Currency and Commodity Derivatives
Lecture 7

1. Derivatives - purchase commodities on a future date for a known price today

• Started in the Middle Ages between farmers and merchants

2. Why use derivatives?

• Reduces price uncertainty - buyer and seller lock in a price today for a future transaction

• Reduces interest rate risk

  • Bank will grant a loan in the future

  • Bank can buy a derivative to borrow money for a loan

  • Prevent the bank from loaning at a low interest rate and borrowing at a high interest rate

• Reduces exchange rate risk

  • Corporation has operations in a foreign country

  • If that country's currency depreciates, it reduces that firm's assets and improves that firm's liabilities

3. Types of investors

• Hedgers - want to protect against price changes

  • Purchase a derivative to "lock" in a price

• Speculators - make money by predicting market changes

  • Gambling

  • Example - Baring Brothers and Company was a London investment firm

  • Founded in 1763

  • Nick Leeson, a trader, lost about $1.3 billion in the derivatives market in 1995

  • Bankrupted Barings

  • Speculators are important, because they increase the liquidity of the market

1. Futures markets - standardized contracts (same duration, size, collateral)

• Futures Contracts - Traded on organized exchanges

  • Contracts are standardized

  • Chicago Board of Trade - futures for corn, soybeans, ethanol, etc.

  • New York Mercantile Exchange - electricity, etc.

  • Chicago Mercantile Exchange - currency futures

• Forward markets - tailor-made contracts

  • Reputation/collateral guarantees the contract

  • Usually issued by banks and brokers

• Terminology

  • Short is agreement to sell

  • Long is agreement to buy

  • Contract size - specifies number of units in each contract

  • Maturity date - the date when the transaction is completed

  • Futures price - the selling price of the asset on the maturity date

• Margin account: - buyer or seller deposits money with a broker to cover possible losses from a futures contract

  • Guarantees the contract will be honored

  • Market price has to exceed some threshold before margin call

2. Example 1 - A Margin Call

• A refinery buys 10 contracts of petroleum that matures in six months

• Contract size is 10,000 barrels of petroleum

• Contract price is $100 per barrel

What happens if the petroleum price is $115 per barrel? Which party deposits funds with broker?

• The seller (issuer) deposits 10*10,000*($115 - $100) = $1.5 million with his broker

• If this contract matured today, then the buyer would purchase this oil for $100, and could sell it for $115, making $1.5 million in profits

• Speculator's profits = ($115 - $100)(10)(10,000) = $1.5 million

What happens if petroleum price is $85 per barrel? Which party deposits funds with broker?

• The buyer (refinery) deposits 10*10,000*($100 - $85) = $1.5 million with his broker

• If this contract matured today, then the seller could buy oil on the spot market for $85 per barrel, and sell it to the buyer for $100, earning $1.5 million in profits

• Speculator's profits = ($85 - $100)(10)(10,000) = -$1.5 million

3. Example 2 - Margin Call for a currency futures

• Exxon has U.S. dollars and purchased chemicals from Malaysia

  • Contract is for ringgits

• Exxon needs to make a 3 million ringgit payment in 90 days

• Contract size is 1 million ringgits

• Contract price is $1 / 3 rinngits (or exchange rate is $1 = 3 ringgits)

  • Exxon needs the amount = ($1 / 3 ringgits)(3,000,000 ringgits) = $1 million

What happens if the exchange rate is $1 = 3.1 ringgits (or $1 / 3.1 ringgits)?

• The dollar appreciated while ringgits depreciated.

• The market value of contract decreased.

• Exxon has U.S. dollars and contracted to pay a lower exchange rate.

• Exxon must deposit money into the margin account.

  • Spot market: amount = ($1 / 3.1 ringgit) (3 million ringgits) = $967,742

  • Futures market: amount = $1 million

• Who issued this contract benefits:

  • Their profit is $32,258 because bank could buy 3 million ringgits for $967,742 and sell them for $1 million.

What happens if the exchange rate is $1 = 2.9 ringgits (or $1 / 2.9 ringgits)?

• The ringgit appreciated while dollar depreciated.

• The market value of contract increased.

• Who issued this contract must put money into a margin account.

  • Spot market: amount = ($1 / 2.9 ringgit)(3 million ringgits) = $1,034,482

  • Futures market: amount = $1 million

• Exxon would profit by $34,482. It could buy 3 million ringgits for $1 million and sell them for $1,034,482.

1. Types of option contracts:

1. Call options give the holder the right to buy the asset

2. Put options give the holder the right to sell the asset

2. An option specifies:

1. Exercise or strike price - the asset price listed on the option

2. Expiration date - date when the right expires

3. American options - holder can exercise the option anytime until maturity

   • Construct binomial tree diagram

   • Covered in higher finance classes

4. European options - holder can only exercise the option on expiration date

   • European options are priced using Black-Scholes formula

   • Black-Scholes is covered in higher finance classes

   • Note - a mathematical proof shows the call options are the same for both the American and European, while the put is different

3. Holder pays a premium - an option is like insurance

• Currency premiums are affected by five factors:

  1. Spot market price - if the spot price rise, then the call option's premium increases while the put option's premium falls

     • Remember - investors buy low and sell high

     • Investor is likely to exercise if the market price exceeds the strike price a call option

     • Investor buys at the lower price at the sttike price and sells at the greater price

     • Put option is the opposite

  2. Strike price - if the spot price rises, then the call option's premium falls while the put option's premium rises

     • Investor would not exercise a call option if the strike price exceeds the spot price

     • He can't make a profit

     • Put option is the opposite

  3. Expiration date - the longer the expiration date, the greater the premium

     • Events could happen that increase likelihood of being exercised

  4. Volatility (variance or standard deviation) of commodity price

     • From spot market

     • The more variable the commodity price, the greater the premium

     • More likely to be exercised

     • Commodity A fluctuates between $10 and $20 while Commodity B fluctuates between $50 and $150

     • Commodity B would have greater premiums

  5. Increasing interest rates

     • Increasing interest rates lower bond's market prices

     • Present value formula

     • Put option's value falls while call option's value rises

4. All examples are for European options.

• Example 1 - European call option

• The strike price is $80 per barrel of petroleum

• The premium is $0.1 per barrel

• The quantity is 10,000 barrel

• A company buys 10 call options

Petroleum quantity = 10(10,000 barrels) = 100,000 barrels

Premium = ($0.1 per barrel) (10)(10,000 barrels) = $10,000

If the spot price exceeds $80 (strike price), company exercises call option. Company buys petroleum at $80 and could sell petroleum on spot market for a profit.

If spot price (revenue) > premium (cost) + strike price (cost), then holder earns a profit by selling the commodity

If market price (spot) is below $80 per barrel, then company does not exercise option. However, the company loses the premium, which is a loss.

• Example 2 - European put option

• The strike price is $40 per ton of corn

• The premium is $0.07 per ton

• The quantity is 10,000 tons

• A farmer buys 5 put options.

• Corn quantity = 5(10,000 tons) = 50,000 tons

Premium = ($0.07 per ton)(5)(10,000 tons) = $3,500

If spot price exceeds $40 (strike price), farmer does not exercise put option. Farmer can sell corn for a higher price on spot market. Farmer loses the premium.

If spot price is below $40 per ton, then farmer exercises put option.  Farmer could buy corn from spot market and sell to party who bought put option.

If strike price (revenue) > premium (cost) + spot price (cost)

5. Currency Options - More complicated

• Two markets for options:

  1. Interbank (OTC) market located in London, New York, and Tokyo

     • OTC options are tailor-made as to size, maturity, and exercise price.

  2. Exchange markets located in Philadelphia

     • Maturities are 1, 3, 6, and 12 months

• Example 3 - European call option

• The strike price is $0.00833 /1 tenge ($1 = 120 tenge)

• The premium is $0.005 / 1 tenge

• Contract size is 50,000 tenge

• Person want to buy 10 million tenge and has U.S. dollars

Person needs (10 million tenge) / (50,000 tenge) = 200 contracts

Premium = ($0.005 / 1 tenge)(10 million tenge) = $50,000

Expiration date and European option

If exchange rate is $0.01 / tenge ($1 = 100 tenge), then calculate both situations

• If person exercises call option, then he needs: ($0.00833 / 1 tenge)(10 million tenge) = $83,300

• If person does not exercise call option, then he needs ($0.01 / 1 tenge) = $100,000

• Thus, exercise call option because it cost less in dollars; the contracts become more valuable

If exchange rate is $0.005 / 1 tenge, then calculate both situations

• If person exercises call option, then he needs $83,300

• If person does not exercise call option, then he needs ($0.005 / 1 tenge)(10 million tenge) = $50,000

• Thus, don't exercise call option, because it is cheaper; the contracts become less valuable

• Example 4 - European put option

• The strike price is $0.8 / 1 Euro

• The premium is $0.03 / 1 Euro

• Contract size is 25,000 Euros

• A person wants to sell 500,000 Euros and has U.S. dollars

The person has to buy (500,000 Euros) / (25,000 Euros) = 20 contracts

Premium = ($0.03 / 1 Euro)(500,000 Euros) = $15,000 for premium.

Expiration date

If the spot exchange rate is $0.9 /1 Euro, then calculate both situations

• If the person exercises the put option, he collects ($0.8 /1 Euro)(500,000 Euros) = $400,000

• If the person does not exercise put option, then he collects ($0.9 / 1 Euro) (500,000 Euros) = $450,000

• Thus, this person does not exercise the put options, because he can sell it for a higher price on spot market

If exchange rate is $0.7 / 1 Euro, then calculate both situations

• If the person exercises the put options, he collects $400,000

• If the person does not exercise the put options, then he collects ($0.7 / 1 Euro)(500,000 Euros) = $350,000

• Thus, he exercises the put options, because he can receive more revenue than the spot market

Did you notice investors exercise call and put options "as opposites" when investor exercises option.

1. Securitization - take a variety of loans or securities with a known cash flow, pool them together into a fund, and sell shares to investors

• Mortgage Asset Backed Securities (ABS) - use securitization to package mortgages

• Investors purchase bonds to this fund

  • tranche - French term - means slice or portion

  • Each fund has different types of bonds with different risk levels

  • One bond could be rated AAA and have low return

  • Another bond could be speculative (i.e. junk) and have a high return and high risk

  • David Li invented a way to value the different tranches in 2000

• Banks used securitization to get rid of mortgages

  • Mortgages become liquid assets

  • Liquid - ease of converting an asset to cash

• Banks earned profits from mortgage fees and fund management

• Bank has money to grant more mortgages, and process continues

• Result - a mortgage became a liquid security that could be bought and sold

2. Collateralized Debt Obligations (CDOs)

• Investment banks - help government issue new bonds or corporations to issue new stock or bonds

  • Investment banks wanted to profit from the mortgage market

  • They packaged the bonds from securitization into a fund

  • Used tranches to offer different returns and risk levels

  • CDOs were marketed to investors around the world and avoid U.S. regulations

  • Form of re-securitization

  • Banks earned fees from fund setup and management

• Credit Agencies

  • CDOs always were packaged with a AAA credit rating

  • Pension plans for government workers, teachers, police officers etc. require a AAA rating to invest using pension funds

  • Some CDOs had subprime mortgages

  • Subprime mortgage - someone with low or bad credit

  • Possible fraud or incompetence of rating agencies

• Possible fraud

  • Companies packaged their debt into CDOs

  • Then they became investors and purchased their bonds

  • Companies converted a liability into an asset

  • Estimates of market ranged from $0.5 trillion to $2 trillion in 2006

• 2008 Financial Crisis

  • ABS and CDOs attracted large sums of money to U.S. housing market

  • Housing prices rapidly appreciated

  • Banks kept lowering their lending standards to grant more people a mortgage

  • Joke in Houston - if you have a heartbeat and paycheck stub in your pocket, then you had a mortgage loan

  • 2007 Great Recession

    • Unemployment rate increases

    • Defaults in mortgages

    • Investors stop investing in CDOs

    • Banks and investment banks were stuck with billions in unsold CDOs

1.Stock Market Index - financial companies offer call and put options on a stock market index

• No commodities are traded; cannot have futures and forwards

• Financial companies could earn option premiums as profits

• Chicago Board of Trade offers options on the Dow Jones Industrial Average, called DJX

• If investors exercise option, then the issuers settle accounts in cash

• Example - Nick Leeson

  • Used a straddle

  • The Tokyo stock exchange fluctuated over a narrow range

  • He issued an equal number of calls and puts on Tokyo stock exchange

  • The option premiums were pure profit until the Kobe earthquake

  • Leeson bet the exchange would rise; instead, the stock exchange quickly fell

2. The Volatility Index (VIX)

• Volatility is a measure of risk

• "Investor fear gauge"

• Chicago Board of Options Exchange (CBOE) - calculates VIX from Standard & Poor's 500 stock index

  • Sells put/call options on VIX

  • Options are not tied to an asset

  • On maturity, if payment exists, then payment is settled in cash

  • Exposure - if VIX increases or decreases dramatically, then CBOE may incur large losses from exercised options

• If the VIX = 20, investors expect the S&P 500 index to swing by 20% over the next 12 months

  • If the VIX increases

    • Investors become more pessimistic

    • Markets become more volatile

3. Credit Default Swaps

• Investors want to earn the high returns from risky securities

• Investors lose if the risky company bankrupts

• Investors bought CDS as insurance

  • pay a premium

  • if company bankrupts, then the bonds become worthless

  • CDS would pay the bondholders a payout for the worthless securities

• CDS contracts are sold on the derivatives market

4. Problems with CDSs

1. Investors could buy CDS contracts, even if they had no financial ties to the company specified in contract

   • Gambling that a certain firm will fail

   • Your cost is the premium

   • Your revenue is the payout if company bankrupts

   • Like buying insurance on your neighbor's house, hoping it will burn down

2. Multiple CDS contracts can be layered on the same debt

   • An dealer buys a CDS contract on a risky bond from a Company X at 2% premium

   • The financial health of Company X deteriorates

   • The dealer can issue a new CDS contract with a premium of 4%, earning 2% in profits

   • If Company X bankrupts, then the dealer pays out his contract with the money from the first CDS contract

3. CDSs and CDOs are not transparent

   • Many people did not understand them

4. Lehman Brothers

   • Issued $400 billion in CDS contracts on debt valued at $155 billion

   • Financial meltdown in October 2008, as Lehman Brothers could not meet its obligations

   • U.S. government would not bail it out

5. During good times, companies rarely defaulted, usually less than 4%

• Premiums from CDS contracts are pure profits

• CDS contracts were valued at $47 trillion

• U.S. GDP was $15 trillion

• During recession, default rates climb over 10% during a recession for risky companies

  • Junk securities (speculative grade)

  • Default rates are still low for companies with good credit ratings

  • Issuers of CDS contracts did not consider a recession, and they had large payouts as CDS holders requested payouts

6. Some investors bought CDS contracts that the CDOs would lose value

• They bet the real estate market would collapse

• Remember - they do not have to purchase CDOs to get CDS contracts

1. Swaps - a periodic exchange of foreign currencies between 2 parties.

• Currency swaps is a collection of forward currency contracts
• One of the parties is a swap dealer usually a bank.
• Each payment to the counter-party is called a “leg.”
• Swap contract specifies
  • Frequency of the payments
  • Duration of the swap (T)
• Swap payments (legs) are calculated
  • One leg is a fixed payment and the other leg is a floating payment
  • The fixed payment has a fixed rate
    • Called the coupon of the swap
• Four different swaps.
  • They differ in how the payments (legs) are indexed
  • Not covered in class
• Currency Swaps
• Both legs of the swap are denominated in different currencies.

2. Valuation of a swap

At T=0, the value of a swap to both parties should be 0 or very close to 0.

Example

• Company XYZ enters into a 10 year swap agreement with a dealer
• 9 years have passed
• Payments are semi-annual
  • 2 payments are left
• Payments are $200M and 210M Euros
  • Coupon payment: is 4% for USD and 5% for Euros
  • Coupon payment are $4M and 5.25 Euros
  • The implicit exchange rate is $4M/5.25M Euros = $0.762 / Euro
• Exchange are is S _t=.$1.25/Euro
• Discount rate:
  • In the US is 5% APR
  • In Europe is = 6% APR

Note - If Company XYZ wants to liquidate the swap, the company has to receive $61.9M to sell the swap.

Note - The value of the swap for both parties has to be zero or very close to zero. Nobody would enter into a swap with a big negative value for them.

Note - The swap has a credit risk.  The counter-party, the dealer, has a large negative present value and could default.

• Why does the value of the IBM currency swap change?
  • The terms of the swap are fixed
  • Periodic payments and coupon interest rates
  • Value of swap changes
  • From domestic holder of this swap
    • Exchange rate
      • If domestic exchange rate appreciates, then value of swap decreases
    • Domestic interest rate
      • If domestic interest rate increases, then value of swap increases
    • Foreign interest rate
      • If foreign interest rate increases, then value of swap decreases
  • The opposite are true for the issuer of the swap (the swap dealer)