Chapter 10
Mechanics of Options Markets
Date: 02-03-2025
1
• Types of options
• Option payoffs and profits
• Hedging with options vs hedging with futures
2
Option Basics
• Financial Option
•
A contract that gives its owner the right (but not the
obligation) to purchase or sell an asset at a fixed price (strike
price or exercise price) at some future date
• Call Option
•
A financial option that gives its owner the right to buy an
asset
• Put Option
•
A financial option that gives its owner the right to sell an
asset
• Strike Price (Exercise Price)
•
The price at which an option holder buys or sells a
share of stock when the option is exercised
Option expiration dates
• Expiration Date
•
The last date on which an option holder has the right
to exercise the option
• American Option
•
Options that allow their holders to exercise the option
on any date up to, and including, the expiration date
• European Option
Options that allow their holders to exercise the option
only on the expiration date
• The names American and European have nothing to
do with the location where the options are traded.
•
• Most options that are traded on exchanges are
American. However European options are easier
to analyze. American option properties are often
deduced from their European counterpart
Buyer and Seller of Options
• The option buyer (holder)
•
Holds the right to exercise the option and has a long
position in the contract
• The option seller (writer)
Sells (or writes) the option and has a short position in
the contract
• Because the long side has the option to exercise, the
short side has an obligation to fulfill the contract if it is
exercised.
• Margin is required from the seller when options are
transacted
•
Moneyness of options
• At-the-money
•
Describes an option whose exercise price is equal
to the current stock price
• In-the-money
•
Describes an option whose value if immediately
exercised would be positive
• Out-of-the-money
•
Describes an option whose value if immediately
exercised would be negative
Moneyness of options
7
Payoff and Profit for Holding
an Option to Expiration
• Payoffs at expiration on a long position in an
option contract are never negative.
• The Profit from purchasing an option and
holding it to expiration could be negative.
•
The Payoff at expiration might be less than the
initial cost of the option.
Payoff Long European Call
(Figure 10.1)
option price = $5, strike price = $100, option life = 2 months
Payoff ($) 30
20
10
70
0
-5
80
90
100
Terminal
stock price ($)
110 120 130
9
Profit Long European Call
(Figure 10.1)
option price = $5, strike price = $100, option life = 2 months
Profit ($)
30
20
10
70
0
-5
80
90
100
Terminal
stock price ($)
110 120 130
10
Payoff Short European Call
(Figure 10.3)
Payoff from writing one European call option:
option price = $5, strike price = $100 life=2 months
Payoff ($)
5
0
-10
-20
-30
110 120 130
70
80
90 100
Terminal
stock price ($)
Profit Short European Call
(Figure 10.3)
Profit ($)
Profit from writing one European call option:
option price = $5, strike price = $100 life=2 months
5
0
-10
-20
-30
110 120 130
70
80
90 100
Terminal
stock price ($)
Payoff Long European Put
(Figure 10.2 Question 10.11 )
Payoff from buying a European put option:
option price = $7, strike price = $70 life=2 months
Payoff ($)
30
20
10
0
-7
Terminal
stock price ($)
40
50
60
70
80
90 100
Profit Long European Put
(Figure 10.2)
Profit from buying a European put option:
option price = $7, strike price = $70
Profit ($)
30
20
10
0
-7
Terminal
stock price ($)
40
50
60
70
80
90 100
14
Payoff Short European Put
(Figure 10.4)
Payoff from writing a European put option: option
price = $7, strike price = $70
Payoff ($)
7
0
-10
-20
-30
40
50
Terminal
stock price ($)
60
70
80
90 100
Profit Short European Put (Figure
10.4)
Profit from writing a European put option:
option price = $7, strike price = $70
Profit ($)
7
0
-10
-20
-30
40
50
Terminal
stock price ($)
60
70
80
90 100
Payoffs from Options (Figure 10.5)
K = Strike price, ST = Price of asset at maturity
Long
Short
K
Call
K
Put
S
S
T
T
K
K
S
S
T
T
European Option Payoff
Hedging long position with buy Put Option
Payoff at Maturity
K
0
Long position
Buy put (K)
Floor on Inflows (K)
K
Share Price
At maturity
Hedging Long Position
Hedging a short position with long Call Option
Payoff at Maturity
K
0
K
-K
Buy at future date
Buy Call (K)
Cap on outflows
Share Price
At maturity
Hedging a long position
Hedging (Options vs Futures)
Payoff at Maturity
Hedging long position with Collar
on inflows
Payoffs at Maturity
K2
K1
K2
0
Sell at future date
Buy put (K1)
Sell Call (K2)
Collar
K1
Share Price
At maturity
Hedging long position with
Collar on inflows
Hedging a short position with collar on outflows
Payoff at Maturity
K
Buy at future date
Sell Put (K1)
Buy Call (K2)
Collar on outflows
K1
0
K2
-K1
-K2
Share Price
At maturity
Hedging a short position with
collar on outflows
Miscellaneous
Long Call Profit
Long Put Profit
Stock splits
Stock Splits
Stock Splits: Example 10.1
Stock Dividend: Put Option
Hedging a long position (sell at a future date)
with (sell) forward
Payoff
F0
0
F0
Price of Underlying
at Maturity, ST
Sell at future date
Sell forward
Lock forward price
35
Hedging a short position (buy at a future date)
with (buy) forward
Buy at a future date
Buy forward
Lock forward price
Payoff
0
F0
Price of Underlying
at Maturity, ST
-F0
36