Derivatives Workshop

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 value determined by price of something else A contract whose value depends on what something else is worth Futures  Swaps  – Options – 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, then immediately 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 be made 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 is based 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  FORWARD CONTRACT   Must pay net option premium Pay strike price 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 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) 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 price changes 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