Lecture outline

Portfolio Theory and
Investment Analysis

• Options contracts
• Pricing of the options contract
• Investment strategies with options

Lecture 8:
Financial Derivatives Options contracts
BKM: Chapters 20&21
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2

Options Contracts

1. Options contract
Learning objectives
• Understand the basic terminology with options contracts.
• Be able to calculate the profit/loss to various options positions as a function of ultimate security prices.

• An option contact gives its holder the right to buy or sell a specified asset at a fixed price on or before a fixed date.
– European option vs. American option

• Buyer (holder) has the long position and seller (writer) has the short position.
• Key terminology
– Exercise or strike price
– Maturity or expiration
– Premium or price

3

Options Contracts

4

Options trading

• Call option vs. Put option

• Standardised contracts are supervised and guaranteed by the Clearing House.
• As discussed later, selling an option entails a sizable risk. Hence, selling an option requires depositing a margin, unless the seller also owns the asset on which the option is written.

– A call option gives the holder (buyer) the right to buy the underlying asset.
– A put option gives the holder (buyer) the right to sell the underlying asset.

• In all cases, the seller of the option contract, the writer, is subject to the buyer’s decisions, and the buyer exercises the option only if it is profitable to him or her.
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6

1

Example

Other terminologies

• You buy an European call options on IBM stock with a strike price of $140, expiring in three months. The current price is $138 and the option price is $5. Calculate the payoff (value) of the contract at maturity.
• Suppose at the maturity, the stock price (ST) is

• In the Money - exercise of the option would be profitable Call: market price>exercise price
Put: exercise price>market price

• Out of the Money - exercise of the option would not be profitable

@ $155
@ $120
@ $140
@ $142

Call: market priceX
0
if ST < X profit to call writer payoff + premium

80

90
Terminal
stock price ($)

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2

Long put on IBM

Short put on IBM

• Profit from buying a put option on IBM: option price = $7, strike price = $90

• Profit from writing a put option on IBM: option price = $7, strike price = $90

payoff to put holder
0
if ST > X if ST < X
(X - ST) profit to put holder payoff - premium

30 Profit ($)
20
10
0
-7

Terminal stock price ($)
60

70

80

90

Profit ($)
7
0

70

Terminal stock price ($)

80
90

100 110 120

-10
-20
-30

100 110 120

60

payoff to put writer
0
if ST > X if ST < X
-(X - ST) profit to put writer payoff + premium

13

A closer look at profit/loss

Payoffs from Options

• Profit/loss is a zero sum

• What is the option position in each case?

– the profit from buying a call (put) option is the mirror image of the profit from selling a call (put) option. X = Strike price, ST = Price of asset at maturity
Payoff

Payoff
X
X

ST

Payoff

• Asymmetric payoff profile
ST

Payoff
X
X

ST

14

ST
15

– buyer of either call or put faces a liability in that his/her loss is capped at the initial option premium paid, and the gain is unlimited.
– The seller of a call or put faces unlimited liability as the price of the underlying asset could rise or drop without limit.
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Option pricing and valuation

2. Option valuation

• Value of option comes from two sources:
– Intrinsic value: Profit that could be made if the option was immediately exercised.

Learning objectives
• Understand how to use Black-Scholes model to value/pricing options contract
• Have a thorough understanding of the factors affecting option prices
• Understand the put-call parity relationship

call: stock price - exercise price

put: