Derivatives Derivatives WorkshopWorkshop

Actuarial SocietyActuarial Society

October 30, 2007October 30, 2007

AgendaAgenda

Intro to DerivativesIntro to Derivatives Buying/Short-sellingBuying/Short-selling ForwardsForwards OptionsOptions SwapsSwaps

What are Derivatives?What are Derivatives?

A financial instrument that has a A financial instrument that has a value determined by price of value determined by price of something elsesomething else

A contract whose value depends on A contract whose value depends on what something else is worthwhat something else is worth

Futures Futures –– OptionsOptions SwapsSwaps – Insurance– Insurance

Why use Derivatives?Why use Derivatives?

Risk managementRisk management HedgingHedging

SpeculationSpeculation Reduced transaction costsReduced transaction costs Regulatory arbitrageRegulatory arbitrage

Buying an Asset - Long Buying an Asset - Long PositionPosition

Offer price (ask price)Offer price (ask price) Bid priceBid price Bid-ask spreadBid-ask spread Commission (flat or percentage)Commission (flat or percentage)

ExampleExample

Bid price = $50; Ask price = $50.25Bid price = $50; Ask price = $50.25 Commission = $1/transactionCommission = $1/transaction How much does it cost to buy 100 How much does it cost to buy 100

shares, then immediately sell it?shares, then immediately sell it? Cost = $50.25*100 - $50*100 + $2Cost = $50.25*100 - $50*100 + $2

= $27= $27

Short-SellingShort-Selling

Borrow nowBorrow now Sell nowSell now Buy later (covering the short Buy later (covering the short

position)position) Return laterReturn later

Lease rate of asset – payments that Lease rate of asset – payments that must be made before repaying assetmust be made before repaying asset

Why Short-sell?Why Short-sell?

SpeculationSpeculation FinancingFinancing HedgingHedging

ExampleExample

Stock price now = $50Stock price now = $50 Stock price one year from now = Stock price one year from now =

$49.50$49.50 Commission = $1/transactionCommission = $1/transaction How much can you make short How much can you make short

selling 100 shares?selling 100 shares? Profit = $50*100-$49.50*100-$2Profit = $50*100-$49.50*100-$2

= $48= $48

Forward ContractsForward Contracts

Sets terms now for the buying or Sets terms now for the buying or selling of an asset at specified time selling of an asset at specified time in futurein future Specifies quantity and type of assetSpecifies quantity and type of asset Sets price to be paid (forward price)Sets price to be paid (forward price) Obligates seller to sell and buyer to buyObligates seller to sell and buyer to buy

Settles on expiration dateSettles on expiration date

Forward ContractsForward Contracts

Forward price -- price to be paidForward price -- price to be paid Spot price -- market price nowSpot price -- market price now Underlying asset -- asset on which Underlying asset -- asset on which

contract is basedcontract is based Buyer = long; Seller = shortBuyer = long; Seller = short

Long position makes money when priceLong position makes money when price Short position makes money when price Short position makes money when price

Payoffs in Forward Payoffs in Forward ContractContract

Payoff to long forward (buyer) = Payoff to long forward (buyer) = Spot price at expiration - forward Spot price at expiration - forward priceprice Agreed to buy at fixed (forward) priceAgreed to buy at fixed (forward) price

Payoff to short forward (seller) =Payoff to short forward (seller) =Forward price - spot price at Forward price - spot price at expirationexpiration Agreed to sell at fixed priceAgreed to sell at fixed price

Call OptionsCall Options

Contract where buyer has the Contract where buyer has the right right but no obligationbut no obligation to buy to buy Seller is obligated to sell, if the buyer Seller is obligated to sell, if the buyer

chooses to exercise the optionchooses to exercise the option Since seller cannot make money, Since seller cannot make money,

buyer must pay premium for optionbuyer must pay premium for option Forwards have no premiumForwards have no premium

Call OptionsCall Options

Strike price - amount buyer pays for the Strike price - amount buyer pays for the assetasset

Exercise - act of paying strike price to Exercise - act of paying strike price to receive the assetreceive the asset

Expiration - when option must be Expiration - when option must be exercised, or become worthlessexercised, or become worthless

European style - only exercise on x-dateEuropean style - only exercise on x-date Bermudan style - during specified periodsBermudan style - during specified periods American style - entire life of optionAmerican style - entire life of option

Payoff of Call Option - Payoff of Call Option - LongLong

Buyer is not obligated to exercise -- Buyer is not obligated to exercise -- will only do so if payoff is greater will only do so if payoff is greater than 0than 0

Purchased call payoff =Purchased call payoff =max[0, spot price at x-date - strike max[0, spot price at x-date - strike price]price] Must pay premium to sellerMust pay premium to seller

Profit = payoff - future value of Profit = payoff - future value of premiumpremium

Payoff of Call Option - Payoff of Call Option - ShortShort

Opposite to payoff/profit of buyerOpposite to payoff/profit of buyer Written call payoff =Written call payoff =

-max[0, spot price at x-date - strike -max[0, spot price at x-date - strike price]price] Only profits from premiumOnly profits from premium

Profit = - payoff + future value of Profit = - payoff + future value of premiumpremium

Put OptionsPut Options

Contract where seller has the Contract where seller has the right right but no obligationbut no obligation to sell to sell Buyer is obligated to buy, if the seller Buyer is obligated to buy, if the seller

chooses to exercise the optionchooses to exercise the option Since buyer cannot make money, Since buyer cannot make money,

seller must pay premium for optionseller must pay premium for option Seller of asset = buyer of put Seller of asset = buyer of put

optionoption

Insurance StrategiesInsurance Strategies

Buying put option – floor (min sale Buying put option – floor (min sale price)price)

Buying call option – cap (max price)Buying call option – cap (max price) Covered writing – writing option Covered writing – writing option

with corresponding long positionwith corresponding long position Naked writing – no position in assetNaked writing – no position in asset

Covered writingCovered writing

Covered callCovered call Same as selling a putSame as selling a put Asset whose price is unlikely to changeAsset whose price is unlikely to change

Covered putCovered put Same as writing a callSame as writing a call

Synthetic ForwardsSynthetic Forwards

BUY CALL & BUY CALL &

SELL PUTSELL PUT

Must pay net Must pay net option premiumoption premium

Pay strike pricePay strike price

FORWARD FORWARD CONTRACTCONTRACT

Zero premiumZero premium

Pay forward pricePay forward price

Put-Call ParityPut-Call Parity

No arbitrageNo arbitrage Net cost of index must be same Net cost of index must be same

whether through options or forward whether through options or forward contractcontract

Call (K,T) – Put(K,T) = PV(FCall (K,T) – Put(K,T) = PV(F00,,TT – – K)K)

Spreads – Only calls/only Spreads – Only calls/only putsputs

Bull: buy call, sell call with higher strike Bull: buy call, sell call with higher strike priceprice

Bear: buy higher strike price, sell lowerBear: buy higher strike price, sell lower Box: synthetic long forward and synthetic Box: synthetic long forward and synthetic

short forward at different pricesshort forward at different prices Ratio spread: buy m calls and sell n calls Ratio spread: buy m calls and sell n calls

at different strike pricesat different strike prices Can have zero premium (only pay if you need Can have zero premium (only pay if you need

the insurance)the insurance)

CollarsCollars

Buy put, sell call with higher strikeBuy put, sell call with higher strike Collar width – difference between Collar width – difference between

call and put strikescall and put strikes Similar to short forward contractSimilar to short forward contract

StraddlesStraddles

Buying call and put with same Buying call and put with same strike pricestrike price

Profits from volatility in both Profits from volatility in both directionsdirections

Premiums are costly (paying twice)Premiums are costly (paying twice)

StrangleStrangle

Same as straddle, but buy out-of-the-Same as straddle, but buy out-of-the-money optionsmoney options

Premiums will be lowerPremiums will be lower Stock price needs to be more volatile Stock price needs to be more volatile

in order to make profitin order to make profit

Written StraddleWritten Straddle

Sell call and put with same strike Sell call and put with same strike priceprice

Profits when volatility is lowProfits when volatility is low Potential unlimited loss from stock Potential unlimited loss from stock

price changes in either directionprice changes in either direction

Butterfly SpreadsButterfly Spreads

Insures against losses from a written Insures against losses from a written straddlestraddle

Out-of-the-money put provides Out-of-the-money put provides insurance on the downsideinsurance on the downside

Out-of-the-money call provides Out-of-the-money call provides insurance on the upsideinsurance on the upside

SwapsSwaps

Contract for exchange of payments Contract for exchange of payments over timeover time

Forward is single-payment swapForward is single-payment swap Multiple forwards, but as single Multiple forwards, but as single

transactiontransaction