deriv slides
TRANSCRIPT
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Derivatives Workshop
Actuarial Society
October 30, 2007
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Agenda
Intro to Derivatives
Buying/Short-selling
Forwards Options
Swaps
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What are Derivatives?
A financial instrument that has a valuedetermined by price of something else
A contract whose value depends on what
something else is worth
Futures – Options
Swaps – Insurance
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Why use Derivatives?
Risk management
Hedging
Speculation Reduced transaction costs
Regulatory arbitrage
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Buying an Asset - Long Position
Offer price (ask price)
Bid price
Bid-ask spread Commission (flat or percentage)
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Example
Bid price = $50; Ask price = $50.25
Commission = $1/transaction
How much does it cost to buy 100 shares, thenimmediately sell it?
Cost = $50.25*100 - $50*100 + $2
= $27
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Short-Selling
Borrow now
Sell now
Buy later (covering the short position) Return later
Lease rate of asset –
payments that must bemade before repaying asset
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Why Short-sell?
Speculation
Financing
Hedging
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Example
Stock price now = $50
Stock price one year from now = $49.50
Commission = $1/transaction How much can you make short selling 100
shares?
Profit = $50*100-$49.50*100-$2= $48
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Forward Contracts
Sets terms now for the buying or selling of an
asset at specified time in future
Specifies quantity and type of asset
Sets price to be paid (forward price)
Obligates seller to sell and buyer to buy
Settles on expiration date
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Forward Contracts
Forward price -- price to be paid
Spot price -- market price now
Underlying asset -- asset on which contract isbased
Buyer = long; Seller = short
Long position makes money when price Short position makes money when price
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Payoffs in Forward Contract
Payoff to long forward (buyer) =
Spot price at expiration - forward price
Agreed to buy at fixed (forward) price
Payoff to short forward (seller) =
Forward price - spot price at expiration
Agreed to sell at fixed price
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Call Options
Contract where buyer has the right but no
obligation to buy
Seller is obligated to sell, if the buyer chooses to
exercise the option
Since seller cannot make money, buyer must pay
premium for option
Forwards have no premium
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Call Options
Strike price - amount buyer pays for the asset
Exercise - act of paying strike price to receive
the asset
Expiration - when option must be exercised, or
become worthless
European style - only exercise on x-date Bermudan style - during specified periods
American style - entire life of option
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Payoff of Call Option - Long
Buyer is not obligated to exercise -- will only do
so if payoff is greater than 0
Purchased call payoff =
max[0, spot price at x-date - strike price]
Must pay premium to seller
Profit = payoff - future value of premium
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Payoff of Call Option - Short
Opposite to payoff/profit of buyer
Written call payoff =
-max[0, spot price at x-date - strike price] Only profits from premium
Profit = - payoff + future value of premium
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Put Options
Contract where seller has the right but no obligation
to sell
Buyer is obligated to buy, if the seller chooses to
exercise the option
Since buyer cannot make money, seller must pay
premium for option
Seller of asset = buyer of put option
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Insurance Strategies
Buying put option – floor (min sale price)
Buying call option – cap (max price)
Covered writing –
writing option with
corresponding long position
Naked writing – no position in asset
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Covered writing
Covered call
Same as selling a put
Asset whose price is unlikely to change
Covered put
Same as writing a call
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Synthetic Forwards
BUY CALL &
SELL PUT
Must pay net optionpremium
Pay strike price
FORWARD
CONTRACT
Zero premium
Pay forward price
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Put-Call Parity
No arbitrage
Net cost of index must be same whether
through options or forward contract
Call (K,T) – Put(K,T) = PV(F0, T – K)
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Spreads – Only calls/only puts
Bull: buy call, sell call with higher strike price
Bear: buy higher strike price, sell lower
Box: synthetic long forward and syntheticshort forward at different prices
Ratio spread: buy m calls and sell n calls at
different strike prices Can have zero premium (only pay if you need the
insurance)
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Collars
Buy put, sell call with higher strike
Collar width – difference between call and put
strikes
Similar to short forward contract
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Straddles
Buying call and put with same strike price
Profits from volatility in both directions
Premiums are costly (paying twice)
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Strangle
Same as straddle, but buy out-of-the-money
options
Premiums will be lower
Stock price needs to be more volatile in order to
make profit
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Written Straddle
Sell call and put with same strike price
Profits when volatility is low
Potential unlimited loss from stock pricechanges in either direction
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Butterfly Spreads
Insures against losses from a written straddle
Out-of-the-money put provides insurance on
the downside
Out-of-the-money call provides insurance on
the upside