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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