Day 3: Mechanics of futures trading & pricing/valuation of forwards and futures Selected discussion from Chapter 8 (pp ) & Chapter 9 (pp. 284 – 292)

Mechanics of futures trading - Intro Similar to option trading mechanics discussed last class. Figure 8.2 in Chance and Brooks is virtually identical to Figure 2.2. Difference is that both buyer and seller must deposit “initial margin.”

Mechanics of futures trading – order process Order is placed by customer. –Buy (long) futures contracts. –Sell (short) futures contracts. –Market, limit, day order, good-till-canceled, etc. Broker calls trading desk on exchange floor. Order is “run” to the trading floor. When order is filled, details are relayed back to customer.

Mechanics of future trading – clearing process After order is filled, customer’s initial margin must be deposited (with clearinghouse). –Margin money reflects good-faith deposit that customer will satisfy obligation. At end of each trading day, “settlement price” of futures contract is established. –Customers’ futures contracts are “marked-to-market.” –Is customer’s margin account greater than maintenance margin? If “No,” then customer needs to deposit additional funds into margin account (“variation margin”).

Examples of daily settlement Table 8.2 in Chance & Brooks –Treasury bond futures example –Each 1/32 point = $31.25 –Assume initial margin = $2,500, and maintenance margin = $2,000. Class example –Crude oil spreadsheet Students: do problem 16 in Chance & Brooks –Stock index futures

What happens if customer does not place “offsetting” order? One of the great advantages of futures over forwards is the ease of entering into an “offsetting” trade. –Example: Buy October futures on August 5, Sell October futures before expiration of contract. If original trade is not offset, then the “long” futures position must take delivery, and “short” futures position must make delivery. –Exchange matches longs and shorts. –One exception: Exchange for Physical (EFP)

Cost of carry (carry abitrage) model - Introduction What does “futures price” or “forward price” mean? What does “value” mean when discussing futures or forward contracts? Unlike stocks, bonds, options, etc., price and value are entirely different concepts for futures/forward contracts.

Cost of carry model: Initial value of futures or forward Price of futures or forward is merely the agreed-upon price at which the future delivery will be made. Value refers to how much is paid by buyer to enter into contract. At inception of futures or forward contract, the value is always “zero!”

Cost of carry model: Notation V t (0,T) = Value of forward contract created at time 0, as of time t, with expiration at time T. V t (T) = Value of corresponding futures contract. F(0,T) = price at time t of forward contract with expiration at time T. f t (T) = price at time t of corresponding futures contract.

Cost of carry model: Value of forward contract F(T,T) = S T –Forward price of forward created at time of expiration. –Forward price = spot price of asset (S). –Trivial case, but HAS to be true (or arbitrage). V T (0,T) = S T – F(0,T) –Value of forward contract at expiration. –Example: entered into “long” forward to buy asset for $500 in 1 month. One month later, spot price of asset is $550. How much (opportunity) profit did you earn on the forward contract? V t (0,T) = S t – F(0,T)(1+r) -(T-t) –Value of forward contract prior to expiration. –Use the same example, but suppose it’s 10 days into contract and spot price is at $540 and annual interest rate is 10% (assume 365 days per year). –Value = $42.60 (SHOW IT!!!!)

Cost of carry model: Forward price (relative to spot) Based on last equation and fact that forward contract has zero value at creation, –V 0 (0,T) = S 0 – F(0,T)(1+r) -T = 0 Solving last equation for F(0,T), –F(0,T) = S 0 (1+r) T –Forward price is the spot price compounded to the contract’s expiration. –If not true, then an arbitrage opportunity exists. Examples –What’s the forward price (in US$) of NZ$100,000 to be delivered in 6 months if 6-month T-bills yield 1% per year? At 5% per year? (see x-rates.com for spot price) –What must the spot price of gold be if 2-year forward contracts for gold are priced at $850? Assume 2-year T-bills yield 1.5% per year? (see kitco.com)

Cost of carry model: Value of futures contract f T (T) = S T –Futures price at expiration of contract. –Same result as with forward price. v t (T) = f t (T) – f t-1 (T) before contract is marked-to-market. –Suppose I bought November crude oil at $99.00 at market open on Oct 1, but at 1 PM, November crude is trading at $ –The contract is worth negative 50 cents per barrel to me. v t (T) = 0 as soon as the contract is marked-to-market. –Suppose settlement price for November crude is $ –My account is credited with the $0.30 per barrel gain, so the futures contract itself has zero value once this happens.

Cost of carry model: Futures price relative to spot f t (T) = S 0 (1+r) T This fact is true immediately after each daily settlement (i.e., after marking to market). Thus, futures price = forward price.

Next class Cost of carry model when underlying asset generates cash flows (single stock futures and dividends) Commodities and storage costs Risk premiums and futures prices