Financial Engineering 6

References: Villalobos, Luenberger, CBOE

Lecture 17

Introduction to Options

Lecture Topics • Introduction • Call and Put Options • European and American Options • Examples

Definition of an Option • Option is a privilege sold by one party to another that offers the

buyer the right, but not the obligation, to buy (call) or sell (put) a security at an agreed-upon price during a certain period of time or on a specific date.

• Call Option is an option contract giving the owner the right, but not the obligation, to buy a specified amount of an underlying security at a specified price within a specified time.

• Put Option is an option contract giving the owner the right, but not the obligation, to sell a specified amount of an underlying security at a specified price within a specified time.

Definition of an Option • An Option is:

– A type of derivative. – A security, just like a stock, bond, or index. – A binding contract with strictly defined terms

and properties. – Insurance. – Hedge!

Home Depot Put Example • You hold 1,000 shares of HD

– Stock is currently trading at $50/share. – Uncertainty causes you to buy a “put” option. – A “put” option is a right, not an obligation to sell. – The “put” option will cost you a premium such as $1/share.

• Strike Price = $50/share • If the stock falls below, you sell to the underwriter at $50. • If the stock price remains above, option is worthless. • In this case the options serve as an insurance policy against

the risk of the underlying stock falling in price below the strike price of $50.

• Notice that you could achieve a similar defensive strategy by selling short the stock.

• This is very similar to buying insurance for your car in which you pay a premium, and collect on it if you damage your car so as to bring it back to its original value.

Home Depot Call Example • Call Options is simply a reversal of a Put Option.

– Gives the buyer (holder) the right to purchase a stock from the seller (writer) at a specified price.

• So, if you think HD stock will rise: – Currently at $50. – Purchase a “call” for $50/share with a premium = $1/share. – Stock Price goes up to $80 in two weeks.

• You have a net of $29/share. • In this case you can benefit from a surge in the price of a stock

without having to invest on purchasing the underlying stock.

• Call Option is like a security deposit for a rental property. • If you wanted to rent a certain property, and left a security

deposit for it, the money would be used to insure that you could, in fact, rent that property at the price agreed upon when you returned.

European vs American Options • European Option is an option that can only be exercised at the

end of its life.

• American Option is an option that can be exercised anytime during its life.

– The majority of exchange-traded options are American.

• Since investors have the freedom to exercise their American options at any point during the life of the contract, they are more valuable than European options which can only be exercised at maturity.

Profit

Stock Price

Put Option

Profit

Stock Price

Value of an Option

Strike Price

Strike Price

Call Option

Value = max(0, Stock Price – Strike Price) Value = max(0, Strike Price – Stock Price)

Option Terminology • The price at which an underlying stock can be purchased or

sold is called the strike price.

• This is the price a stock price must go above for calls, or go below for puts, before a position can be exercised for a profit.

– This must occur before the expiration date.

• An option that is traded on a national options exchange such as the Chicago Board Options Exchange (CBOE) is known as a listed option.

– These have fixed strike prices and expiration dates.

• Each listed option represents 100 shares of company stock (known as a contract).

Option Terminology • For call options, the option is said to be “in-the-money” if the

share price is above the strike price. • A put option is “in-the-money” when the share price is below

the strike price. • The amount by which an option is “in-the-money” is referred to

as intrinsic value. • The total cost (the price) of an option is called the premium. • This price is determined by factors including the stock price,

strike price, time remaining until expiration (time value) and volatility.

• Long-Term Equity Anticipation Securities (LEAPS) are options contracts that expire greater than nine months out.

• Normal options tend to last no more than nine months.

Option Terminology

Call Put

Buyer or “holder” The right, but not the obligation to buy at the strike price

The right, but not the obligation to sell at the strike price

Seller or “writer” The potential obligation to sell at the strike price

The potential obligation to buy at the strike price

Options Table (old style newspaper)

Investopedia

Strike Price

Expiration Date (3rd Fri.) Put or Call Volume # traded

Willing to pay

Willing to sell

Open Interest # unexercised or not expired

The Option Code • The components of an Option Symbol are:

Root Symbol + Expiration Month Code + Strike Price Code • Expiration Month Codes are:

• Strike Price Codes are:

JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Calls A B C D E F G H I J K L Puts M N O P Q R S T U V W X

Code A 5 105 205 305 405 505 B 10 110 210 310 410 510 C 15 115 215 315 415 515 D 20 120 220 320 420 520 E 25 125 225 325 425 525 F 30 130 230 330 430 530 G 35 135 235 335 435 535 H 40 140 240 340 440 540 I 45 145 245 345 445 545 J 50 150 250 350 450 550 K 55 155 255 355 455 555 L 60 160 260 360 460 560 M 65 165 265 365 465 565

Strike Prices Code N 70 170 270 370 470 570 O 75 175 275 375 475 575 P 80 180 280 380 480 580 Q 85 185 285 385 485 585 R 90 190 290 390 490 590 S 95 195 295 395 495 595 T 100 200 300 400 500 600 U 7.5 37.5 67.5 97.5 127.5 157.5 V 12.5 42.5 72.5 102.5 132.5 162.5 W 17.5 47.5 77.5 107.5 137.5 167.5 X 22.5 52.5 82.5 112.5 142.5 172.5 Y 27.5 57.5 87.5 117.5 147.5 177.5 Z 32.5 62.5 92.5 122.5 152.5 182.5

Strike Prices

http://biz.yahoo.com/opt/calendar.html

New Yahoo Finance Symbols

Root symbol + Expiration Year(yy)+ Expiration Month(mm)+ Expiration Day(dd) + Call/Put Indicator (C or P) + Strike price

Option Type

Underlying Symbol

Expiration Year

Expiration Month

Expiration Day

Call/Put Strike Price

Old Symbol

New Symbol

Call YHOO 2010 04 16 C 20.00 YHQDD.X YHOO100416C00020000

Put YHOO 2010 04 16 P 20.00 YHQPD.X YHOO100416P00020000

Examples

http://www.cboe.com

http://finance.yahoo.com/options/

Apple Example – October 26, 2016 Stock = AAPL, Price = 115.42 $/share, Options = Calls, exp 11/18/2016

Strike Symbol Last Bid Ask Chg Vol Open Int 107.00 AAPL161118C00107000 7.79 8.15 8.30 0.00 533 170 108.00 AAPL161118C00108000 7.20 7.25 7.40 0.00 9 51 109.00 AAPL161118C00109000 6.15 6.30 6.45 0.00 224 8 110.00 AAPL161118C00110000 5.34 5.45 5.55 -3.51 2,574 54,487 111.00 AAPL161118C00111000 4.55 4.60 4.70 0.00 168 53 112.00 AAPL161118C00112000 3.80 3.80 3.90 0.00 863 68 113.00 AAPL161118C00113000 3.20 3.15 3.25 0.00 1,581 243 114.00 AAPL161118C00114000 2.56 2.56 2.58 0.00 3,005 646 115.00 AAPL161118C00115000 2.02 2.02 2.02 -2.98 14,479 72,620 116.00 AAPL161118C00116000 1.45 1.55 1.56 0.00 2,342 738 117.00 AAPL161118C00117000 1.20 1.19 1.20 0.00 2,494 1,878 118.00 AAPL161118C00118000 0.89 0.89 0.90 0.00 5,083 10,459 119.00 AAPL161118C00119000 0.67 0.67 0.68 0.00 875 953

Apple Example – October 26, 2016 Stock = AAPL, Price = 115.42 $/share, Options = Calls, exp 7/21/2017

Strike Symbol Last Bid Ask Chg Vol Open Int 50.00 AAPL170721C00050000 67.40 65.00 65.75 0.00 7 21 70.00 AAPL170721C00070000 43.00 42.35 43.40 0.00 1 0 90.00 AAPL170721C00090000 29.50 26.40 26.95 0.00 1 1 95.00 AAPL170721C00095000 24.36 22.15 22.65 0.00 2 64

100.00 AAPL170721C00100000 16.97 18.10 18.45 -3.33 9 1,031 105.00 AAPL170721C00105000 14.40 14.65 14.95 -2.10 62 159 110.00 AAPL170721C00110000 11.25 11.50 11.70 -2.02 115 11,009 115.00 AAPL170721C00115000 8.80 8.60 8.80 -1.82 66 3,038 120.00 AAPL170721C00120000 6.25 6.45 6.65 -2.00 88 736 125.00 AAPL170721C00125000 4.49 4.65 4.80 -1.30 92 469 130.00 AAPL170721C00130000 3.10 3.20 3.35 -1.05 101 758 135.00 AAPL170721C00135000 2.02 2.21 2.31 -0.94 39 548 140.00 AAPL170721C00140000 1.47 1.48 1.58 -0.64 33 125

Which option has the higher price, exp 11/18/2016 or exp 7/21/2016

Dell Example – March 8, 2012

Strike Symbol Last Bid Ask Chg Vol Open Int 97.50 AAPL170120P00097500 0.43 0.42 0.43 0.01 56 19,656

100.00 AAPL170120P00100000 0.57 0.56 0.57 0.01 1,224 59,782 105.00 AAPL170120P00105000 1.12 1.11 1.13 0.10 2,949 49,343 110.00 AAPL170120P00110000 2.24 2.22 2.24 0.21 5,618 80,017 115.00 AAPL170120P00115000 4.20 4.20 4.25 0.60 4,847 57,344 120.00 AAPL170120P00120000 7.24 7.10 7.20 1.19 1,055 62,727 125.00 AAPL170120P00125000 11.05 10.95 11.10 1.84 40 21,772 130.00 AAPL170120P00130000 16.55 15.45 15.55 3.35 31 13,933 135.00 AAPL170120P00135000 20.40 20.25 20.40 2.47 12 11,857 140.00 AAPL170120P00140000 22.36 25.15 25.35 0.00 28 25,778 145.00 AAPL170120P00145000 30.25 30.10 30.30 2.60 5 7,338 150.00 AAPL170120P00150000 32.70 35.05 35.25 0.00 21 27,460 155.00 AAPL170120P00155000 41.50 40.05 40.25 3.75 2 1,351

Stock = AAPL, Price = 115.42 $/share, Options = Puts, exp 1/20/2017

Expiration Date • The expiration date for “most” listed stock options in the U.S. is

the third Friday of the month, unless it falls on a holiday where it is Thursday.

Synthetic Instrument • Synthetic is a financial instrument that is created artificially by

simulating another instrument based on the combined features of a collection of other assets.

• For example, you can create a synthetic stock by purchasing a call option and simultaneously selling a put option on the same stock.

– The synthetic stock would have the same capital gain potential as the underlying security.

• Basically, we can build something more complex from simple financial instruments.

• We are engineering a financial instrument!

Simple Synthetic Example • What if a particular stock was not available to us, but we wanted

to invest in it anyway?

Profit Stock Price

Strike Price

K

Buy a call option

Buy a put option

Sell a put option

Stock Price

Spreads • The majority of options traded on U.S. exchanges are known

as outrights, such that the purchase or sale of an option on its own.

• A more complex trade involves the trading of more than one option at the same time.

– This type of complex trade is known as an Option Spread. • In its most basic instance an option spread consists of trading

two different option strikes on the same underlying security as strategy to limit risk.

– Typically we would buy an option and sell an option. – Each one of the options are known as the “legs” of the

spread. • Examples include Vertical and Butterfly Spreads.

Vertical Spread Call • Vertical Spread: Buy an out-of-the-money (OTM) call option and then

sell a further out-of-the-money (FOTM) call option. • It is consider a “bullish” spread because we expect the value of the

underlying security to increase.

• You might do this when you expect the stock to go up, but not above the second strike price, and you want to offset the cost of the options.

Profit

Stock Price

K1

K2

Buy a call option

Sell a call option

Net payoff

Butterfly Spread • It combines a bull and bear spread. • It uses three strike prices.

– The lower two strike prices are used in the bull spread, and the higher strike price in the bear spread.

– The spread is constructed by buying two calls, one with strike price K1 and another with strike price K3 and selling two units of a call with a strike price K2.

• We get a positive profit if the stock price at expiration is near K2; otherwise, the loss is quite small.

Profit

Stock Price

K1

K2

K3

Sell 2 call options

Buy a 2nd call option

Net payoff Buy a call option

Spreads

• It is possible to approximate virtually any payoff function by a sequenced of straight line segments.

Option Pricing • One of the main questions asked in Financial Engineering is the

“fair” or market price for an option.

• Essentially there are two types of analytical models to answer this question:

– Discrete (binomial lattices). – Continuous (Black-Scholes formula).

• We will start exploring these models next lecture.

• In the mean time let’s introduce some terminology.

Put – Call Parity • Let C and P be the prices of a European Call and Put option,

exercised only at expiration date, both with a strike price of K. • Then the following relationship holds:

C – P + dK = S

Where d is the discount factor in the period to expiration and S the current price of the stock.

C = S - K then we buy a call option

-P = -(K-S) then we sell a put option

C - P + dK = S

S

dK

Assignments • Check out options in Yahoo Finance. • Find the price of an option with a maturity of:

– One month – Three months – Six months

• Go to the following link and take the brief class on options from CBOE http://www.cboe.com/learncenter/courses.aspx