Other Derivatives Professor Brooks BA /28/08

Other Derivatives Options on Futures Underlying contract for the option is the futures contract Derivative on a derivative Warrants Rights to purchase stock Foreign Currency Options When-Issued Trading Trading in pre-split stock prices

Options on Futures (Futures Options) Call Option Long -- Right but not the obligation to buy a futures contract (futures price pre-set) Short – Must sell futures contract if option is exercised Put Option Long – Right but not the obligation to sell a futures contract (futures price pre-set) Short – Must buy a futures contract if option is exercised

Look at Table 15-2 Soybeans…Long Call Position (Hedge – Short the Inventory, Processor) Call on the Mar 8500 Soybean is $ per bushel (5,000 bushels) cost is $ If exercised…you take delivery of a Soybeans futures contract that has a futures price of $8.50 per bushel with a delivery date of March Futures contract “market-to-market” immediately and you get the price difference Say settle on March Soybeans is $9.00 Long makes ($ $8.50) x 5,000 = $2,500

Table 15-2 Continued Net Gain for Long Call Position…i $2,500 at exercise - $ cost Net is $2, Net for Processor if you buy 5,000 bushels of Soybeans… Spot at $9.00 means cost $45,000 “Profit from Call” is $2, Net cost is $42,987.50

Table 15-2 Continued Staying with Long Call Position What if prices fall on Soybeans? Do not exercise the option Buy soybeans at the spot price Say spot is $8.00 per bushel Total Cost for Soybeans, Spot at $8,000 x 5,000 = $40,000 Plus cost of option, $ Total Cost $40, Option allowed you to enjoy “falling” prices but with insurance against “rising” prices

Table 15-2 Continued Soybeans…Short Call Position (Speculator Only) Call on the Mar 8500 Soybean is $ per bushel (5,000 bushels) cost is $ Call Writer gets the $ up front Hopes futures prices fall (option will not be exercised) If exercised must deliver futures contract If futures rises to $9.00 – loses $2, Still a zero-sum game in the option

Table 15-2 Put Option – April 8500 ($ per bushel) Long Put -- Buyer of put option (Hedger – producer of soybeans (farmer) that wants to be able to sell a futures contract if prices fall) Short Put – Speculator betting prices of futures will rise and put will not be exercised Long position has insurance against falling prices but can enjoy rising prices What would happen at $8.00 futures price? What would happen at $9.00 futures price?

Pricing Futures Options Back to Black and Sholes (Table 15-5) Call = e -RT [F x N(a) – K x N(b)] Where F is futures price, K is strike price, N is the cumulative normal distribution function, R is the risk free interest rate and T is time to expiration a is the solution to equation below and b is a – σ times the square root of t

Futures Option Prices Put formula Put = e -RT [K x N(-b) – F x N(-a)] All variables as previously noted And like all options we have Put-Call Parity P = C - e -RT [F– K ] or 0 = C – P - e -RT [F– K ] A note about sigma, the implied volatility This is the standard deviation of returns of the underlying asset…the futures contract not the commodity

Warrants A warrant is a call option on a stock where the stock will be delivered by the issuing company Warrants are tradable assets Set purchase price Typically long-term (years from expiration) May have very unusual exercise terms Single warrant may be for fractional share (for example it may take 10 warrants to buy one share) Not very common in US More common overseas

Warrants Example Coca-Cola wants to raise some money…about $500,000,000 via warrants. Each warrant will entitle the holder to buy 0.2 shares of Coca-Cola at $65 per share (need five warrants per share) The stock is currently selling at $60 per share and there are 2,320,000,000 shares outstanding. Black-Sholes prices the warrants at $4 with five years to maturity (risk-free rate at 4% and standard deviation at 30%)

Warrants Example If Coca-cola offers these warrants and issues them (it will take 125,000,000 warrants), what is Coca-Cola’s obligation? If prices rise above $65 warrants would be exercised…they would need to be able to deliver 25,000,000 shares of stock Coca-Cola would receive $500,000,000 now and at exercise $1,625,000,000 for stock Where will the 25,000,000 additional shares come from?

Warrant Hedge Say you want to do a warrant hedge… You buy 100 shares of Coca-Cola at $60 You short 500 warrants at $4 per warrant Net Cash Flow today -- $4,000 outflow What are your profits or losses above $65 Deliver you stock to “exercised warrants” and get $65 per stock -- $6,500 inflow (profit of $500 on stocks + $2,000 from warrants, total profit is $2,500 or max of $25 per share) Without hedge profit is (Price - $60) x 100, must be $85 to beat the hedge… What are your profits or losses below $65 Warrants out-of-the-money, made $4 per warrant, $4 x 500 =$2,000, But lost ((Price - $60) x 100), break even at $40 per share Without hedge, loss is (Price - $60) x 100, always lose $2,000 more than with hedge

Foreign Currency Options Two concepts here… Option on Foreign Currency Underlying asset is the foreign currency Call option is the right to buy the foreign currency at a pre-set exchange rate ($ per unit of foreign currency) Put option is right to sell the currency…if dominated in U.S. dollars, same as the call (you are delivering US dollars to get foreign currency Option on Foreign Currency Futures Underlying is a futures exchange contract Be careful how you use the terms

Foreign Currency Option Let say you want the right to buy euros in the future at a pre-set exchange rate but will use the spot if the rates fall (in $ per €). Strike price of call option is $1.35 per € and contract size is €62,500 Exercise if rates rise above $1.35 per € Let expire if rates fall below $1.35 per € Option exercise requires you to deliver $ for € $84,375 per contract for €62,500, but may be required upfront on the purchase of the call

Option on Foreign Currency Futures You want the right but not the obligation to buy a Foreign Currency Futures contract Today, Futures has a “price” of $1.35 per € and is for €125,000, lock in maximum delivery of $168,750 You buy call option on FX Futures…(price is only outflow) Tomorrow, Futures “price” has risen to $1.40 per € Exercise call option and get Futures at $1.35 per € Mark-to-Market and get difference in cash $0.05 x 125,000 = $6,250 but now must deliver $175,000 per contract, net is still original $168,750 Futures price falls, do not exercise and buy in spot with less than $168,750

When-Issued Stock When-Issued is short for “When and If Issued” With Bonds you are buying ahead of the auction With Pre-emergence from Chapter 11 you are buying prior to regular way trading resuming With Stock-Splits you are buying at the post-split price prior to the ex-date Stock-Split When Issued Example, INTC (Intel) is going to split their stock 4 for 1 For each current share you hold you will get three more and end up with four shares This is just a paper transaction…like breaking a $20 bill into four $5 bills

When-Issued Stock Split Assume INTC is currently selling at $20.80 Shares after the split will sell for $5.20 Approximately 20 days prior to the split you could buy when-issued shares at $5.20 per share When-issued shares will be “settled” after the split date (ex-date) Simultaneously you can still be buying INTC in the regular way at $20.80

When-Issued Stock Split Choi and Strong (1983) found a premium in the when-issued market INTC would be selling for $5.30 in the when- issued market and $20.80 in the regular way Thus you sell your shares in the when-issued market Brooks and Chiou (1995) found the premium was artifact of the way prices were measured Bid-ask spread eliminated some premium Clustering at the ask eliminated remainder