FINC 306

The following are differences between futures and forward contracts

Futures contracts are more standardised than forwards. Forward contracts are traded over-the-counter whereas futures contracts are traded on an exchange. Forward contracts have higher credit risk than futures contracts.

The no-arbitrage principle states that

In financial markets you cannot make a profit without taking risk

Put-Call Parity says:

Long a call and short a put with the same strike K and same maturity is equivalent to long a forward contract with delivery price K

A strangle is a strategy of trading volatility, it is a position of:

Long a put with a lower strike price and long a call with a higher strike price

If you are bearish on the underlying stock market the cheapest option you could take is:

Short a call

The following statements are true

The current value of a call option is always positive. The current value of a put option is always positive. The current value of a bull spread is always positive.

The following is true regarding Forward Rate Agreements

They can be synthetically replicated using zero-coupon bonds. They can be settled at maturity (in arrears). They are not exchange traded contracts. They can be settled at the time of borrowing.

The liquidity of a financial market can be measured by

Trading Volume

A floor is an insurance strategy where

You are long the underlying and long a put

What is a call?

∙A call is an option that gives the buyer the right but not an obligation to buy an asset in the future, at a price set today

Insuring a short position: Caps

∙A call option is combined with a position in the underlying asset ∙The goal is to ensure against an increase in the price of the underlying asset (when one has a short position in that asset)

Collars

∙A collar represents a bet that the price of the underlying asset will decrease and resembles a short forward ∙A zero-cost-collar can be created when the premium of the call and the put exactly offset one another

What is a derivative?

∙A financial instrument that has a value determined by the price of something else. Mostly non-binding

What is a Forward Contract?

∙A forward contract is a binding agreement to buy/sell an underlying asset in the future at a price set today

What is a put?

∙A put is an option that gives the owner the right but not an obligation to sell an asset in the future, at a price set today

Insuring a long position: Floors

∙A put option is combined with a position in the underlying asset ∙The goal is to ensure against a fall in the price of the underlying asset (when one has a long position in the asset)

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 mean to hedge a risky stream of payments ∙A single payment swap is the same thing as a cash-settled forward contract ∙A prepaid swap is a single payment today to obtain multiple deliveries in the future

Synthetic Forwards

∙A synthetic long forward contract is when you buy a call and sell a put on the same underlying asset, with each option having the same strike price and time to expiration ∙The difference between a synthetic long forward contract and the actual forward is that the forward contract has a zero premium, while the synthetic forward requires that we pay the net option premium. With the forward contract we pay the forward price, while with the synthetic forward we pay the strike price

What is an option?

∙An option is a non-binding agreement that gives you the right but not an obligation to buy or sell an asset in the future at a price set today

Quanto Future

∙Any derivative with an underlying in another currency, but quoted in your currency (e.g. Chinese asset traded in US$) ∙Means you don't have exposure to changes in currency value (risk)

Spreads

∙Bull spread: a position in which you buy a call and sell an otherwise identical call with a higher strike price. It is a bet that the price of the underlying will increase. Can also be constructed using puts ∙Bear spread: a position is which one sells a call and buys an otherwise identical call with a higher strike price ∙Box spread: accomplished by using options to create a synthetic long forward at one price and a synthetic short forward at a different price. A box spread is a means of borrowing or lending money. It has no stock price risk ∙Ratio spread: constructed by selling m calls at one strike price and selling n calls at a different strike, with all options having the same time to maturity and underlying asset. Ratio spreads can also be constructed using puts

Bullish and Bearish

∙Bullish: market is expected to go up and reflects a call Bearish: market is expected to go down and reflects a put

Straddles

∙Buying a call and a put with the same strike price and time to maturity ∙A straddle is a bet that volatility will be high relative to the markets assessment

Strangles

∙Buying an out-of-the-money call and put with the same time to expiration ∙A strangle can be used to reduce the high premium cost, associated with a straddle

What are the three core subjects in the area of finance?

∙Derivatives ∙Investments ∙Corporate Finance

Perspectives on derivatives

∙End users: corporations, investment managers, investors ∙Intermediaries: market-makers, traders ∙Economic observers: regulators, researchers

Exercise style of options

∙European-style: Can be exercised only at expiration date ∙American-style: Can be exercised at any time before expiration ∙Bermudan-style: Can be exercised during specific periods ∙Value rankings: 1) American 2) Bermudan 3) European

Financial engineering principles

∙Facilitate hedging of existing positions ∙Allow for creation of customised products ∙Enable understanding of complex positions ∙Render regulation less effective

Selling Insurance

∙For every insurance buyer there must be an insurance seller ∙Strategies used to sell insurance: ∙Covered writing: (option overwriting or selling a covered call) is writing an option when there is a corresponding long position in the underlying asset is called covered writing ∙Naked writing: is writing an option when the writer does not have a position in the asset

What is the main difference between a forward and a futures contract?

∙Forward contracts are customised to the individual customers needs, whereas futures contracts are standardised, making them far more liquid than forward contracts and allowing them to be publicly traded on an exchange with ease ∙Futures contracts are also marked-to-market daily so that settlement occurs over a range of dates, whereas forward contracts only have one settlement date

Moneyness

∙In-the-money: positive payoff if exercised immediately ∙At-the-money option: zero payoff if exercised immediately ∙Out-of-the-money option: negative payoff if exercised immediately

Within different kinds of derivatives, which one has the largest market size

∙Interest rates ∙The total size of the derivatives market is $650 trillion

Covered Call

∙Is a kind of strategy of selling insurance where you take a long position in the underlying asset while writing a call

Covered Put

∙Is a kind of strategy of selling insurance where you take a short position in the underlying while writing a put

How can we replicate a forward contract using fundamental securities?

∙Long a stock and short a bond

Payoff function of forward contracts

∙Long forward: Vt = St - Fot ∙Short forward: Vt = Fot - St

The role of financial markets

∙Markets make risk sharing more efficient. ∙Diversifiable risks vanish ∙Non-diversifiable risk is reallocated to those most willing to hold it

Speculating on volatility

∙Options can be used to create positions that are non-directional with respect to the underlying asset ∙Examples: straddles, strangles, butterfly spreads ∙Who would use non-directional positions? Investors who do not care whether the stock price goes up or down, but only how much it moves, e.g. speculating on volatility

Alternative ways to buy a stock

∙Outright purchase: ordinary transaction ∙Fully leveraged purchase: investors borrow the full amount ∙Prepaid forward contract: pay today, receive the share later ∙Forward contract: agree on price now, pay/receive later

Forward Rate Agreements (FRAs)

∙Over-the-counter contracts that guarantee a borrowing or lending rate on a given notional principle amount ∙Can be settled at maturity (in arrears) or in the initiation of the borrowing or lending transaction

The uses of derivatives

∙Risk management: Derivatives are a tool for companies and other users to reduce risks ∙Speculation: Derivatives can serve as investment vehicles ∙Reduce transaction costs: Sometimes derivatives provide a lower cost way to undertake a particular financial transaction ∙Regulatory arbitrage: It is sometimes possible to circumvent regulatory restrictions, taxes and accounting rules by trading derivatives

Spreads and Collars

∙Spread: A position consisting of only calls or only puts, in which some options are purchased and some are written ∙Collar: 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 time to expiration

Futures prices versus Forward prices

∙The difference of price is negligible for short lived contracts ∙Can be significant for long-lived contracts and/or when interest rates are correlated with the price of the underlying asset

Issues in forward pricing

∙The forward price does not predict the future price, it normally underestimates the future stock price ∙Forward pricing formula and the cost of carry

Describe the meaning of a forward price, delivery date and payoff of a forward contract

∙The forward price is the price at which two parties agree today to transact/deliver in the future ∙The delivery date is the time at which the contract is settled ∙The payoff of a forward contract is the value created by the position at expiration

Put-Call Parity

∙The net cost of buying the index using options must be equal to the net cost of buying the index using a forward contract ∙Call(K,T) - Put(K,T) = PV(Fot, K) ∙Call(K,T) and Put(K,T) denote the premiums of options with strike price K and expiration T, and PV(Fot,K) is the present value of the forward price

Describe the meaning of strike price, maturity date and payoff of an option. Write down the payoff functions of a call and a put

∙The strike price is the price the option buyer pays for the underlying if they exercise their option. For a put it is the price the seller receives if they exercise their option. ∙The maturity date is the date by which the option must be exercised of becomes worthless ∙The payoff of an option is the value of the position at the maturity date ∙Payoff long call: Vt = max(St-K, 0) ∙Payoff short call: Vt = -max(St-K, 0) ∙Payoff long put: Vt = max(K-St, 0) Payoff short put: Vt = -max(K-St, 0)

What is the value of a forward when it is first initiated? How about its value sometime after initiation?

∙The value of a forward when it is first initiated is 0. ∙Sometime after initiation its value would have changed due to the information we would have obtained

What is the meaning of replicating a derivatives contract?

∙To use existing strategies to match the payoff of a derivative/strategy

Trading volume and trading value

∙Trading volume = the number of units of claims (that change hands annually or daily) ∙Trading value = trading volume x price of claims

Written straddle

∙Unlike a purchased straddle, a written straddle is a bet that volatility will be low relative to the markets assessment

The over-the-counter market (OTC)

∙When large traders trade many financial claims directly with a dealer, bypassing organised exchanges ∙Exchange activity is public and highly regulated ∙Over-the-counter trading is not easy to observe or measure and is generally less regulated ∙For many categories of financial claims, the value of OTC trading is generally greater than that traded on exchanges

Uses of Index Futures

∙Why buy an index futures contract instead of synthesising it using the stocks in the index? Lower transaction costs ∙Asset allocation: Switching investments among asset classes ∙Cross-hedging with perfect correlation ∙Cross-hedging with imperfect correlation ∙General asset allocation: futures overlay ∙Risk management for stock pickers

Currency contracts

∙Widely used to hedge against changes in exchange rates

Butterfly spreads

∙Write a straddle + add a strangle = insured written straddle ∙A butterfly spread insures against large losses on a straddle ∙You make money at the start with a premium. You then either get to keep the premium or at most make a loss of the butterfly spread

Is the current value of an option positive? What will happen if it is not positive?

∙Yes the current value of an option is positive. This is because the value of an option is made up of both intrinsic value, the difference between the strike price and the spot price, and time value that results from the time the option has to become more valuable. The payoff of an option can only be positive so the value must be positive. ∙If the value is not positive, investors will be receiving money if they purchase the option, essentially making free money

The following is true for a swap

A swap is a contract to exchange multiple payments at certain future times Ti.

To replicate a derivative means to

Match the payoff using other derivatives and/or fundamental securities

The following is true for the payoff of a derivative

The payoff of a derivative determines the nature of the derivative. The payoff function of a derivative is important in determining its current value. The payoff of a derivative is the value of the derivative at maturity.

The trading of a financial asset involves at least four discrete steps

∙1) A buyer and seller must locate each other and agree on a price ∙2) The trade must be cleared (the obligations of each party are specified) ∙3) The trade must be settled (the buyer and the seller must deliver the cash or securities necessary to satisfy their obligations) ∙4) Ownership records are updated

Four different measures of a market and its activity

∙1) Trading volume: This counts the number of financial claims that trade hands (number of claims traded) ∙2) Market value: The market value is the sum of the market value of the claims that could be traded, without regard to whether they have traded (number of derivatives x price) ∙3) Notional value: measures the scale of a position, usually with reference to some underlying asset (number of units of underlying per contract x price of the underlying x number of derivatives) ∙4) Open interest: measures the total number of contracts for which counter parties have a future obligation to perform