Derivatives Workshop

1
Derivatives Workshop

• Actuarial Society
• October 30, 2007

2
Agenda

• Intro to Derivatives
• Buying/Short-selling
• Forwards
• Options
• Swaps

3
What are Derivatives?

• A financial instrument that has a value
  determined by price of something else
• A contract whose value depends on what something
  else is worth
• Futures Options
• Swaps Insurance

4
Why use Derivatives?

• Risk management
• Hedging
• Speculation
• Reduced transaction costs
• Regulatory arbitrage

5
Buying an Asset - Long Position

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

6
Example

• Bid price 50 Ask price 50.25
• Commission 1/transaction
• How much does it cost to buy 100 shares, then
  immediately sell it?
• Cost 50.25100 - 50100 2 27

7
Short-Selling

• Borrow now
• Sell now
• Buy later (covering the short position)
• Return later
• Lease rate of asset payments that must be made
  before repaying asset

8
Why Short-sell?

• Speculation
• Financing
• Hedging

9
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 50100-49.50100-2 48

10
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

11
Forward Contracts

• Forward price -- price to be paid
• Spot price -- market price now
• Underlying asset -- asset on which contract is
  based
• Buyer long Seller short
• Long position makes money when price
• Short position makes money when price

12
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

13
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

14
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

15
Payoff of Call Option - Long

• Buyer is not obligated to exercise -- will only
  do so if payoff is greater than 0
• Purchased call payoff max0, spot price at
  x-date - strike price
• Must pay premium to seller
• Profit payoff - future value of premium

16
Payoff of Call Option - Short

• Opposite to payoff/profit of buyer
• Written call payoff -max0, spot price at
  x-date - strike price
• Only profits from premium
• Profit - payoff future value of premium

17
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

18
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

19
Covered writing

• Covered call
• Same as selling a put
• Asset whose price is unlikely to change
• Covered put
• Same as writing a call

20
Synthetic Forwards

• BUY CALL
• SELL PUT
• Must pay net option premium
• Pay strike price

• FORWARD CONTRACT
• Zero premium
• Pay forward price

21
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)

22
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 synthetic short
  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)

23
Collars

• Buy put, sell call with higher strike
• Collar width difference between call and put
  strikes
• Similar to short forward contract

24
Straddles

• Buying call and put with same strike price
• Profits from volatility in both directions
• Premiums are costly (paying twice)

25
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

26
Written Straddle

• Sell call and put with same strike price
• Profits when volatility is low
• Potential unlimited loss from stock price changes
  in either direction

27
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

28
Swaps

• Contract for exchange of payments over time
• Forward is single-payment swap
• Multiple forwards, but as single transaction