Lecture Notes 14

Foundations of Finance: Options: an Overview Prof. Alex Shapiro

Lecture Notes 14

Options: an Overview

I. Readings and Suggested Practice Problems

II. Options: Characteristics and Payoffs

III. Options Portfolios

IV. Options Trading

V. Additional Readings

Buzz Words: European Options, American Options, Executive Stock Options, Exotic Options, Naked Call/Put, Straddle, Spread, Portfolio Insurance

1 Foundations of Finance: Options: an Overview

I. Readings and Suggested Practice Problems

BKM, Chapter 20

Suggested Problems, Chapter 20: 2, 4, 6, 8.

II. Options: Characteristics and Payoffs

A. Introduction

• Options, futures and forwards are the basic derivative securities:

Their payoffs are closely tied to (“derived from”) the price of an underlying security.

• Derivatives are used for Hedging / Risk Management and for Speculation (often Hedgers and Speculators are the counter- parties of a transaction).

• Our analysis will concentrate primarily on stock options. (But there are also options traded on bonds, currency, commodities, etc.)

2 Foundations of Finance: Options: an Overview

• Our discussion will concentrate primarily on publicly traded options.

But many options are nontraded or implicit, and our analysis applies to those as well:

For example: options can be used to analyze Levered Equity, Oil fields, Callable Bonds, etc.

In recent years, options gained popularity as a tool for employee and executive compensation (see the Economist and the NYT articles in the additional readings), but lately some companies reversed to stock compensation due to incentive problems with options, and due to debates on how to expense option in the financial statements.

B. Stock Options

• An [American] call option gives the holder the right (but not the obligation) to buy a share of the underlying stock at the prespecified exercise (or strike) price at any time up to the expiration date.

• A put option is the right to sell the underlying stock. at the prespecified exercise (or strike) price at any time up to the expiration date.

• A European option can be exercised only on the expiration date.

3 Foundations of Finance: Options: an Overview

• Exchange-traded puts and calls are standardized as to quantity (e.g., 100 shares per option), price and expiration dates. [For example: See the Chicago Board Options Exchange (CBOE) webpage (www.cboe.com) for more details.]

Over-the-counter (OTC) puts and calls are custom contracts sold to clients by brokers.

Example: IBM and Microsoft Call and Put Options (Monday 4/3/2000, closing prices) are given on the next page.

The first column is the stock price:

IBM stock price: 121

Microsoft stock price: 90 7/8

[For option valuation, which we will discuss later, it may be useful to note that Microsoft shares dropped $15 3/8 per share on that day – the day Justice Thomas Penfield Jackson of the U.S. District Court of Washington D.C. ruled that Microsoft violated the antitrust law (the Sherman Act) in the way it preserved its monopoly status. Side Remark: Some see that day as the turning point, which signaled the “beginning of the end” of the Bull market of the 1990s.]

4 Foundations of Finance: Options: an Overview

[options quote here]

5 Foundations of Finance: Options: an Overview

C. Example: Microsoft call options

• The Oct 85 call gives us the right to purchase MSFT at $85/share (through Saturday, Oct 21, 2000, “the Saturday following the 3rd Friday of the month”).

• If we owned this call, we could exercise it, and sell the stock.

Proceeds = S – X

S = stock price X = exercise price

• At close, Proceeds = S – X = 90 7/8 - 85 = 5 7/8 (per share)

This call is in the money (X < S).

• For the Oct 95 call, Proceeds = 90 7/8 - 95 = -4 1/8

This call is out of the money (X > S), It wouldn’t pay to exercise.

• The intrinsic value of a call is Maximum[S-X, 0]

• The market price of an option is also called the premium.

6 Foundations of Finance: Options: an Overview

• The premia (last sale prices) for the Oct 85 and Oct 95 calls exceed their intrinsic values:

Int Val Premium Oct 85 5 7/8 17 1/4 Oct 95 0 12 1/2

• A call option is created when someone “writes” the option. This means:

– The writer is “short” the call. – For everyone who owns (is “long”) the call, someone is short. – The net amount outstanding of the call is zero. – Options are “zero-sum” games.

D. Example: Option Writing

• To sell (write) the Oct 85 call, we simply communicate this intention this to our broker.

The call is sold and we receive the premium (last sale price = 17 1/4)

We do not necessarily have to own the stock. (But if we don’t, we will have to post margin.)

• Writing a call is like selling short: our liability is potentially unlimited.

• If the MSFT price rises, we can avoid further loss by repurchasing the Oct 85 call.

7 Foundations of Finance: Options: an Overview

E. Example: Microsoft put options

• The Oct 95 put option gives the holder the right to sell the stock at 95 per share (through Saturday, Oct 21).

• If we buy MSFT in the market and exercise the put,

Proceeds = X - S = 95 - 90 7/8 = 4 1/8

This put is in the money (X >S).

• The Oct 85 put is out of the money (X < S). If we bought MSFT and exercised this option,

Proceeds = 85 - 90 7/8 = - 5 7/8

• For a put option,

Intrinsic value = Max[X-S, 0]

8 Foundations of Finance: Options: an Overview

III. Options Portfolios

We now use a spreadsheet to analyze costs, payoffs and profits of portfolios that involve options. The portfolios may consist of puts, calls, stock, bonds (riskless borrowing or lending).

[Market prices for the options are Black-Scholes values for European options. Market price for a $1 par bond is (with continuous compounding) e-rT, where T is time to maturity.]

A. Long one share of stock

Stock Price 15 ($ per share) 35 Std. Dev. 20% per year 30 Risk-free rate 8% per year 25 20 Maturity (years) 1/2 15 10 Security Amt Price Cash Flow 5 Stock 1 $15.000 -$15.000 0 Portfolio -5 Bond ($1 par) 0 $0.961 Value -10 Call: X= 15 0 $1.156 Profits Call: X= 20 0 $0.039 -15 -20 Put: X= 10 0 $0.000 0 10203040 Put: X= 20 0 $4.254 Stock Price at Expiration(ST) Total: -$15.000

B. Long one call

Stock Price 15 ($ per share) 20 Std. Dev. 20% per year Risk-free rate 8% per year 15 Maturity (years) 1/2 10 Security Amt Price Cash Flow 5 Stock 0 $15.000 Portfolio Value Bond ($1 par) 0 $0.961 0 Call: X= 15 1 $1.156 -$1.156 Profits Call: X= 20 0 $0.039 -5 Put: X= 15 0 $0.568 010203040

Put: X= 20 0 $4.254 Stock Price at Expiration (S T) Total: -$1.156

9 Foundations of Finance: Options: an Overview

C. Long one put

Stock Price 15 ($ per share) 20 Std. Dev. 20% per year Risk-free rate 8% per year 15 Maturity (years) 1/2 10 Security Amt Price Cash Flow 5 Stock 0 $15.000 Portfolio Value Bond ($1 par) 0 $0.961 0 Call: X= 15 0 $1.156 Profits Call: X= 20 0 $0.039 -5 Put: X= 15 1 $0.568 -$0.568 0 10203040

Put: X= 20 0 $4.254 Stock Price at Expiration(ST) Total: -$0.568

D. Writing an uncovered (“naked”) call

Stock Price 15 ($ per share) 5 Std. Dev. 20% per year Risk-free rate 8% per year 0 Maturity (years) 1/2 -5 Security Amt Price Cash Flow -10 Stock 0 $15.000 Portfolio Bond ($1 par) $0.961 Value 0 -15 Call: X= 15 -1 $1.156 $1.156 Profits

Call: X= 20 0 $0.039 -20 Put: X= 15 0 $0.568 010203040

Put: X= 20 0 $4.254 Stock Price at Expiration (S T) Total: $1.156

10 Foundations of Finance: Options: an Overview

E. Writing and uncovered (“naked”) put

Stock Price 15 ($ per share) 5 Std. Dev. 20% per year Risk-free rate 8% per year 0 Maturity (years) 1/2 -5 Security Amt Price Cash Flow -10 Stock 0 $15.000 Portfolio Value Bond ($1 par) 0 $0.961 -15 Call: X= 15 0 $1.156 Profits Call: X= 20 0 $0.039 -20 Put: X= 15 -1 $0.568 $0.568 0 10203040

Put: X= 20 0 $4.254 Stock Price at Expiration (ST) Total: $0.568

F. Straddle: long one call, one put

Put: X= 20 0 $4.254 Stock Price at Expiration(ST) Total: -$1.724

The Components of the Straddle:

+ = Straddle

X S X S Long Call Long Put

11 Foundations of Finance: Options: an Overview

G. A spread: short call (X=15), long call (X=20)

Stock Price 15 ($ per share) 5 Std. Dev. 20% per year Risk-free rate 8% per year Maturity (years) 1/2 0

Security Amt Price Cash Flow

Stock 0 $15.000 -5 Portfolio Bond ($1 par) 0 $0.961 Value Call: X= 15 -1 $1.156 $1.156 Profits Call: X= 20 1 $0.039 -$0.039 -10 Put: X= 15 0 $0.568 010203040

Put: X= 20 0 $4.254 Stock Price at Expiration (ST) Total: $1.117

The components of the spread:

15 20 + 15 20 15 20 = S S S

Short call X=15 Long call X=20 Spread

12 Foundations of Finance: Options: an Overview

H. Writing a covered call (short call, long stock)

Stock Price 15 ($ per share) 20 Std. Dev. 20% per year 15 Risk-free rate 8% per year 10 Maturity (years) 1/2 5

Security Amt Price Cash Flow 0 -5 Stock 1 $15.000 -$15.000 Portfolio Bond ($1 par) 0 $0.961 -10 Value Call: X= 15 -1 $1.156 $1.156 -15 Profits Call: X= 20 0 $0.039 -20 Put: X= 15 0 $0.568 010203040

Put: X= 20 0 $4.254 Stock Price at Expiration (ST) Total: -$13.844

The components of the covered call:

15 15 15 + = S S

Short Call Long Stock Covered Call

13 Foundations of Finance: Options: an Overview

I. Portfolio Insurance I: long bonds and call

Stock Price 15 ($ per share) 35 Std. Dev. 20% per year 30 Risk-free rate 8% per year 25 Maturity (years) 1/2 20

Security Amt Price Cash Flow 15 10 Stock 0 $15.000 Portfolio Bond ($1 par) 15 $0.961 -$14.412 5 Value Call: X= 15 1 $1.156 -$1.156 0 Profits Call: X= 20 0 $0.039 -5 Put: X= 15 0 $0.568 0 10203040

Put: X= 20 0 $4.254 Stock Price at Expiration (ST) Total: -$15.568

The components of portfolio insurance I

15 15 + =

S X=15 S X=15 S Bond Long Call

14 Foundations of Finance: Options: an Overview

J. Portfolio Insurance II: long stock, put

Stock Price 15 ($ per share) 35 Std. Dev. 20% per year 30 Risk-free rate 8% per year 25 Maturity (years) 1/2 20

Security Amt Price Cash Flow 15 10 Stock 1 $15.000 -$15.000 Portfolio Bond ($1 par) 0 $0.961 5 Value Call: X= 15 0 $1.156 0 Profits Call: X= 20 0 $0.039 -5 Put: X= 15 1 $0.568 -$0.568 010203040

Put: X= 20 0 $4.254 Stock Price at Expiration (S T) Total: -$15.568

Components of portfolio insurance II

15 + = S X=15 S X=15

Stock Long Put

15 Foundations of Finance: Options: an Overview

IV. Options Trading

A. Exchange Traded Options

• The Chicago Board Options Exchange (CBOE) started trading in 1973 (http://www.cboe.com).

It is currently the largest options exchange.

• Listed options are standardized by contract size, strike price, expiration.

Some companies have options listed on several exchanges. This multiple trading is a recent phenomenon. Only in 1999 options of companies with large open interest (number of contracts outstanding) have been cross listed (e.g., IBM, Lucent, Nike).

• Trading occurs between brokers or between brokers and market makers on the floor of the exchange (but electronic trading is also being introduced; e.g., RAES – Retail Automatic Execution System on the CBOE for order of 10 contracts or less).

• Options Clearing Corporation assumes credit risk.

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B. The Role of the Options Clearing Corporation (OCC)

In the absence of a clearing corporation, the buyer of the option assumes the seller’s credit risk:

At time of trade:

Negotiate price

premium Call Buyer Call Seller

At exercise: X

stock

At the time of exercise, there is a chance that the call seller might default.

17 Foundations of Finance: Options: an Overview

With exchange-traded options, the clearing corporation becomes an intermediary in the deal, immediately after the price is agreed:

At time of trade:

Negotiate price

Call Buyer Call Seller

Option Clearing Corporation

The buyer’s contract is now with the clearing corporation. The seller’s contract is also with the clearing corporation.

Formally, OCC is the sole issuer of all exchange traded options. The OCC has a AAA credit rating from S&P’s Corp.

V. Additional Readings