pricing of option

8/14/2019 Pricing of Option

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Pricing of OptionsPricing of Options

Presented byPresented by

John C. George 08PG0318John C. George 08PG0318

Mathew John 08PG0323Mathew John 08PG0323

Midhun Jose 08PG0324Midhun Jose 08PG0324Nidhin SkariahNidhin Skariah 08PG032608PG0326

Raja Rakesh 08PG0331Raja Rakesh 08PG0331


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Basic Concepts of OptionsBasic Concepts of Options

RelationshipRelationship

CallsCalls PutsPutsA > SA > S in-the-moneyin-the-money out-of-theout-of-the

moneymoney

A = SA = S at-the-moneyat-the-money at-the-moneyat-the-money

A < SA < S out-of-the-out-of-the- in-the-moneyin-the-money

moneymoney

A denotes the current price of the underlying assetA denotes the current price of the underlying asset

S denotes the strike price of the optionS denotes the strike price of the option


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A Transaction on an OptionA Transaction on an Option

ExchangeExchange

Buyer BuyersBroker

OptionsExchange

3

Buyers BrokersFloor Broker

OptionsClearingHouse

Buyers BrokersClearing Firm

Buyers BrokersClearing Firm

Sellers BrokersFloor Broker

SellersBroker

Seller

1a 1b Buyer and seller instruct their respective brokers to conduct an option transaction.

2a 2b Buyers and sellers brokers request their firms floor brokers execute the transaction.

3 Both floor brokers meet in the pit on the floor of the options exchange and agree on a price.

4 Information on the trade is reported to the clearinghouse.

5a 5b Both floor brokers report the price obtained to the buyers and sellers brokers.

6a 6b Buyers and sellers brokers report the price obtained to the buyer and seller.

7a 7b Buyer deposits premium with buyers broker. Seller deposits margin with sellers broker.

8a 8b Buyers and sellers brokers deposit premium and margin with their clearing firms.

9a 9b Buyers and sellers brokers clearing firms deposit premium and margin with clearinghouse.

1a

6a

7a

2a5a

48a 8b

9a 9b

2b5b

1b

6b

7b

Note: Either

buyer or seller

(or both) could

be a floor trader,

eliminating the

broker and floor

broker.


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Value of an OptionValue of an Option

The two components are,The two components are,Intrinsic Value:Intrinsic Value: of call = Max [A-S, 0]of call = Max [A-S, 0]

of put = Max [S-A, 0]of put = Max [S-A, 0]

Time value:Time value: It is the value in excess of theIt is the value in excess of the

intrinsic value and indicates options potential tointrinsic value and indicates options potential to

become more valuable before it expires. It decaysbecome more valuable before it expires. It decays

with passage of time.with passage of time.


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How is Value of OptionsHow is Value of Options

Affected*?Affected*?

FactorFactor Call ValueCall Value Put ValuePut Value

Increase in asset valueIncrease in asset value IncreaseIncrease DecreaseDecrease

Increase in strike priceIncrease in strike price DecreaseDecrease IncreaseIncrease

Increase in variance ofIncrease in variance ofunderlying assetunderlying asset

IncreaseIncrease IncreaseIncrease

Increase in time toIncrease in time to

expirationexpiration

IncreaseIncrease IncreaseIncrease

Increase in interest rateIncrease in interest rate IncreaseIncrease DecreaseDecrease

Increase in dividend paidIncrease in dividend paid DecreaseDecrease IncreaseIncrease

*American O

ptions


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Call OptionCall Option

Pay-off Diagram:Pay-off Diagram:Net payoffNet payoff

on callon call

StrikeStrike

PricePrice

Price of underlyingPrice of underlying

assetasset


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Put OptionPut Option

Pay-off Diagram:Pay-off Diagram:Net payoffNet payoff

on puton put

StrikeStrike

PricePrice

Price of underlying assetPrice of underlying asset


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Options other than Calls andOptions other than Calls and

PutsPuts

Convertible Bonds: Purchaser buys aConvertible Bonds: Purchaser buys a

straight bond and a call optionstraight bond and a call option

Callable bonds: Purchaser buys a straightCallable bonds: Purchaser buys a straight

bond and sells a call option to issuerbond and sells a call option to issuer

An equity share can be viewed as a callAn equity share can be viewed as a call

option on the assets of a company.option on the assets of a company.


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Buying and Selling Stock:Buying and Selling Stock:

Long PositionLong Position

400

EMP (T)

Profit

(-) 400Loss

0


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Buying and Selling Stock:Buying and Selling Stock:

Short PositionShort Position

MP (T)

Profit240

Loss

0240

E


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Elementary InvestmentElementary Investment

StrategiesStrategies

Long CallLong Call

Short CallShort Call

Long PutLong Put

Short PutShort Put


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Long CallLong Call

MP (T)

Profit

Loss

0400

440

E

(-) 40

This refers to the purchase of a call

These are cash flows when a

bullish

Investor buys a 3-month call on

the


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Short CallShort Call

MP (T)

Profit

Loss

0

400

440

E

(+) 40

This involves writing a call without owning theunderlying asset

These cash flows relate to writing a

3-month call on a stock at an exercise

price of Rs.400 per share

by receiving a premium of Rs.40.


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Long PutLong Put

MP (T)

Profit

Loss

0240

216

E

(-) 24

(+) 216

This involves buying a put the right to sell theUnderlying asset at a specified price

These cash flows relate to a bearish investor

Buying 3-month put with a exercise price of

Rs.240 per share by paying a premium of Rs.24


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Short PutShort Put

MP (T)

Profit

Loss

0240216

E

(-) 216

This involves writing a put

These cash flows relate to a bullish investor

Writing a put at an exercise price of Rs.240

Per share receiving a premium of Rs.24.


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Complex InvestmentComplex Investment

StrategiesStrategies

Covered Call WritingCovered Call Writing

Protective PutProtective PutStraddlesStraddles

StranglesStrangles

SpreadsSpreads


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Covered Call WritingCovered Call Writing

It involves buying the stock and writing callIt involves buying the stock and writing call

on that.on that.Profit

MP (T)

(+)48

(-)302

302350

E

These are cash flows when webuy100 shares @310 and write aMay 350 call for Rs.8 so thatinitialInvestment is Rs.302


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Covered Call:Covered Call:Why better than stock or only short calls?Why better than stock or only short calls?

Reduces the risk of uncovered call writing.Reduces the risk of uncovered call writing. Downside risk is reduced by the premium amount.Downside risk is reduced by the premium amount.

Loss of upward gains can be minimized by rolling up the exerciseLoss of upward gains can be minimized by rolling up the exercise

price.price.

When call ends up out-of-the-money, profits increase by every dollarWhen call ends up out-of-the-money, profits increase by every dollarby which the stock price exceeds the original price.by which the stock price exceeds the original price.

Has a lower B.E.P. compared to only stock.Has a lower B.E.P. compared to only stock.

Writing a covered call at lower exercise price is conservative, itWriting a covered call at lower exercise price is conservative, it

reduces the loss but also the upward gains.reduces the loss but also the upward gains.

Writing at higher exercise price is risky. Downside loss is higherWriting at higher exercise price is risky. Downside loss is higher

(less protective) and also gains are higher.(less protective) and also gains are higher.

A short holding period reduces the stock movement possibility and isA short holding period reduces the stock movement possibility and is

the best.the best.


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Protective PutProtective Put

It involves buying the stock and buying put onIt involves buying the stock and buying put on

that.that.Profit

Loss

(-)42

MP (T)270 312

E

These are cash flows when

buy

100 shares @ Rs.310 and buy

a


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Protective PutProtective Put

Guards against fall and also participate in gains. Put ensuresGuards against fall and also participate in gains. Put ensuresmin. selling price for stock.min. selling price for stock.

Gain on upside movement is restricted by the premium.Gain on upside movement is restricted by the premium.

Smaller downside risk and smaller upward gains and higherSmaller downside risk and smaller upward gains and higher

BEP.BEP.

Higher strike price costs maximum but also provides maximumHigher strike price costs maximum but also provides maximum

protection. Reduces the profits maximum.protection. Reduces the profits maximum.

Lower strike price costs less, less protective and reduces profitsLower strike price costs less, less protective and reduces profits

less.less.

Long holding period has chances of recovery of time value dueLong holding period has chances of recovery of time value due

to more chances of price movements.to more chances of price movements.


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Synthetic Put and CallSynthetic Put and Call

AA synthetic putsynthetic put involves long calls andinvolves long calls and

short sale of an equal number of sharesshort sale of an equal number of shares

of stock.of stock.

Synthetic callSynthetic call involves buying stockinvolves buying stock

and an equal number of puts and isand an equal number of puts and is

nothing but protective put.nothing but protective put.


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Long StraddleLong Straddle

Involves buying a put and a call, each with sameInvolves buying a put and a call, each with sameexercise priceexercise price

and same time to expiration.and same time to expiration.Profit247

Loss

(-)63

MP (T)247 373

E1

Buying a Jun 310 call for Rs.21

And Jun 310 put for Rs.42 per

Share. Initial investment Rs63.

310

E2


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Short StraddleShort Straddle

Involves selling a put and a call, each with sameInvolves selling a put and a call, each with sameexercise priceexercise price

and same time to expiration.and same time to expiration.

Profit

Loss(-)247

(63)

MP (T)247 310

E2

373

E1


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Straddle VariantsStraddle Variants

Straps:Straps:

A bullish variation of straddle, involves two callsA bullish variation of straddle, involves two calls

and one put. Investors are more bullish thanand one put. Investors are more bullish than

bearish and therefore increase calls.bearish and therefore increase calls.

Strips:Strips:

It is a slightly bearish variation of straddle, hasIt is a slightly bearish variation of straddle, haslong position in two puts and one call andlong position in two puts and one call and

involves ones bet that the market will go down.involves ones bet that the market will go down.


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Long StrangleLong StrangleInvolves buying a call and a put on the same underlyingInvolves buying a call and a put on the same underlying

assetasset

for same expiration period atfor same expiration period at different exercise pricesdifferent exercise prices

Profit247

-23

Loss

E1 E2333247

270 310

Buy Jun 310 call for Rs.21 and Jun 270

Put for Rs. 2. Initial investment Rs.23.

Usually one in-the-money and another

Out-of-the-money. Initial investment

Can be less than straddle

MP (T)


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SpreadsSpreads

Involve buying of one option and selling of another.Involve buying of one option and selling of another.

Offer potential for small profit and limit the risk.Offer potential for small profit and limit the risk.

VerticalVertical Spreads also calledSpreads also called StrikeStrike oror MoneyMoney spreads.spreads.

Could be written as say, July 120/125 Spread.Could be written as say, July 120/125 Spread.HorizontalHorizontal Spreads also called asSpreads also called as TimeTime oror CalendarCalendar

Spreads. Could be written as June/July 120 Spread.Spreads. Could be written as June/July 120 Spread.


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SpreadsSpreads

For Vertical Spreads:For Vertical Spreads:

A July 120/125 call spread is a net longA July 120/125 call spread is a net long

position and is called Buying the Spread,position and is called Buying the Spread,sometimes referred to as Debit Spread.sometimes referred to as Debit Spread.

A July 120/125 put spread is a net shortA July 120/125 put spread is a net short

position and is called Selling the Spread,position and is called Selling the Spread,

sometimes referred to as Credit Spread.sometimes referred to as Credit Spread.


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SpreadsSpreads

For Horizontal Spreads:For Horizontal Spreads:

A June/July 120 call spread is a net shortA June/July 120 call spread is a net short

position and is called Selling the Spread,position and is called Selling the Spread,sometimes referred to as Credit Spread.sometimes referred to as Credit Spread.

A July/June 120 call spread is a net longA July/June 120 call spread is a net long

position and is called Buying the Spread,position and is called Buying the Spread,

sometimes referred to as Debit Spread.sometimes referred to as Debit Spread.


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Horizontal SpreadsHorizontal Spreads(Across Expiration(Across ExpirationMonths)Months)

Involve buying an option and selling another of sameInvolve buying an option and selling another of same

type with same exercise price but with differenttype with same exercise price but with different

expiration time.expiration time.

In a horizontal bull spread, we buy back month and sellIn a horizontal bull spread, we buy back month and sellthe front month. In a horizontal bear spread, we buythe front month. In a horizontal bear spread, we buy

front month and sell back month.front month and sell back month.

Horizontal bull spread has similar pay-off as that of aHorizontal bull spread has similar pay-off as that of a

short straddle and horizontal bear spread has similarshort straddle and horizontal bear spread has similar

payoff as that of a long straddle.payoff as that of a long straddle.


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Diagonal SpreadsDiagonal Spreads

They are vertical and horizontalThey are vertical and horizontal

at the same time i.e. the areat the same time i.e. the are

across both strike price andacross both strike price and

expiration month.expiration month.


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Butterfly SpreadButterfly Spread

Involves four options, all calls or all puts.Involves four options, all calls or all puts.

All have same expiration month and sameAll have same expiration month and same

underlying asset.underlying asset.

One option has high strike price, one hasOne option has high strike price, one has

low strike price and two have same strikelow strike price and two have same strike

price which is between those of high strikeprice which is between those of high strike

and low strike.and low strike.

Two middle strike price are sold and the twoTwo middle strike price are sold and the two

end options are purchased.end options are purchased.


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Reverse Butterfly or SandwichReverse Butterfly or Sandwich

SpreadsSpreads

This is strategy reverse of theThis is strategy reverse of the

butterfly spread.butterfly spread.

The two middle strike price optionsThe two middle strike price options

are purchase and the two end strikeare purchase and the two end strike

price options are sold.price options are sold.


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Evaluation of theEvaluation of the

StrategiesStrategies Transaction costs have not been considered andTransaction costs have not been considered and

should be kept in mind.should be kept in mind.

Bid-ask spreads may affect payoffs.Bid-ask spreads may affect payoffs.

They are not dividend protected.They are not dividend protected.

Margin requirements are applicable to optionMargin requirements are applicable to option

writing.writing.

Possibility of early exercise may pose new risks.Possibility of early exercise may pose new risks.

Timing of cash flows can make a difference.Timing of cash flows can make a difference.


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Futures vs. Options:Futures vs. Options:PerformancePerformance

Option purchasers do not post margins sinceOption purchasers do not post margins since

they have no obligationsthey have no obligations

An option clearing house serves the similarAn option clearing house serves the similar

functions as those of clearing associations infunctions as those of clearing associations in

futures tradingfutures trading

Option writers have to post margins toOption writers have to post margins toclearing housesclearing houses

Options are also OTC and dealers may requireOptions are also OTC and dealers may require

margins or guarantees.margins or guarantees.


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pricing of option

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