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Derivatives Workshop

Actuarial Society

October 30, 2007



Agenda

Intro to Derivatives

Buying/Short-selling

Forwards Options

Swaps



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



Why use Derivatives?

Risk management

Hedging

Speculation Reduced transaction costs

Regulatory arbitrage



Buying an Asset - Long Position

Offer price (ask price)

Bid price

Bid-ask spread Commission (flat or percentage)



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



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



Why Short-sell?

Speculation

Financing

Hedging



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



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



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



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



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



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



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



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



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



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



Covered writing

Covered call

Same as selling a put

Asset whose price is unlikely to change

Covered put

Same as writing a call



Synthetic Forwards

BUY CALL &

SELL PUT

Must pay net optionpremium

Pay strike price

FORWARD

CONTRACT

Zero premium

Pay forward price



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)



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)



Collars

Buy put, sell call with higher strike

Collar width – difference between call and put

strikes

Similar to short forward contract



Straddles

Buying call and put with same strike price

Profits from volatility in both directions

Premiums are costly (paying twice)



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



Written Straddle

Sell call and put with same strike price

Profits when volatility is low

Potential unlimited loss from stock pricechanges in either direction



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



Swaps

Contract for exchange of payments over time

Forward is single-payment swap

Multiple forwards, but as single transaction

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