1 Financial Options In Depth Zachary Emig MBA Class of 2005 Ross School of Business Finance Club.

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Financial OptionsFinancial OptionsIn DepthIn Depth

Zachary EmigZachary Emig

MBA Class of 2005MBA Class of 2005

Ross School of Business Finance Ross School of Business Finance ClubClub

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Today’s AgendaToday’s AgendaI. What are options?I. What are options?

II. Payoff diagrams and risk profilesII. Payoff diagrams and risk profiles

III. Option pricing: the intuitionIII. Option pricing: the intuition

IV. Binomial models and Black-ScholesIV. Binomial models and Black-Scholes

V. Implied volatilityV. Implied volatility

VI. Other terminologyVI. Other terminology

VII. Uses of optionsVII. Uses of options

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What Are Options?What Are Options?

Options are securities which give the Options are securities which give the holder the right, but not the obligation, holder the right, but not the obligation, to buy or sell another instrument at a to buy or sell another instrument at a fixed price before or at a fixed expiration fixed price before or at a fixed expiration date.date.

Options that grant the holder the right to Options that grant the holder the right to buy are buy are callcall options; those that grant options; those that grant the holder the right to sell are the holder the right to sell are putput options.options.

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What Defines Options?What Defines Options?What would you need to know in order to What would you need to know in order to identify an option?identify an option?

1. Whether it is a Call or a Put.1. Whether it is a Call or a Put.

2. What the underlying security is. Options 2. What the underlying security is. Options can be written on almost anything: stock can be written on almost anything: stock prices, stock indexes, FX rates, interest rates, prices, stock indexes, FX rates, interest rates, etc.etc.3. The expiration date (tomorrow? Next 3. The expiration date (tomorrow? Next month? Next year?)month? Next year?)

4. The fixed price (called the 4. The fixed price (called the strike pricestrike price or or exercise priceexercise price) you can buy or sell at.) you can buy or sell at.

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What Else Defines Options?What Else Defines Options?There are many different styles of options, There are many different styles of options, related to when you can exercise.related to when you can exercise.

European option: holder can only exercise on European option: holder can only exercise on the expiration date. Most common type.the expiration date. Most common type.

American option: holder can exercise anytime American option: holder can exercise anytime up through the expiration date.up through the expiration date.

Bermudan option: holder can exercise every Bermudan option: holder can exercise every nn months up until the expiration date.months up until the expiration date.

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II. Payoff diagrams and risk II. Payoff diagrams and risk profilesprofiles






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Payoff DiagramsPayoff Diagrams

When speaking about options, using When speaking about options, using “hockey stick” payoff diagrams “hockey stick” payoff diagrams greatly simplifies things.greatly simplifies things.

An option’s payoff takes into account An option’s payoff takes into account only what the holder gets at only what the holder gets at expiration (or when exercised), not expiration (or when exercised), not what they paid for the option up what they paid for the option up front.front.

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An Example: Union Pacific An Example: Union Pacific (UNP)(UNP)

• Closed at $64.69 on Nov. 12Closed at $64.69 on Nov. 12• Considerable volatility over past yearConsiderable volatility over past year• All examples represent European optionsAll examples represent European options

http

://finance

.yahoo.co

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://finance

.yahoo.co

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Payoff DiagramsPayoff Diagrams

UnderlyinUnderlying Priceg Price

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$0

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$75$75 UnderlyinUnderlying Priceg Price

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Payoff diagrams plot option holder’s payoff Payoff diagrams plot option holder’s payoff versus the price of the underlying security. versus the price of the underlying security. K=Strike Price.K=Strike Price.

Call Option, Call Option, K=$75K=$75

Put Option, Put Option, K=$55K=$55

With a put, on the other With a put, on the other hand, holder won’t exercise hand, holder won’t exercise right to sell at $55 if they right to sell at $55 if they

can sell UNP for $65.can sell UNP for $65.

Why exercise call and Why exercise call and pay $75, when you buy pay $75, when you buy UNP on the market for UNP on the market for

less than $75?less than $75?

Once UNP is above Once UNP is above $75, call holder will $75, call holder will

exercise option to buy exercise option to buy UNP at $75.UNP at $75.

But say UNP drops to $45, But say UNP drops to $45, the put holder will exercise the put holder will exercise to sell at $55, a difference to sell at $55, a difference

of $10.of $10.

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TerminologyTerminology• An option is said to be An option is said to be in the moneyin the money if, were it if, were it

able to be exercised immediately, the payoff able to be exercised immediately, the payoff would be positive.would be positive.

• An option is An option is at the moneyat the money if the underlying is at if the underlying is at the strike price.the strike price.

• An option is An option is out of the moneyout of the money if the holder if the holder wouldn’t execute immediately, were they able to.wouldn’t execute immediately, were they able to.


Optio

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Payoff

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Put Option, Put Option, K=$55K=$55

In the In the moneymoney

Out of the Out of the moneymoneyIn the In the

moneymoneyOut of the Out of the

moneymoney

At the At the moneymoney

At the At the moneymoney

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Too Good To Be True?!?Too Good To Be True?!?


Optio

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Payoff

$0

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$75$75

Payoff diagrams suggest that holding options Payoff diagrams suggest that holding options has no downside. Is this possibly true?has no downside. Is this possibly true?


Of course not. To buy Of course not. To buy a call or put option, a call or put option, investors must pay a investors must pay a premiumpremium, which must , which must equal the value of equal the value of option. This is option. This is reflected by changing reflected by changing the payoff diagram to the payoff diagram to a P&L daigram.a P&L daigram.

Optio

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Optio

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Pro

fit

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Option Option PremiumPremium

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Risk ProfilesRisk ProfilesThink about the risk profile for the 4 basic option Think about the risk profile for the 4 basic option positions.positions.


Optio

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Long Call PositionLong Call Position Long Put Long Put PositionPosition


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$0

$0


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$55$55

Short Call Short Call PositionPosition

Short Put Short Put PositionPosition

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Example: Option PricingExample: Option Pricing

• Let’s say you bought UNP back in August at Let’s say you bought UNP back in August at $55, and have seen a 19% gain since$55, and have seen a 19% gain since

• Now you want to lock in some profits, and Now you want to lock in some profits, and protect yourself in case it plummetsprotect yourself in case it plummets

• How much would you pay for a Feb ’05 $60 put?How much would you pay for a Feb ’05 $60 put?

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If UNP is still above If UNP is still above K=$60 in February, K=$60 in February,

the put expires the put expires worthless, and all worthless, and all you’ve lost is the you’ve lost is the

premium you paid for premium you paid for it.it.

What Does the Put Do For What Does the Put Do For You?You?

You are here!

But if UNP has fallen But if UNP has fallen to $55 by the end of to $55 by the end of Feb. ’05, you’ll be Feb. ’05, you’ll be

able to exercise the able to exercise the put and sell at $60, put and sell at $60, recouping $5 of that recouping $5 of that

loss.loss.

If UNP is at the If UNP is at the strike on strike on

expiration, there’s expiration, there’s no point in no point in

exercising; the put exercising; the put expires worthless.expires worthless.

A long put position like “insurance” for a long stock A long put position like “insurance” for a long stock position.position.

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Think About It: What Factors Think About It: What Factors Go Into Pricing An Option?Go Into Pricing An Option?

• What changes would make this put What changes would make this put option more valuable?option more valuable?

• What would make it less valuable?What would make it less valuable?

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Option Pricing FactorsOption Pricing Factors1. How does option value move in relation to 1. How does option value move in relation to underlying price?underlying price?

For a put option, it’s value goes up when the For a put option, it’s value goes up when the underlying price goes down: the holder can underlying price goes down: the holder can sell at price K something available at the sell at price K something available at the market for < K (for a call, the opposite is true).market for < K (for a call, the opposite is true).


Optio

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Payoff

$0

$0

$K$K

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Option Pricing FactorsOption Pricing Factors2. How does option value move in relation to 2. How does option value move in relation to strike price?strike price?

For a put option, the lower the strike price, the For a put option, the lower the strike price, the lower it’s value (for a call, the opposite is lower it’s value (for a call, the opposite is true). It is less likely the put will end up below true). It is less likely the put will end up below the strike price.the strike price.

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Option Pricing FactorsOption Pricing Factors3. How does option value move in relation to 3. How does option value move in relation to time to expiration?time to expiration?

Whether it’s a put or call, the longer the time Whether it’s a put or call, the longer the time to expiration, the more valuable the option is. to expiration, the more valuable the option is. This is intuitive from the graph below; the This is intuitive from the graph below; the stock has less chance of dropping into the stock has less chance of dropping into the money by the end of next week than it does by money by the end of next week than it does by the end of Feb. 05.the end of Feb. 05.

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Option Pricing FactorsOption Pricing Factors4. How does option value move in relation to 4. How does option value move in relation to underlying volatility?underlying volatility?

For a both calls and puts, the greater the For a both calls and puts, the greater the underlying stock’s volatility, the more likely underlying stock’s volatility, the more likely that the option will move into the money.that the option will move into the money.

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Option Pricing FactorsOption Pricing Factors5. How does option value move in relation to 5. How does option value move in relation to interest rates?interest rates?

Options provide potential future payouts to Options provide potential future payouts to holders; the present value of those potential holders; the present value of those potential payouts is discounted by the interest rate, so payouts is discounted by the interest rate, so the higher the rate, the less valuable those the higher the rate, the less valuable those payouts (whether a call or put).payouts (whether a call or put).

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Summary of Pricing Factor Summary of Pricing Factor RelationshipsRelationships

Call ValueCall Value Put ValuePut Value

Underlying Underlying PricePrice

PositivePositive NegativeNegative

Strike PriceStrike Price NegativeNegative PositivePositive

Time to Time to MaturityMaturity

PositivePositive PositivePositive

Underlying Underlying VolatilityVolatility

PositivePositive PositivePositive

Interest RatesInterest Rates NegativeNegative NegativeNegative

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IV. Binomial models and Black-IV. Binomial models and Black-ScholesScholes




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Period 2Stock Price: $83.09Option Value: $13.09 Payoff

Hedge Ratio : -

B: -

Period 1Stock Price: $73.33Option Value: $6.42Hedge Ratio : 0.7122

B: -45.8013

Period 0 Period 2Stock Price: $64.71 Stock Price: $64.71Option Value: $3.15 Option Value: $0.00 Payoff

Hedge Ratio : 0.3958 Hedge Ratio : -

B: -22.4636 B: -

Period 1Stock Price: $57.11Option Value: $0.00Hedge Ratio : 0.0000

B: 0.0000

Period 2Stock Price: $50.40Option Value: $0.00 Payoff

Hedge Ratio : -

B: -

Option Pricing: Binomial Option Pricing: Binomial ModelsModels

Basic method for option pricing is through Basic method for option pricing is through Binomial Models: assume stock can either go Binomial Models: assume stock can either go up or down.up or down.

Method also Method also provides provides hedging hedging ratios as a ratios as a convenient convenient side effect.side effect.

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Option Pricing: Black-Option Pricing: Black-ScholesScholes

Black-Scholes is a formula that incorporates Black-Scholes is a formula that incorporates statistical methods to more accurately statistical methods to more accurately determine option value; it, and customized determine option value; it, and customized variants, are widely used throughout the variants, are widely used throughout the street.street.Do you have to memorize the Do you have to memorize the Black-Scholes formula for Black-Scholes formula for interviews? No, but you should interviews? No, but you should know the 5 inputs (s=stock know the 5 inputs (s=stock price, r=riskfree rate, x=strike price, r=riskfree rate, x=strike price, t=time to maturity, price, t=time to maturity, =volatility), how they affect =volatility), how they affect value.value.

http://www.riskglossary.com/articles/http://www.riskglossary.com/articles/black_scholes_1973.htmblack_scholes_1973.htm

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How to Find Option PricesHow to Find Option PricesYahoo! Finance lists options prices for different Yahoo! Finance lists options prices for different maturities and strike prices.maturities and strike prices.

Here are the Nov. 15 UNP call prices for Dec. Here are the Nov. 15 UNP call prices for Dec. 04, Jan. 05, and Feb. 05 expiration.04, Jan. 05, and Feb. 05 expiration.

As expected, increasing maturity = increasing As expected, increasing maturity = increasing value.value.As expected, increasing strike = decreasing As expected, increasing strike = decreasing value.value. http://finance.yahoo.com/q/op?http://finance.yahoo.com/q/op?

s=UNPs=UNP

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Implied VolatilityImplied VolatilityThink about it; Black-Scholes is:Think about it; Black-Scholes is:

PPoptionoption=f(S=f(Sstockpricestockprice,K,Kstrikestrike,T,Tmaturitymaturity,V,Vvolatilityvolatility,R,Rriskfreerateriskfreerate))

Set by Set by the the

marketmarket


marketmarket

Contract Contract specificspecific

Contract Contract specificspecific


marketmarket??

Knowing 5 of the 6 properties above, we can Knowing 5 of the 6 properties above, we can easily solve for volatility. This is called the easily solve for volatility. This is called the implied volatilityimplied volatility of the stock, because it is of the stock, because it is the volatility the market is pricing in for the the volatility the market is pricing in for the next T years.next T years.In I-Banks, often times options traders are In I-Banks, often times options traders are called “volatility traders”, since going long an called “volatility traders”, since going long an option implies you are going long vol.option implies you are going long vol.

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0

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Daily VIX Closing Prices

Volatility TradingVolatility TradingCBOE (Chicago Board Option Exchange) CBOE (Chicago Board Option Exchange) created Volatility Index (VIX) in 1993. VIXcreated Volatility Index (VIX) in 1993. VIX

““measures the market's expectation of measures the market's expectation of 30-day volatility30-day volatility, but , but in a way that conforms to the latest thinking and research in a way that conforms to the latest thinking and research among industry practitioners. The New VIX is based on among industry practitioners. The New VIX is based on S&P S&P 500 index option prices500 index option prices and incorporates information from and incorporates information from the volatility "skew" by using a wider range of strike prices the volatility "skew" by using a wider range of strike prices rather than just at-the-money series.”rather than just at-the-money series.”

VIX futures VIX futures trade at a value trade at a value of 10x the VIX of 10x the VIX index value. index value. Also known as Also known as the “fear the “fear gauge”.gauge”.http://www.cboe.com/micro/vix/historical.aspx http://www.cboe.com/micro/vix/faq.aspxhttp://www.cboe.com/micro/vix/faq.aspx

http://www.cboe.com/micro/vix/historical.aspx

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Volatility SurfacesVolatility SurfacesMost trading desks get daily reports with the Most trading desks get daily reports with the charts of the vol surface (implied volatility for charts of the vol surface (implied volatility for different maturities and strike prices). What different maturities and strike prices). What should that look like?should that look like?

1 2 3 6 12 18 2445

6030%

40%

50%

60%

70%

Months

Strike Prices

Volatility Surface

Unlike what might Unlike what might be expected, be expected, implied vol is not implied vol is not flat; it shows both flat; it shows both smilesmile and and skewskew. . Read Hull for Read Hull for more details.more details.

http://www.riskglossary.com/articles/http://www.riskglossary.com/articles/volatility_skew.htmvolatility_skew.htm

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The GreeksThe GreeksTraders will often Traders will often talk about “the talk about “the Greeks” in relation Greeks” in relation to securities with to securities with optionality; what do optionality; what do they mean?they mean?

No, the Greeks are five No, the Greeks are five letters used to describe letters used to describe an option’s behavior. an option’s behavior. For interviews, it’s For interviews, it’s probably enough just to probably enough just to know what each know what each represents:represents:

•Delta – Sensitivity of option to underlying’s price Delta – Sensitivity of option to underlying’s price changeschanges

•Gamma – Sensitivity of Delta to underlying’s price Gamma – Sensitivity of Delta to underlying’s price changeschanges

•Vega – Sensitivity of implied vol to underlying’s price Vega – Sensitivity of implied vol to underlying’s price changeschanges

•Theta – Sensitivity of option to the passage of timeTheta – Sensitivity of option to the passage of time

•Rho – Sensitivity of option to interest rate changesRho – Sensitivity of option to interest rate changes

http://www.riskglossary.com/articles/http://www.riskglossary.com/articles/greeks.htmgreeks.htm

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How are the Greeks used?How are the Greeks used?Trading desks with complex option positions Trading desks with complex option positions

will have daily reports on their exposures to will have daily reports on their exposures to different risks.different risks.

Volatility/Variance swap Volatility/Variance swap trader: sample Vega trader: sample Vega reportreport

Book: S&P Volatility Swaps Current S&P: 1,181.94Maturity Position VegaZ4 $811,223.00 1.23F5 $1,941,578.00 1.27G5 $1,756,614.00 1.34H5 $423,014.00 1.36J5 ($148,914.00) 1.37K5 $2,141,048.00 1.39M5 ($570,140.00) 1.45N5 ($104,184.00) 1.50Q5 $98,014.00 1.51U5 $234,189.00 1.59V5 $174,911.00 1.63X5 ($80,141.00) 1.67Z5 $560,002.00 1.69F6 $284,014.00 1.77

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Other Concepts: Intrinsic Other Concepts: Intrinsic ValueValueOption prices can be decomposed into the Option prices can be decomposed into the option’s intrinsic value and time value.option’s intrinsic value and time value.

Intrinsic valueIntrinsic value is the payoff value of the is the payoff value of the option were it possible to exercise option were it possible to exercise immediately; if out of the money, zero, immediately; if out of the money, zero, otherwise the difference between the strike otherwise the difference between the strike and current stock price.and current stock price.Example: The Jan’05, $40 Example: The Jan’05, $40 strike call is selling for strike call is selling for $24.70. The closing UNP $24.70. The closing UNP price was $64.47. So price was $64.47. So $64.47-$40.00=$24.47 is $64.47-$40.00=$24.47 is the intrinsic value of the the intrinsic value of the option. option.

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Other Concepts: Time ValueOther Concepts: Time ValueExample: The Jan’05, $40 strike call is selling for Example: The Jan’05, $40 strike call is selling for $24.70. The closing UNP price was $64.47. So $64.47-$24.70. The closing UNP price was $64.47. So $64.47-$40.00=$24.47 is the intrinsic value of the option. $40.00=$24.47 is the intrinsic value of the option. The remaining $0.23 of the option’s price is it’s The remaining $0.23 of the option’s price is it’s time time valuevalue, i.e. what you’ll pay for the chance that over the , i.e. what you’ll pay for the chance that over the next 2 months it’s payoff will increase. For a deep in next 2 months it’s payoff will increase. For a deep in the money call option, this is small compared to it’s the money call option, this is small compared to it’s [current] intrinsic value.[current] intrinsic value.In comparison, the out of In comparison, the out of the money $70 option has the money $70 option has $0 intrinsic value. So its $0 intrinsic value. So its $0.35 price is all time $0.35 price is all time value, i.e. the chance that value, i.e. the chance that over 2 months the stock over 2 months the stock price will rise to above $70.price will rise to above $70.

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What’s the Big Deal?What’s the Big Deal?So, why are options so important?So, why are options so important?

Because of the breakthrough of Black-Scholes Because of the breakthrough of Black-Scholes in 1973, we now have a standard, accurate in 1973, we now have a standard, accurate way of valuing them. Almost every security way of valuing them. Almost every security either has optionality in or can be represented either has optionality in or can be represented with options.with options.

• Convertible bonds are straight corporate Convertible bonds are straight corporate debt with the owner holding a call option on debt with the owner holding a call option on the stock.the stock.

• Mortgage securities are straight debt with Mortgage securities are straight debt with the homeowner holding a the homeowner holding a callcall option option (repayment).(repayment).

• Common stock can be thought of as a call Common stock can be thought of as a call option on a firm’s assets with strike price of option on a firm’s assets with strike price of $0!$0!

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Option Strategies - StraddleOption Strategies - StraddleOptions also allow investors to take “quirky” Options also allow investors to take “quirky” views on underlying securities.views on underlying securities.

Example: StraddlesExample: Straddles

View: Believe that by View: Believe that by January UNP will either January UNP will either go up or down by a lot. go up or down by a lot. Go long a call and a Go long a call and a put.put.

Pure volatility play; Pure volatility play; investor neutral on investor neutral on stock stock appreciation/depreciatiappreciation/depreciation.on.


P&

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Net P&L

Long Call P&L

Long Put P&L

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Option Strategies – Covered Option Strategies – Covered CallCall

In a covered call, investor expects mild stock In a covered call, investor expects mild stock appreciation but not a large increase.appreciation but not a large increase.

Investor goes long the Investor goes long the stock and then writes stock and then writes (sells) an OTM (out of (sells) an OTM (out of the money) call option the money) call option for its premium.for its premium.

See Yahoo! Finance for See Yahoo! Finance for all the basic options all the basic options strategies.strategies.


P&

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Long Stock P&L

Short Call P&L

http://biz.yahoo.com/opt/education.htmlhttp://biz.yahoo.com/opt/education.html

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ConclusionConclusion•Nearly every trading desk I sat on this Nearly every trading desk I sat on this summer used options or option pricing in some summer used options or option pricing in some way.way.

•What to know for interviews? The underlying What to know for interviews? The underlying concepts: risk profiles, inputs to Black-Scholes, concepts: risk profiles, inputs to Black-Scholes, the Greeks, basic option strategies.the Greeks, basic option strategies.

•The jargon The jargon isis tricky. Traders now a days talk tricky. Traders now a days talk about going “long gamma” or “long vega”. about going “long gamma” or “long vega”. Focus on what that actually means (“long Focus on what that actually means (“long vega”=“long volatility”=“holding an option”?).vega”=“long volatility”=“holding an option”?).

•Remember: almost any security can be Remember: almost any security can be represented as an option.represented as an option.

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The Next StepsThe Next StepsIf you are set on going into sales and trading, If you are set on going into sales and trading, you you willwill have to know this stuff. Courses to have to know this stuff. Courses to take:take:

•FIN 580 – Options & Futures – Very good FIN 580 – Options & Futures – Very good introduction to valuing optionsintroduction to valuing options

•FIN 618 – Derivatives – Builds upon FIN 580FIN 618 – Derivatives – Builds upon FIN 580

•FIN 615/645 – Valuations/Adv. Valuations – FIN 615/645 – Valuations/Adv. Valuations – Touches upon real optionsTouches upon real options

•FIN 622 – Corporate Financial Engineering – FIN 622 – Corporate Financial Engineering – Discuss uses of options and derivatives for Discuss uses of options and derivatives for solving corporate financing needs.solving corporate financing needs.

1 Financial Options In Depth Zachary Emig MBA Class of 2005 Ross School of Business Finance Club.

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Transcript of 1 Financial Options In Depth Zachary Emig MBA Class of 2005 Ross School of Business Finance Club.