless the asset is worth less than the exercise price.
Value of a put option at expiration
Payoff to put holder:
0 if 𝑆𝑇 ≥ 𝑋
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