Reading 49: Basics of Derivative Pricing and Valuation

Question 1

Explain the arbitrage opportunity if the actual price of the call option is different from the value computed from the binomial model.

Answer 1

If the price of the option is greater than the value computed from the model, the option is overpriced. To exploit this opportunity, we would sell the option and buy n units of the underlying stock for each option sold.

If the price of the option is lower than the value computed from the model, the option is underpriced. To exploit this opportunity, we would buy the option and sell n units of the underlying stock for each option purchased.

Question 2

Identify the payoffs to the pay-fixed (receive floating) side of a plain-vanilla interest rate swap.

Answer 2

A payment must be made if interest rates fall below the swap fixed rate.

A payment is received if interest rates rise above the swap fixed rate.

Question 3

Describe a protective put.

Answer 3

When a portfolio is composed of (1) a European put option on a stock and (2) a share of the same stock.

Question 4

List the 4 main types of underlying items on which derivatives are based.

Answer 4

1. Equities
2. Fixed-income securities/interest rates
3. Currencies
4. Commodities

Question 5

Distinguish between LIBOR at forward rate arrangement (FRA) expiration when greater or lower than the FRA rate.

Answer 5

If LIBOR at FRA expiration is greater than the FRA rate, the long position benefits. Effectively, the long position has access to a loan at lower-than-market rates, while the short position is obligated to give out a loan at lower-than-market interest rates.

If LIBOR at FRA expiration is lower than the FRA rate, the short position benefits. Effectively, the short position is able to invest funds at higher-than-market interest rates, while the long position is obligated to take a loan at higher-than-market interest rates.

Question 6

Define a plain-vanilla interest rate swap.

Answer 6

It involves the exchange of fixed interest payments for floating-rate payments.

Question 7

Explain marking-to-market.

Answer 7

The process of adjusting the balance in an investor’s futures account to reflect the change in value of the futures position since the last mark-to-market adjustment was conducted. Most exchanges require daily marking-to-market based on settlement price. This periodic settlement through the mark-to-market process prevents accumulation of losses in investors’ accounts and ensures the party that earns a profit from a futures transaction won’t have to worry about collecting the money, which helps to eliminate default risk.

Question 8

Define cash-settled forwards.

Answer 8

Cash-settled forwards are also known as non-deliverable forwards (NDFs) or contracts for differences. Both cash-settled and delivery-based forwards have the same economic effects.

Question 9

Differentiate between the pay-fixed side of the swap and the pay-floating side of the swap.

Answer 9

The party that wants to receive floating-rate payments and agrees to make fixed-rate payments is known as the pay-fixed side of the swap or the fixed-rate payer/floating-rate receiver.

The party that wants to receive fixed payments and make floating-rate payments is the pay-floating side of the swap or the floating-rate payer/fixed-rate receiver.

Question 10

How is the price or value of a financial asset determined?

Answer 10

As the present value of expected future price plus (minus) any benefits (costs) of holding the asset, discounted at a rate appropriate for the risk assumed.

Question 11

Differentiate between the price and value of a stock.

Answer 11

The price of a stock refers to its current market price, while the value of a stock refers to its intrinsic or fundamental value, which is generally estimated through some valuation model.

Question 12

Describe the initial margin in the futures market.

Answer 12

It is the amount that must be deposited by each party—the long and the short—to be able to trade in the market. The initial margin requirement in the futures market is a relatively low proportion of the contract’s total value and is usually based on the historical daily price volatility of the underlying.

Question 13

Distinguish between the put option holder/buyer and the writer/seller.

Answer 13

A put option gives the holder/buyer the right to sell (or put) the underlying asset, for the given exercise price, at the option’s expiration date.

A put option writer/seller has the obligation to buy the asset from the put option holder at the option’s expiration date, for the given exercise price, should the holder choose to exercise the option.

Question 14

Define a forward rate arrangement (FRA). What does the price of an FRA represent?

Answer 14

A forward rate agreement (FRA) is a forward contract where the underlying is an interest rate (usually LIBOR).

The price of an FRA represents the interest rate at which the long (short) position has the obligation to borrow (lend) funds for a specified period (term of the underlying hypothetical loan) starting at FRA expiration.

Question 15

Differentiate among an option that is in-the-money, out-of-the-money, and at-the-money.

Answer 15

An option is in-the-money when immediate exercise of the option will generate a positive payoff for the holder.

An option is out-of-the-money when immediate exercise will generate a negative payoff for the holder.

An option is at-the-money when immediate exercise will result in neither a positive nor a negative payoff for the holder.

Question 16

What is the maintenance margin in the futures market?

Answer 16

It is the minimum balance that must be maintained in an investor’s account to avoid a margin call (a call for more funds to be deposited in the account).

Question 17

Distinguish between the higher exercise price of a call option and a put option.

Answer 17

For call options, the higher the exercise price, the lower the exercise value of the option.

For put options, the higher the exercise price, the higher the intrinsic value.

Question 18

Explain the intrinsic value or exercise value of an option.

Answer 18

It is the amount an option is in-the-money. It would be the amount received by the option holder if he were to exercise the option immediately. An option has zero intrinsic value if it is at, or out-of-the money.

Question 19

When is it beneficial to exercise an American put prior to expiration?

Answer 19

When a company is in or nearing bankruptcy, and its stock price is close to zero.

Question 20

Identify the assumptions used in the binomial valuation of options.

Answer 20

Time moves in discrete (not continuous) increments.

Given the current price of the underlying asset, over the next period the price can move to one of two possible new prices.

Question 21

Distinguish between a European option and an American option.

Answer 21

A European option is one that can only be exercised at the option’s expiration date.

An American option can be exercised at any point in time up to and including the option’s expiration date.

Question 22

Identify the limits to arbitrage.

Answer 22

The transaction may require a very large amount of capital, which the arbitrageur may not have access to.

The transaction may require additional capital down the line to maintain the position.

The transaction may require shorting assets that are difficult to short.

The transaction may entail significant risk, especially if the relevant derivative pricing models are based on complex models whose parameters are subject to modeling risk.