Financial Derivatives

Forward contracts

A binding agreement to buy/sell an underlying asset in the future, at a price set today

Payoff for a long forward

= spot price at expiration - forward price

Payoff for a short forward

= forward price - spot price at expiration

A derivative

An agreement between two parties which has a value determined by the price of something else

- options

- futures

- swaps

Trading of derivatives

- stock exchanges

- derivatives exchanges

- dealers

- organised exchanges

- OTC market

Uses of derivatives

- hedging (risk management)

- speculation

- reduced transaction costs

- regulatory arbitrage (deferring taxes, having voting rights without owning the stock)

End users

- corporations

- investment managers

- investors

Intermediaries

- market makers

- traders

Economic observers

- regulators

- researchers

Financial engineering

The creation of new financial products from other products

- facilitate hedging of existing positions

- enable understanding of complex positions

- allow for creation of complex positions

- render regulation less effective

Open interest

The total number of contracts outstanding

Market value

The sum of the value of the claims that could be traded

Trading volume

The number of contracts that are traded daily

Notional value

The scale of a position usually with reference to the number of shares or how much $ the contract is worth

Stock and bond markets

- companies raise funds to finance investments

- either by selling ownership claims (stock) or borrowing money (bonds)

Exchange traded derivatives

Chicago mercantile exchange

- corn

- soybeans

- Japanese yen

New York mercantile exchange

- crude oil

- gold

- copper

Eurex

- DAX stock index

- DAX index volatility

Risk sharing

Financial markets allow risk to be shared, for example insurance buyers pay a premium, and these premiums are pooled and used to help those who suffer unexpected circumstances.

- diversifiable risks vanish

- non diversifiable risks are reallocated

E.g. Catastrophe bonds

Bid-ask spread

The difference between the price at which you buy and the price at which you sell an adset

Market order

Trades a specific quantity of the asset immediately, at the best price currently available

Limit order

Trades a specific quantity of the asset at a specified price, or a better price (possibility of the order not being filled)

Short selling

The sale of a stock you do not already own.

Short position (expect St to fall)

- borrow shares and sell asset

- invest at risk free rate

- buy back asset and return shares

Long position (expect St to rise)

- lend shares and buy asset

- lend at risk free

- receive shares and sell asset

Closing a position

- replacing the borrowed stock

Why short sell?

- speculation (expectations of price movements)

- financing

- hedging (offset risk of owning stock)

Futures contracts

Standardised forward contracts

- exchange traded

- specified delivery dates, locations, procedures

- clearinghouse

- mark-to-market process

- harder to customise

- highly liquid

Settlement

- cash settlement (less costly)

- physical delivery (significant costs-avoided)

Credit risk of the counter party

- issue for OTC contracts

- requires credit check

- less severe for exchange traded contracts

Call options

A non binding agreement to buy an asset in the future, at a price set today

- eliminates downside risk

- seller charges a premium

Strike (exercise) price

The amount paid by the option buyer for the asset if he/she decides to exercise

Exercise style

- European style: can be exercised only at expiration date

- American style: can be exercised at any tie before expiration

- Bermudan style: can be exercised during specific periods

Payoff of a long call

= max[0, spot price at expiration - strike price]

Profit of a long call

= payoff - future value of option premium

Payoff of a short call

= -max[0, spot price at expiration - strike price]

Profit of a short call

= payoff + future value of option premium

Put options

A non binding agreement to sell an asset in the future, at a price set today

Payoff of a long put

= max[0, strike price - spot price at expiration]

Profit of a long put

= payoff - future value of option premium

Payoff of a short put

= -max[0, strike price - spot price at expiration]

Profit of a short put

= payoff + future value of option premium

Bullish

- seeks to profit from rising prices

- long position

Bearish

- seeks to profit from falling prices

- short position

Moneyness

In-the-money:

- positive payoff if exercised immediately

At-the-money:

- zero payoff if exercised immediately

Out-the-money:

- negative payoff if exercised immediately

Long positions

Forward: an obligation to buy at a fixed price

Call: the right to buy if it is advantageous to do so

Put: the put writer is obligated to buy the underlying asset at a fixed price if it is advantageous to the put owner to sell at that price

- right or obligation to buy the underlying asset

- long positions benefit from rising prices

Options

- options serve as insurance against loss

- options are much more expensive if the underlying asset is riskier

Short positions

Forward: an obligation to sell at a fixed price

Call: the call writer is obligated to sell the underlying asset at a fixed price if it is advantageous to the option holder to buy at that price

Put: the right to sell at a fixed price if it is advantageous to do so

- right or obligation to sell an underlying asset

- short positions benefit from falling prices

Insuring a long position: Floors

- long index and long put

- the goal is to insure against a fall in the price of the underlying asset

- looks like a call position

Insuring a short position: Caps

- short index and long call

- the goal is to insure against an increase in the price of the underlying asset

- looks like a put position

Selling insurance

- covered writing is writing an option when there is a corresponding long position in the underlying asset

- naked writing is writing an option when the writer does not have a position in the asset

Covered Calls

- writing a covered call generates the same profit as selling a put

- long index and short call

- limits profits if the index increases, but losses are offset by the premium earned from selling the call

Covered Puts

- writing a covered put generates the same profit as writing a call

- short index and short put

- if the index decreases, the loss on the written put offsets the stock

Synthetic Forwards

- mimics a long forward position by buying a call and a selling a put with the same strike price and time to expiration

- whether the price of the index moves up or down, when the options expire we buy the index for the strike price of the options

Synthetic Forward vs Actual Forward

- a forward contract has a zero premium, while the synthetic forward requires that we pay the net option premium

- with a synthetic forward we pay the strike price, rather than the forward price

- "off market forward" where the premium is not zero

Put-Call Parity

- the net cost of buying the index using options must equal the net cost of buying the index using a forward contract

Spread

An option spread is a position consisting of only calls or only puts, in which some options are purchased and some written

Collar

A collar is the purchase of a put option and the sale of a call option with a higher strike price, with both options having the same underlying asset and having the same expiration date

- can be zero cost if premiums are equal

- represents a bet that the price of the underlying asset will decrease

- resembles a short forward

Bull spread

A position in which you buy a call and sell an otherwise identical call with a higher strike price

- a bet that the price of the underlying asset will increase

- can also be constructed using puts

Bear spread

A position in which one sells a call and buys an otherwise identical call with a higher strike price

- a bet that the price of the underlying asset will decrease

- can also be constructed using puts

Box spread

Uses options to create a synthetic long forward at one price and a synthetic short forward at a different price

- zero stock price risk

- a means of borrowing or lending money

Ratio spread

Is constructed by buying m calls at one strike and selling n calls at a different strike, with all options having the same time to maturity and the same underlying asset

- can also be constructed using puts

Speculating on volatility

Options can be used to create positions that are nondirectional with respect to the underlying asset.

Investors use these to speculate on volatility.

- straddles

- stangles

- butterfly spreads

Straddles

Buying a call and a put with the same strike price and time to expiration

- bets that volatility will be high relative to the markets assessment

Strangle

Buying an out-of-the-money call and a put with the same time to expiration but different strikes

- can be used to reduce the high premium cost associate with a straddle

Written straddle

Selling a call and put with the same strike price and time to maturity

- bets that volatility will be role relative to the markets assessment

Butterfly spreads

A position created from selling a straddle and buying a strangle

- makes money is there is low volatility but insures against the large losses on a straddle

Outright purchase

- ordinary transaction

- pay at time zero

- receive security at time zero

Fully leveraged purchase

- investor borrows the full amount

- pay at time T

- receive security at time zero

Prepaid forward contract

- pay today, receive the share later

- pay at time zero

- receive security at time T

Forward contract

- agree non price now, pay later

- pay at time T

- receive security at time T

Pricing prepaid forwards

- pricing by analogy

- pricing by discounted present value

- pricing by arbitrage

- proof by contradiction

Pricing by analogy

- in the absence of dividends, the timing of delivery is irrelevant

- price of the prepaid forward contract is the same as current stock price

Pricing by arbitrage

- since arbitrage profits are traded away quickly and cannot persist, at equilibrium we expect the prepaid forward price to equal the current stock price

Pricing prepaid forwards with dividends

- the holder of the forward will not receive dividends that will be paid to the holder of the stock

- the prepaid forward price should be cheaper to compensate for not receiving dividends

Forward premium

The difference between the current forward price and the stock price. Can be used to infer the current stock price from the forward price.

Cash and carry arbitrage

- buy the index

- short the forward

- creates a synthetic forward

- transaction fees and bid-ask spread make arbitrage harder

- creates no arbitrage bounds

- a tailed position is where you pay slightly less than one share so at maturity it equals one share

Futures prices versus Forward prices

- negligible for short lived contracts

- can be significant for long lived contracts or when interest rates are correlated with the price of the underlying asset

Does the forward price predict the future price?

- the forward price conveys no additional information beyond what the stock price, interest rate and dividend yield provides

- the forward price underestimates the future stock price

Clearinghouse (futures)

- matches buyers and sellers

- tracks obligations

- becomes the counter party

Mark to market

- settled daily

- lower credit risk

- highly liquid

- easy to offset an existing position

Margin

- initial margin is collateral/insurance for the counter party

- maintenance margin (percentage of initial margin)

- margin call if the balance falls below the required amount

- lower transaction costs than stocks

Uses of index futures

- lower transaction costs than synthesising the futures using stocks in the index

- asset allocation: switching investments among asset classes

- risk management

- cross hedging

Currency contracts

- widely used to hedge against changes in exchange rates

Covered interest arbitrage

Synthetically creating a yen forward contract by borrowing in dollars and lending in yen

US Treasury

Bills

- <1 year maturity

- no coupons

- sells at discount

Notes/Bonds

- 1-10 years/10-30 years

- sells at par

- coupons

Strips

- claim to single coupon or principal

- zero coupon

Swaps

A swap is a contract calling for an exchange of payments, on one or more dates, determined by the difference in two prices

- a swap provides a means to hedge a stream of risky payments

- a single payment swap is the same thing as a cash settled forward contract

Prepaid swap

A single payment is made today for multiple deliveries of a commodity in the future

Physical settlement

- the commodity buyer pay $/year and receives the commodity each year

Financial settlement

- the commodity buyer pays the swap counter party the difference between the swap price and the spot price

- the commodity buyer then buys the commodity at the spot price

- if the difference between the swap price and the spot price is negative, the swap counter party pays the buyer

Swap payment

= Spot price - swap price

The swap counterparty

- the swap counterparty is a dealer, who is, in effect, a broker between buyer and seller

- the fixed price paid by the buyer usually exceeds the fixed price received by the seller

- this price difference is the bid-ask spread and is the dealers fee

- the dealer beard the credit risk of both parties but is not exposed to price risk

- a "back-to-back" transaction is where the dealer matches the buyer and seller

- the dealer can hedge the transaction by entering into long forward/futures contracts

Market value of a swap

- the market value of a swap is zero at intersection

- once the swap is struck, market value will not be zero because the forward prices and interest rates will change over time

- a buyer wishing to exit the swap could enter into an offsetting swap with the original counterparty or whomever offers the best price

- the market value of the swap is the present value of payments between the original and new swap rates

Currency swaps

- entails an exchange of payments in different currencies

- equivalent to borrowing in one currency and lending in another

Differential swaps

- a diff swap is a swap where payments are made based on the difference in floating interest rates in two different currencies, with the notional amount in a single currency

- standard currency forward contracts cannot be used to hedge a diff swap

Commodity swap

The commodity swap price is a weighted average of the commodity forward prices

Swaptions

- a swaption is an option to enter into a swap with specified terms

- this contract will have a premium

- a swaption is analogous to an ordinary option, with the present value of the swap obligations as the underlying asset

- can be American or European

- a payer swaption gives it's holder the right, but not the obligation, to pay the fixed price and receive the floating price

- the holder of a payer swaption would exercise when the fixed swap price is above the strike

- a receiver swaption gives it's holder the right, but not the obligation, to pay the floating price and receive the fixed strike price

- the holder of the receiver swaption would exercise if the fixed swap price is below the strike

Total return swaps

- a total return swap is a swap in which one party pays the realised total return (dividends plus capital gains) on a reference asset, and the other party pays a floating return such as LIBOR

- the two parties exchange only the difference between these rates

- the party paying the return on the reference asset is the total return payer

- uses include: avoiding withholding taxes on foreign stocks and management of credit risk

Default swap

- a default swap is a swap, in which the seller makes a payment to the buyer if the reference asset experiences a "credit event" (e.g. Failure to make a scheduled payment on a bond)

- a default swap allows the buyer to eliminate bankruptcy risk, while retaining interest rare risk

- the buyer pays a premium

Risk management

- a firm is profitable is the costs of what is produces exceeds the costs of its inputs

- a firm that actively uses derivatives to alter its risk and protect its profitability is engaging in risk management

The Producers perspective

- a producer selling a risky commodity has an inherent long position in this commodity

- when the price of the commodity increases, the firms profit increases (assuming costs are fixed)

- strategies to hedge profit include selling forward, buying puts, buying collars

Producer: hedging with a forward contract

- a short forward contract allows a producer to lock in a price for his output

Producer: hedging with a put option

- buying a put option allows a producer to have higher profits at high output prices, while providing a floor on the price

Producer: insuring by selling a call

- a written call reduced losses through a premium, but limits possible profits by providing a cap on the price