CFA - Derivatives

The price of a 3 × 5 forward rate agreement (FRA) is the:

2-month implied forward rate 3 months from today.

What are the two arguments for arbitrage?

Arbitrage is defined as the existence of riskless profit without investment and involves selling an asset and simultaneously buying the same asset for a lower price.

What is the settlement price on futures?

It is the average close price during the period the future exists

The value of an American call option is inversely related to:

Its exercise price. The value of an American call option is inversely related to its exercise price and positively related to the volatility of the underlying asset and the risk-free rate.

What is a off-market forward?

When a forward contract is created with a contract rate that gives it a non-zero value at initiation.

When would a person exercise a american option early?

When the underlying asset is giving a dividend.

The value of a European put option at expiration is most likely to be increased by:

a higher exercise price.

From the perspective of the short position in a plain vanilla interest rate swap, an increase in expected short-term interest rates will:

decrease the value, but not the price, of the swap. The short position in an interest rate swap is the floating-rate payer. An increase in expected short-term interest rates will increase the floating-rate payments, which decreases the value of the swap to the floating-rate payer. The price of an interest rate swap is the fixed rate stated in the contract, which does not change.

What is replication?

risky asset + derivative = risk-free asset or any other variation of this formula

An increase in the riskless rate of interest, other things equal, will:

An increase in the risk-free rate of interest will increase call option values and decrease put option values.

What is a credit default swap?

An insurance contract against default. A bondholder pays a series of cash flows to a credit protection seller and riches a payment if the bond issuer defaults.

In a credit default swap (CDS), the buyer of credit protection:

In a credit default swap (CDS), the buyer of credit protection makes a series of payments to a credit protection seller. The credit protection seller promises to make a fixed payment to the buyer if an underlying bond or loan experiences a credit event, such as a default. In a total return swap, the buyer of credit protection exchanges the return on a bond for a fixed or floating rate return. A security that is paid using the cash flows from an underlying bond is known as a credit-linked note.

How does the cost of holding the underlying asset affect option values?

Increases call values and decreases put values.

The price of a fixed-for-floating interest rate swap contract:

Is established at contract initiation. The price of a swap contract is set such that the contract has a value of zero at initiation. The value of a fixed-for-floating interest rate swap contract may vary over its life as the floating rate changes.

What is a exchange-traded derivative?

Standardized and backed by a trading house.

What are swaps?

Swaps are agreements to exchange a series of payments on periodic settlement dates over a certain time period. They are not traded in a secondary market and are mostly unregulated. Most swap participators are institutions.

For a series of forward contracts to replicate a swap contract, the forward contracts must have:

When replicating a swap with a series of forward contracts, each forward contract is likely to be off-market (i.e., have a non-zero value at initiation), but they can replicate a swap with a value of zero at initiation if the values of the forward contracts sum to zero at swap initiation.

Using put-call parity, it can be shown that a synthetic European call can be created by a portfolio that is:

long the stock, long the put, and short a pure discount bond that pays the exercise price at option expiration. A stock and a put combined with borrowing the present value of the exercise price will replicate the payoffs on a call at option expiration.

Over-the-counter derivatives are:

neither standardized nor backed by a clearinghouse.

Put-Call Parity with forwards:

Po - Co = [ X - Fo(T)] / (1 + Rf)^t The value of a call at X plus the present value of X is equal to the value of a put option at X plus the present value of the forward contract price.

For the price of a futures contract to be greater than the price of a otherwise equivalent forward contract, interest rates must be:

positively correlated with future prices.

The contract price of a forward contract is:

The contract price can be an interest rate, discount, yield to maturity, or exchange rate. The forward price is the future value of the spot price adjusted for any periodic payments expected from the asset. An example of when the forward price may be less than the spot price is in the case of an equity index contract where the dividend yield is greater than the risk-free rate.

A synthetic European put option includes a short position in:

A synthetic European put option consists of a long position in a European call option, a long position in a risk-free bond that pays the exercise price on the expiration date, and a short position in the underlying asset.

The settlement price for a futures contract is:

An average of the trade prices during the 'closing period'. The margin adjustments are made based on the settlement price, which is calculated as the average trade price over a specific closing period at the end of the trading day. The length of the closing period is set by the exchange.

Other things equal, the no-arbitrage forward price of an asset will be higher if the asset has:

Costs of holding an asset increase its no-arbitrage forward price. Benefits from holding the asset, such as dividends or convenience yield, decrease its no-arbitrage forward price.

An analyst using a one-period binomial model calculates a probability-weighted average of an option's values following an up-move or a down-move. According to this model, this average is most likely:

Greater than the option's value today. The probability-weighted average calculated by the analyst is the option's value after one period. To estimate the option's value today, this result must be discounted by one period.

What is arbitrage?

Occurs when assets are mispriced.

For interest rate swaps, a replication process is used to determine:

both the value and the price. Replication of a swap with off-market FRAs is used to determine the value of an interest rate swap and to establish the swap price such that its value is zero at initiation.

The put-call-forward parity relationship is similar to the standard put-call parity relationship with a forward price substituted for:

the underlying asset. The put-call-forward parity relationship is the same as the standard put-call parity relationship, with the present value of the forward price substituted for the underlying asset.

What are the 6 factors that determine option prices?

1. Price of the underlying asset: Calls - high price = higher value, puts: higher price = lower value 2. The exercise price: higher price = smaller call option price 3. The risk-free rate of interest: increase causes a higher cal price. Increase will decrease put options 4. Volatility of the underlying asset: increase leads to a increase in both calls and puts 5. Time to expiration: The more time, the higher value for calls and puts. 6. Costs and benefits of holding the asset: If there are any benefits to holding the asset (dividends, interest, etc.), call values are decreased and put values are increased.

What is a credit spread option?

A call option that is based on a bond's yield spread relative to a benchmark. If the credit quality decreases, its yield spread will increase and the bondholder will collect a payoff on the option.

What is a credit derivative?

A contract that provides a bondholder (lender) with protection against a downgrade or a default by the borrower.

What is a forward rate agreement (FRA) ?

A derivative contract that has a future interest rate, rather than a asset, as its underlying. An FRA settles in cash and carries both default risk and interest rate risk, even when based on an essentially risk-free rate. It can be used to hedge the risk/uncertainty about a future payment on a floating rate loan.

One of the principal characteristics of swaps is that swaps:

A swap agreement often requires that both parties agree to a series of transactions. Each transaction is similar to a forward contract, where a party is paying a fixed price to offset the risk associated with an unknown future value. Swaps are over-the-counter agreements but are not highly regulated. One of the benefits of swaps is that they can be customized to fit the needs of the counterparties. Thus, they are not standardized.

A synthetic European call option includes a short position in:

A synthetic European call option consists of a long position in the underlying asset, a long position in a European put option, and a short position in a risk-free bond (i.e., borrowing at the risk-free rate).

How do the payments on swaps work?

At each payment date, the difference between the swap fixed rate and the variable rate is paid to the party that owed the least, that is, a net payment is made from one party to another.

For an underlying asset that has no holding costs or benefits, the no-arbitrage forward price at initiation of a forward contract is:

At initiation of a forward contract on an underlying asset with no holding costs or benefits, the no-arbitrage forward price is the future value of the spot price, compounded at the risk-free rate to the expiration date of the forward contract: Fo(T) = S0(1 + Rf)T. The forward contract has a value of zero at initiation if the forward price in the contract is equal to the no-arbitrage forward price.

Put-Call Parity with European Options

Based on the payoffs of two portfolio combinations, a fiduciary call and a protective put Fiduciary call: Combo of a call with exercise price X and a pure discount, rissoles bond that pays X at maturity. Protective put: Combo of a share of stock together with a put on the stock Formula: C + [X/(1 + Rf)^t] = S + P

When the underlying asset does not pay any cash flows, the value of an American call option is:

Because the right to exercise a call option early is not valuable when the underlying asset does not pay any cash flows, the value of an American call option is equal to the value of an otherwise identical European call option.

Derivatives valuation is based on risk-neutral pricing because:

Because the risk of a derivative is based entirely on the risk of its underlying asset, we can construct a perfectly hedged portfolio of a derivative and its underlying asset. The future payoff of a perfectly hedged position is certain and can therefore be discounted at the risk-free rate.

During the life of a European option, the amount by which its price is greater than its exercise value is most accurately described as its:

Before expiration, an option can have a price greater than its exercise or intrinsic value. This amount by which an option's price is greater than its exercise value is referred to as its time value.

A one-period binomial model is useful for valuing options because it:

Binomial models are used to value options because they can account for contingent payoffs (i.e., the exercise value after an up-move or down-move in the underlying asset price). The size of an up-move in a binomial model represents an assumption about the volatility of the underlying asset price. Binomial models can use risk-neutral pseudo-probabilities and thereby use the risk-free rate to discount the expected future payoff.

Other things equal, a decrease in the value of a put option on a stock is most likely consistent with which of the following changes in the risk-free rate and stock return volatility?

Decreasing volatility of returns on the underlying stock will decrease option values for both puts and calls. An increase in the risk-free rate increases the values of call options on equities and decreases the values of put options on equities.

It is possible to profit from cash-and-carry arbitrage when there are no costs or benefits to holding the underlying asset and the forward contract price is:

Less than the future value of the spot price. An opportunity for cash-and-carry arbitrage exists if the forward price is not equal to the future value of the spot price, compounded at the risk-free rate over the period of the forward contract.

Differences b/w options

Long call=right to buy Long put = right to sell Short call = obligation to sell Short put = obligation to buy

Short Call

Maximum Gain = Premium Received Maximum Loss = Unlimited Breakeven = Strike Price + Premium

Short Put

Maximum Gain = Premium received Maximum Loss = Strike Price - Premium x 100 Breakeven = Strike Price - Premium

Long Put

Maximum Gain = Strike Price - Premium x 100 Maximum Loss = Premium Paid Breakeven = Strike Price - Premium

Long Call

Maximum Gain = Unlimited Maximum Loss = Premium paid Breakeven = Strike price + Premium

At initiation of a forward contract and a futures contract with identical terms, their prices are most likely to be different if:

Short-term interest rates are negatively correlated with futures prices. Forward and futures prices may differ for otherwise identical contracts if interest rates are positively or negatively correlated with futures prices. The difference arises from the fact that futures are marked to market daily while forwards are not. A futures contract holder can earn interest on mark-to-market gains and faces an opportunity cost of interest of mark-to-market losses.

A covered call position is:

The covered call: stock plus a short call. The term covered means that the stock covers the inherent obligation assumed in writing the call. Why would you write a covered call? You feel the stock's price will not go up any time soon, and you want to increase your income by collecting some call option premiums. To add some insurance that the stock won't get called away, the call writer can write out-of-the money calls. You should know that this strategy for enhancing one's income is not without risk. The call writer is trading the stock's upside potential for the call premium. The desirability of writing a covered call to enhance income depends upon the chance that the stock price will exceed the exercise price at which the trader writes the call.

What are the controversies related to derivitaves?

The criticism is that they are too risky. The benefits are that they provide price information, allow risk to be managed and shifted among participants, and reduce transaction costs.

The convenience yield associated with holding the underlying asset of a derivative is most accurately described as:

The nonmonetary benefits of holding the asset. Convenience yield refers to the nonmonetary benefits of holding an asset, for example being in a position to sell an overvalued asset that is difficult to sell short. Convenience yield does not include monetary benefits such as interest and dividend income. The costs of holding the asset, net of the monetary and nonmonetary benefits of holding it, is referred to as the net cost of carry.

What is the open interest?

The number of future contracts outstanding.

The shape of a protective put payoff diagram is most similar to a:

The payoff diagram for a protective put is like that of a call option but shifted upward by the exercise price of the put.

The time value of an option is most accurately described as:

The price (or premium) of an option is its intrinsic value plus its time value. An out-of-the-money option has an intrinsic value of zero, so its entire premium consists of time value. Time value is zero at an option's expiration date. Time value is the amount by which an option's premium exceeds its intrinsic value.

Under which of the following conditions does a forward contract have a positive value to the short party at expiration?

The spot price of the underlying asset is less than the forward price. At expiration, a forward contract has positive value to the short party (and an equal negative value to the long party) if the spot price of the underlying asset is less than the price specified in the forward contract.

The value of a forward or futures contract is:

The value of a forward or futures contract is typically zero at initiation, and at expiration is the difference between the spot price and the contract price. The price of a forward or futures contract is defined as the price specified in the contract at which the two parties agree to trade the underlying asset on a future date.

What is a basis swap?

Trading one set of floating rate payments for another.

What is a over-the-counter derivative?

Where forwards and swaps are traded/created by dealers in a market with no central location. This is a largely unregulated market and each contract is with a counterparty.

What is a protective put strategy?

With a protective put strategy the upside potential is unlimited, but the maximum loss is equal to the stock price plus the put premium minus the exercise price of the put option.

What is a option premium?

intrinsic value + time value

The underlying asset of a derivative is most likely to have a convenience yield when the asset:

is difficult to sell short. It is a non monetary benefit.

Given the put-call parity relationship, a synthetic underlying asset can be created by forming a portfolio of a:

long call, short put, and long risk-free bond. An asset underlying put and call options can be replicated with a long European call option, a short European put option, and a long position in a risk-free bond that pays the exercise price on the expiration date.

What is risk-neutral pricing?

no-arbitrage pricing or the price under a no-arbitrage condition

What is a plain vanilla interest swap?

one party makes a fixed rate interest payment on a notional principal amount specified in the swap in return for floating-rate payments from the other party.

Formulas for Binomials:

risk-neutral probability of an up move: 1 + Rf - D / U - D down move: 1 - above formula

What is the cost of carry?

the net cost of holding an asset, considering both the costs and benefits of holding the asset.