MT (8-10) Derivatives Flashcards by Christophe Fostier

What is a derivative?

A derivative security is a financial security (asset, claim) whose value is derived from other (more primitive) variables such as:
􏰀 Stocks
􏰀 Currencies (exchange rates) 􏰀 Interest rates
􏰀 Indexes
􏰀 Commodities

We will primarily examine two basic (plain vanilla) classes of derivative securities: 􏰀 Forwards and futures
􏰀 Options (European and American Call and Put Options)

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What is a call option?

The right to buy the underlying asset for a pre-specified price and on (or before) a pre-specified date.

The key difference between American and European options relates to when the options can be exercised: A European option may be exercised only at the expiration date of the option, i.e. at a single pre-defined point in time. An American option on the other hand may be exercised at any time before the expiration date.

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What is a put option?

The right to sell the underlying asset for a pre-specified price and on (or before) a pre-specified date.

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What is a future/foward contract?

The obligation to buy/sell the underlying asset at a pre-specified price and on a pre-specified date.

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What is an Over-the-counter (OTC) market?

A market where traders working for banks, fund managers and corporate treasurers contact each other directly.

The OTC market has become more regulated since the final crisis in 2008.

Forwards usuallly traded here.

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What is an Exchange-traded market?

A market where trades are in standardised contracts that have been defined by the exchange.

For example the Chicago Board Options Exchange (CBOE).

Futures usually traded here.

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What are Derivatives mainly used for? (3)

Hedging: Many market participants, for example corporate treasurers in oil firms or exporting firms, use derivatives to remove or reduce the risks associated with their economic activities or investment portfolios.

Speculation (making bets): Investors can use derivatives to deliberately gain exposure to certain risks e.g. if you have a view on the future value of the FTSE- 100, one could exploit this using FTSE futures.

Create Arbitrage Portfolios: As derivatives are based on the prices of underlying assets, one can sometimes construct portfolios of derivatives and the underlying asset that yield risk-free arbitrage profits.

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What are the differences between a fowards and futrue contract?

A forward contract is an obligation (agreement) to buy/sell a certain quantity of an asset for a pre-specified price (forward price) at a particular future date (maturity or expiration date).

Forwards tend to have the following characteristics:

They are bilaterally agreed contracts and are not exchange traded. Thus they are often described as ‘over the counter’ or OTC.

At inception the forward delivery price i.e. the price at which the exchange is to occur in the future, is set such that the value of the contract is zero and, thus, no money changes hands on the inception date.

A futures contract is the same as a forward contract, except that it is typically standardized and traded on an exchange where gains and losses are settled daily (marked to market). Therefore less default risk with a future in comparison to a foward.

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What is the payoff at maturity for a long forward?

St−F0,t

where ST is the market price of the underlying asset at the maturity date, T.

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What is the payoff at maturity for a short forward?

F0,t-St

where ST is the market price of the underlying asset at the maturity date, T.

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Are the total payoffs to long and short sides of a futures contract exactly the same as for a forward?

The total payoffs to long and short sides of a futures contract are exactly as for the forward,

However, money is exchanged over the lifetime of the contract rather than in one lump on the delivery date.

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What is a margin account?

Margin account: An account holding monies deposited by the long party in the futures contract.

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What is the inital margin?

The initial amount the buyer must deposit in the margin account when the contract is opened.

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What is the variation in marked to market?

As the market price of the futures contract changes the balance in the margin account is altered accordingly.

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What is a maintainece margin?

Maintenance margin: if the balance in the account falls to a pre-specified value, the buyer must top up the balance to the initial margin.

The margin account system and marking to market are overseen by the exchange upon which the future is traded. This minimises default risk.

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What is the law of one price?

If two portfolios have identical payoffs in all states of nature, they must have the same price.

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What is The Law of Payoff Dominance?

If portfolio A guarantees a payoff at least as great as portfolio B in all states of nature, then portfolio A must command a greater price than portfolio B.

What is the formula for pricing a foward on an asset with no income?

Fo,t=So(1+Rrf)^t

F0,t = Forward Price
So=Current price of underlying asset at time =0
Rrf= T-year spot rate (Effective annual rate).

What is the formula for Pricing Forwards on Investment Assets with Fixed Cash Income?

Fo,t=(So-I)(1+Rrf)^t
I= present value of fixed income
F0,t = Forward Price
So=Current price of underlying asset at time =0
Rrf= T-year spot rate (Effective annual rate).

Pricing Forwards on Investment Assets with Investment Yield

If the underlying investment asset pays a fixed know yield e.g. dividend yield, then the forward pricing equation is

Fo,t=So(1+Rrf-y)^t
y= yield on the investment asset
F0,t = Forward Price
So=Current price of underlying asset at time =0
Rrf= T-year spot rate (Effective annual rate).

Two special features of commodities?

1) Storage Costs
2) Convenience Yield

Commodities do not pay dividends but there is a convenience yield due to:
1) Seasonality in demand/supply.

2)The potential benefit of holding the spot (commodity) versus holding the futures. There is then a benefit to holding the underlying vs. a long forward. If you hold the spot, you can sell it at a high price in the case of temporary price spike. Then you can buy the underlying back at lower prices to honour the forward contract when it matures.

Pricing Forwards on Investment Commodities with Fixed Storage Costs

the price of a forward contract on an investment commodity that has fixed known storage costs is
(This equation assumes the investment commodity has no convenience yield.)
Fo,t=(So+U)(1+Rrf-y)^t
U= present value pf storage costs
F0,t = Forward Price
So=Current price of underlying asset at time =0
Rrf= T-year spot rate (Effective annual rate).

Pricing Forwards on Consumption Commodities with Net Convenience Yield

Fo,t=So(1+Rrf-y-NCY)^t
NCY (net convenience yield)=Y-S (convenience yield -storage cost as a rate)
F0,t = Forward Price
So=Current price of underlying asset at time =0
Rrf= T-year spot rate (Effective annual rate).

What is an exchange rate?

An exchange rate is the amount of one currency you can exchange for another currency.

Pricing Forwards on Foreign Currency

Fo,t(HC/FC)=So(HC/FC) X [1+R(HC)/1+R(FC)]^t HC=home currency Fc= foreign currency F0,t = Forward exchange rate at time =0 in terms of HC per unit of FC So=Spot exchange rate at time =o in terms of HC per unit of FC R= risk free EAR

What is the value of a call option at maturity?

Exercise when ST > K, CT = ST − K, in-the-money Do nothing when ST < K, CT = 0, out-of-the-money St= value of underlying asset at time T K=strike price (exercise price)

What is the value put option at maturity?

Exercise when ST < K, PT = K - ST, in-the-money Do nothing when ST > K, PT = 0, out-of-the-money St= value of underlying asset at time T K=strike price (exercise price)

What do Profit diagrams show?

Profit diagrams (also known as net payoff diagrams) include the initial cost of establishing the option position i.e. the option premium.

What is the straddle option strategy? And when is it typically used?

The straddle involves going long in a put option with strike price K and going long in a call option on the same underlying with the same exercise date and strike price K. An investor may use the straddle strategy if they believe that a stock's price will move significantly but is unsure as to which direction it will move.

What is the reverse straddle option strategy? And when is it typically used?

The reverse straddle involves going short in a put option with strike price K and going short in a call option on the same underlying with the same exercise date and strike price K. An investor may use the reverse straddle strategy if they believe that the stock will have little volatility and the stock price at time T will be close to the exercise price.

What is the bull spread using calls option strategy? And when is it typically used?

The strategy for the bull spread using calls involves going long a call option withstrike price K1 and going short a call option on the same underlying and exercise date with a higher strike price K2. An investor may use the bull spread strategy if they have a mildly bullish view but who wants a portfolio that’s protected against extreme price moves.

What is the bear spread using puts option strategy? And when is it typically used?

The strategy for the bear spread using puts involves going short a put option with strike price K1 and going long a put option on the same underlying and exercise date with a higher strike price K2. An investor may use the bear spread strategy if they have a mildly bearish view about the price of the underlying but wants a position that’s not too sensitive to extreme market movements.

What is the formula for the Put-Call Parity? And when can it be used?

C+K/(1+Rrf)^T=So+Po The formula above applies to European options only on non dividend paying stocks. (one exception is it can also be used to value American call options on non dividend paying stocks since the option to exercise early is worthless and thus CAmerican= CEuropean). The put and call options both relate to the same stock and both have the same exercise price and exercise date.

If the put-call parity does not hold, how can we generate arbitrage profits?

``` Go short (positive cash flow at t = 0) Overpriced side of equation ``` ``` Go long (negative cash flow at t = 0) underpriced side of equation ``` (Oppositie of going long in investing , is borrowing (shorting))

What is the formula for the Put-Call Parity with dividends?

C+PV(k)+ Pv(Div)=So+Po

What is the butterfly spread option strategy? And when is it typically used?

The butterfly spread strategy involves going long on two call options with strike price K1 and K3 on the same underlying asset and maturity date. Furthermore, this strategy involves going short on two call options with exercise price K2 on the same underlying and same maturity. Where K1

Can you use the put-call parity formula to initally price options?

NO! To price a call using the put call-parity you still need the price of the put. To price a put using the put call-parity you still need the price of the call. Therefore we need another method to price options initially.

Binomial Option Pricing Using the Replicating Portfolio. Call option.

Co=So(delta)+B/1+Rrf Note the formula is written in terms of value rather than cash flows at t=0. Hence we know the first term will be positive and the second term negative. The value of the call will always be greater than or equal to zero. Delta= Cu-Cd/So(U-D) B=Cd(u)-Cu(d)/u-d Note that the final price for the call is entirely unrelated to the probabilities of the up or down move in the binomial process for the underlying.

Binomial Option Pricing Using the Replicating Portfolio. Call option.

Co=So(delta)+B/1+Rrf Again the above formula is written in terms of value rather than cash flows at t=0. Hence we know the first term will be negative and the second term positive. The value of the put will always be greater than or equal to zero. Delta= Pu-Pd/So(U-D) B=Pd(u)-Pu(d)/u-d Note that the final price for the call is entirely unrelated to the probabilities of the up or down move in the binomial process for the underlying.

What is the binomial option pricing formula when using the risk neutral method?

C=qCu+(1-q)Cd/1+Rrf where q = 1+Rrf-d/u-d