(49) Basics of Derivative Pricing and Valuation

Question 1

What is the principle of Arbitrage?

Answer 1

A transaction used when two assets produce identical results but sell for different prices. Pressures for prices to converge. (This means everything is correctly priced)

Question 2

Payoffs on derivatives come directly from what?

Answer 2

The underlying asset

Question 3

4 Types of Underlying assets for derivatives

Answer 3

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

Question 4

Position in underlying + opposite position in derivative equals what kind of return?

Answer 4

Risk-free return Asset (shot/long) + derivative (long/short) = risk-free bond)

Question 5

What is replication in derivatives?

Answer 5

The creation of an asset/portfolio from another asset/portfolio/derivative. In the absence of arbitrage, replication would not produce excess return. Replication can reduce transaction costs

Question 6

What is risk neutrality in derivatives?

Answer 6

This means that investor’s risk aversion is not a factor in determining the price of a derivative but it is important in determining price of assets. Prices of derivatives assume risk neutrality (Derivative pricing is sometimes called risk-neutral or arbitrage-free pricing)

Question 7

How are derivatives priced?

Answer 7

A hedge portfolio is used that eliminates arbitrage opportunities

Question 8

Risk-averse investors expect what to compensate for the risk?

Answer 8

A risk premium

Question 9

Distinguish between value and price of futures/forwared contracts?

Answer 9

Price and value are both $0 at contract inception date. Price of contract is equal to a certain amount that will be paid at some future date Value is the change in the contract price/rate from inception to the valuation date (Value amount changes at the contract goes on)

Question 10

Formula to calculate a forward price at initiation of an asset with and without costs and benefits ?

Answer 10

Without costs and benefits: F₀(T) = S₀ (1+r)^T

With costs and benefits: F₀(T) = (S₀ - PV of benefits + PV of costs) (1+r)^T

The forward price is the spot price compounded at the risk-free rate over the life of the contract

Question 11

Value and price of a forward contract at expiration, during life of contract, and at initiation

Answer 11

Expiration: V_T(T) = S_T - F₀

Initiation: price and value = zero

During life off contract with benefits: V_T(T) = ST - ( Y - gamma)(1+r)^t - F₀(1+r)^-(T-t)

Question 12

Define a forward rate agreement and its uses

Answer 12

A forward contract calling for one party to make a fixed interest payment and the other to make an interest payment at a rate to be determined at the contract expiration

A contract where the underlying is an interest rate

FRAs are based on libor and represent forward rates

Question 13

Why do forward and futures prices differ?

Answer 13

Futures are marked-to market daily, while forwards are not

Differences in the cash flows can also lead to pricing differences.

If futures prices are positively correlated with interest rates, futures contracts are more desirable if in long position

Question 14

Explain how swap contracts are similar to but different from a series of forward contracts

Answer 14

A swap involves the exchange of cash flows. A swap contract is equivalent to a series of forward contracts, each created at the swap price.

For a swap contract, the rate is fixed at each period. For forward contacts, the rate/price is different at each period.

Value of swap is zero at inception

Question 15

What is an off-market forward?

Answer 15

A forward transaction that starts with a nonzero value

Question 16

What is the exercise value of a call and put option?

Answer 16

Call: S_T – X; Underlying price at expiration - exercise price

Value can’t be less than zero

Put: X - S_T; value can’t be less than zero

Question 17

Explain the time value of an option

Answer 17

The time value of an option is the difference between the market price of the option and its intrinsic value.

Value of the option is made of the intrinsic value and time value

Question 18

What is moneyness of an option?

Answer 18

This is comparing the underlying at expiration to the strike price.

In the money is when the underlying at expiration is greater than the strike price. Out of the money is the opposite. At the money is when they are the same

Question 19

Identify factors that determine the value of an option and explain how each factor effects the value of an option

Answer 19

1 and #2 determine option’s intrinsic/exercise value

1. Value of the underlying (call is directly related to the underlying at expiration but are inversely related to the strike price)
2. Exercise price: the more in the money you are, the more expensive the option becomes
3. Risk-free rate: when rates fall, call option prices fall
4. Time: value of a call option is directly related to time
5. Volatility: greater volatililty in the underlying increases both call and put prices

(Put options have opposite affects of call options)

Question 20

Explain put-call parity

Answer 20

Put-call parity relates to stocks.

The put price plus the underlying price equals the call price plus the present value of the exercise price

Fiduciary call is the call price plus the present value of the exercise price

Protective put is the put plus the underlying price

Both the put and call have the same payoff at expiration and also have the same cost

Question 21

Explain put-call forward parity

Answer 21

Put-call forward parity is for forward contracts.

Both the put and call have the same payoff at expiration and also have the same cost

Question 22

How is the value of an option determined using a one-period binomial model?

Answer 22

A model for pricing options in which the underlying price can move to only one of two possible new prices.

The expected payoff/value based on risk-neutral probabilities is discounted at the risk-free rate

Question 23

What are risk-neutral probabilities?

Answer 23

Weights that are used to compute a binomial option price. They are the probabilities that would apply if a risk-neutral investor valued an option

Question 24

Do American options or European options have higher values?

When should American calls be exercised?

Answer 24

American because it can be exercised at any time. American options are not discounted back.

Exercised only if there is a dividend or other cash payment

Question 25

Formula for put-call parity

Answer 25

S₀ + P₀ = C₀ + (x/(1+r)^T)

S = asset

P = put

C = call

Formula with X = bond

A positive value in this equation is in a long position, negative value is in short position

Question 26

A protective put is always equal to a fiduciary call?

Answer 26

Yes; this is put call parity where asset + put = call + risk-free bond