Day 3: Mechanics of futures trading

1
Day 3 Mechanics of futures trading
pricing/valuation of forwards and futures

• Selected discussion from Chapter 8 (pp. 265 -
  283) Chapter 9 (pp. 284 292)

2
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.

3
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.

4
Mechanics of future trading clearing process

• After order is filled, customers 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 customers margin account greater than
  maintenance margin?
• If No, then customer needs to deposit
  additional funds into margin account (variation
  margin).

5
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

6
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)

7
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.

8
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!

9
Cost of carry model Notation

• Vt(0,T) Value of forward contract created at
  time 0, as of time t, with expiration at time T.
• Vt(T) Value of corresponding futures contract.
• F(0,T) price at time t of forward contract with
  expiration at time T.
• ft(T) price at time t of corresponding futures
  contract.

10
Cost of carry model Value of forward contract

• F(T,T) ST
• 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).
• VT(0,T) ST 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?
• Vt(0,T) St F(0,T)(1r)-(T-t)
• Value of forward contract prior to expiration.
• Use the same example, but suppose its 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!!!!)

11
Cost of carry model Forward price (relative to
spot)

• Based on last equation and fact that forward
  contract has zero value at creation,
• V0(0,T) S0 F(0,T)(1r)-T 0
• Solving last equation for F(0,T),
• F(0,T) S0(1r)T
• Forward price is the spot price compounded to the
  contracts expiration.
• If not true, then an arbitrage opportunity
  exists.
• Examples
• Whats the forward price (in US) of NZ100,000
  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)

12
Cost of carry model Value of futures contract

• fT(T) ST
• Futures price at expiration of contract.
• Same result as with forward price.
• vt(T) ft(T) ft-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 98.50.
• The contract is worth negative 50 cents per
  barrel to me.
• vt(T) 0 as soon as the contract is
  marked-to-market.
• Suppose settlement price for November crude is
  99.30.
• My account is credited with the 0.30 per barrel
  gain, so the futures contract itself has zero
  value once this happens.

13
Cost of carry model Futures price relative to
spot

• ft(T) S0(1r)T
• This fact is true immediately after each daily
  settlement (i.e., after marking to market).
• Thus, futures price forward price.

14
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