Chapter 20 - Financial options

Question 1

Define a financial option

Answer 1

A contract that gives the owner a right, but not the obligation, to purchase or sell an asset at a fixed price at some future date.

Question 2

Call vs put

Answer 2

Call is the right to purchase the asset.
Put is the right to sell the asset.

It is about buying or selling an asset a fixed price.

Question 3

Who makes the option?

Answer 3

the option writer

Question 4

What is a warrant?

Answer 4

A warrant is a call option where the writer is the firm itself

Question 5

What is the strike price?

Answer 5

The strike price is the price at which the asset will be bought or sold at the poitn of option exercise.

Question 6

Another word for strike price?

Answer 6

Exercise price

Question 7

What position do we say that the option buyer has?

Answer 7

Has a long position

Question 8

What position do we say that hte option seller has?

Answer 8

A short position

Question 9

Does the option writer have a right to do anytihng+

Answer 9

they ahve the obligation to fulfill the agreement if the long position side choose to exercise his right to buy or sell

Question 10

why do people sell/write options?

Answer 10

They get the option premium, which is the price of the contract

Question 11

What is the largest and oldest exchange for options?

Answer 11

Chicago Board Options Exchange (CBOE).

Question 12

By convention, when do options expire?

Answer 12

Third friday of eahc month. More pooular stocks have more frequent expliraitons.

Question 13

What is Open int?

Answer 13

Open interest. represent teh outstanding number of contracts for the option.

Open interest requires contracts to be active. This means that a seller/writer and a buyer must have made the agreement for it to count towards the open interest.

Question 14

recall ATM options

Answer 14

At the money. Strike price/exercise price is equal to the current share price.

Question 15

What is the volume?

Answer 15

the amount of contracts traded the specific day

Question 16

how many shares per contract

Answer 16

100

Question 17

ITM

Answer 17

In the money. Refers to cases where the strike price/exercise price is more favorable than the current price. For instance, if the option is a call option, if its strike price is less than the current share price, it would be in the money. We could exercise it immediately, and get a profit due to the intrinsic value of the option. Ignoring the cost of the contract of course.

Question 18

using an option to reduce risk is called…?

Answer 18

Hedging

Question 19

Can we use the law of one price to detemrine the value of an option?

Answer 19

Yes, but recall that the law of one price says that the price of the security is equal to the present value of the future cash flows that the investor expect to receive from owning it. Therefore, we must determine what these cash flows are at any given point in time.

Question 20

elaborate on the curve that describe the options worth as a function of share price

Answer 20

If the option is ITM, exercising it is beneficial to us, and we would gain profit equal to the difference between the share price and hte strike price multiplied by the number of shares our contracts apply to.

However, if the option is ATM or OTM, exericsing it would make use loose money. Since we do not have to do this, we simply dont. Therefore, our losses are limited to 0.

This makes a curve that has a break point.

it is the same for puts and calls, th eonly diffreence is that the value is computed by taking the difference of opposite order (striek price vs share price) or equivalently taking the absolute value of the difference.

Question 21

Does the short or long position have obligations?

Answer 21

The short position is the writer of the option. therefore, he has the obligation to follow, should the long position exercise his right.

Question 22

How does the losses of the option writer relate to the profits of the buyer?

Answer 22

The are the opposite. except for the option premium.

Question 23

What can we say about the downside of taking a short position on a call option?

Answer 23

you can be infinitely fucked because there are no limit upwards

Question 24

is there a relationship between the strike price and returns?

Answer 24

the distribution of returns for a DOTM option is more extreme than closer to ATM. They have a higher probability of expiring worthless, where you’d loose the premium, but if they hit, you hit extremely big.

Question 25

What can we say about the returns of options vs the underlying

Answer 25

This applies to call options: Returns of options are amplified. THey are always larger than the underlying. Because of this, we know that they are more risky as well. Therefore, their betas are larger than the beta of the underlying security. This

Question 26

what can we say about the signs of option betas?

Answer 26

Call options have positive betas

Put options have negative betas (relative to the underlying)

Question 27

What is the outcome of put options having negative betas (if the underlying has positive beta)?

Answer 27

The expected value of the puts is lower than that of hte stock.

Put options are generally not held as investment, but rather as a hedge against risk

Question 28

define a straddle

Answer 28

holding a call and put option at the same strike/exercise price.

the death whne holding straddles is when the shite expire ATM.

Straddles are tyypically volatility bets.

Question 29

Define a butterfly spread

Answer 29

Makes money when the strike price and stock price is close together. Sort of the opposite of a straddle.

Question 30

What is a protective put?

Answer 30

A protective put is a hedging strategy where we have a regular long position in a stock, but want to hedge ourselves against large declines in stock price. we do so by buying a put option. This will reduce our overall return when the stock moves up, but we are secured from large swings down.

Question 31

What is portfolio insurance?

Answer 31

Holding protective puts on the enitre portfolio

Question 32

how can we do portfolio insurance without using puts

Answer 32

We buy a risk free zero coupon bonds, and a call option. The call option is instead of holding shares of the underlying.

Say it is Apple shares, and apple is trading currently at 50. If the apple share trade below 50, we can offset this by having a 50 buck risk free bond. If apple shares go beyond 50, you can use the money received from the bond, which is 50, to exercise the call option that was agreed at strike price 50.

Question 33

A straddle makes money when…?

Answer 33

The price moves a lot. Assumign you are long the position.

Straddle has a put and and a call component. Creates a V-shape indicating that if there are no cost of the options, you’d gain 0 if the stock price remains exactly the same, but you’d gain money if the stock moves in either direction.

because of the option contract prices, the V-shape is shifted down. This means that the stock have to move ‘more’ in order for a straddle to be profitable. But the important thing is that the straddle makes money on volatility.

Question 34

In one sentence, when does butterfly spreads make money

Answer 34

Butterfly spreads make money whenever the strike price is close to the stock price at expiration.

You’re essentially betting that volatility is low.

Question 35

elaborate on butterfly spreads

Answer 35

The point is to create a portfolio of options that makes us make money when the stock price is close to expiration.

If the stock price is 30, and we believe it will continue at 30, we can buy a 20-call, and a 40-call. This makes us gain cash if the stock is above 20.
To offset, we short call options (2) at 30. At the point of stock price = 30, we now gain the most cash.

The cash window is between 20 and 40, with top at 30. Beyond this interval, we gain 0. Actually, we loose moeny because of contract prices.

Question 36

elaborate on portfolio insurance

Answer 36

We can use a protective put. The benefit of protective puts is that we can hedge the portfolio vs downswings, but still reap benefits if the share increase a lot. Therefore, it can be a great alternative to simply liquidating the position.

The term portfolio insurance is used to indicate a case where we are using protective puts on our portfolio to hedge against losses.

Question 37

how can we perform portfolio insurance without protective puts?

Answer 37

We purchase a bond and a call option.

If the underlying goes bad, the bond gain offset the call option price.

If the underlying goes good, we use the gain from the bond to buy the stock at the call-option determined price/strike price.

So, if the strike price is at 50, we buy zero-coupon treasury bonds with face value of 50. This allows us to gain cash regardless, but if the call option turns out to be good, we can use the face value to purchase the underlying and exercise the option.

Question 38

If we buy a protective put at strike price 45, and hold the stock as well, how does the payoff picture look?

Answer 38

If the stock price is at 45, we earn 0. If stock price is above 45, we choose to not exercise the put, and we earn money on the stock movement.

If the stock price is below 45, we loose on the underlying, but we gain on the option, and they offset each other.

It creates a scenario where we earn 45 regardless.

Question 39

What can we say about protective put vs bond+call?

Answer 39

If they are constructed so that they yield the same results, they must be worth the same according to the law of one price.

Question 40

Since we know that protective puts and bond+call have the same price when structured the same, what is the relationship between them?

Answer 40

S + P = PV(K) + C

S: Stock price
P: Put price
K: Strike price
C: Call price

K is also the same as the face value of the bond.
recall that the value of a zero coupon bond is simply the present value of its face value, PV(K).

Question 41

Elaborate on put-call parity

Answer 41

C = S + P - PV(K)

C = P + S - PV(K)

We can think of the call option price as the price of a levered position in the stock, S-PV(K) plus the cost of heding against down sides.

Question 42

What happens with put-call parity if there are dividends involved?

Answer 42

Subtract PV(div) just like we subtract PV(K) already

Question 43

When does put call parity apply?

Answer 43

European options with the same expiration and strike price

Question 44

What is worth more, american or european option?

Answer 44

The european cannot be worth more because the american option provides more flexibility.

Question 45

What is the maximum value of a put option?

Answer 45

its strike price

Question 46

Max value of call option

Answer 46

The stock itself

Question 47

What is intrinsic value of an option?

Answer 47

Its value if it expired immediately.

Question 48

Define the time value of an option

Answer 48

The time value of an option is the difference in value between the option’s current price and the instrinsic value

Question 49

Elaborate on exercising options early

Answer 49

Consider a stock that does not pay dividends prior to the expiration date.

According to the put-cal lparity, we have teh relation:

C = P + S - PV(K)

We can make use of the fact that the price of the bond can be written as the differnece between the face value and the amount that is dfiscoutned away in the process of finding the presnet value.

C = P + S - (K - disc(K))

C = P + S - K + discount(K)

C = S - K + P + discount(K)

We know that S -K is equal to the intrinsic value of the call option.

C = intrinsic value + P + discount(K)

So what is the P+discount(K) part? It must be the time value. Why? Because we define time value to be the differnece between the price of the call C, and the intrinsic value.

C = intrinsic value + time value

A European option always has positive time value ( as long as interest rates are positive).

Since the american counterpart option can never be worth less than european, we know that it too must be positive time value.

What can we conclude from this?
If the stock pays no dividends, it is always better to sell the option than to exercise it.

The reasoning is that if you exercise the option, you will only gain the intrinsic value.
However, when you sell it, we also gain the time value.

This has a major outciome result as well: Considering that fact that for non-dividend options the exercise right is worthless, the european option and american option are worth the same.

Applies to calls.

Question 50

elaborate on early exercise of put optins

Answer 50

The case here is a little different than from calls.

Recall put-call parity:

C = P + S - PV(K)

C = P + S - (K - discount(K))

C = P + S - K + discount(K)

C = (S - K )+ (P + discount(K))

C = intrinsic value + time value

We can re-arrange it to solve for the put price:

P = C - S + K - discount(K)

P = (K-S) + C - discount(K)

While the “strike price less stock price” is essentially the same as for hte call, the time value is now different.

There are actually cases where the time value of money is negative, which would mean that early exercise is better than selling it. This simply means that there are cases where the American counterpart is more valuable than the european even for non-dividend paying stocks.

To give an example: A stock goes ad undas. We get the maximum possible return equal to the strike price. If we sell the option, there is no time value to be earned, as it is already gone. If we exercise, we get the full reward

Question 51

What happens when the stock pays a dividend

Answer 51

firstly, the dividend must be witihn the expiration date.

the inclusion of dividends make it generally more valuable with the exercise option. This should make the American option more valuable.

The reason for this is that if the dividend is large enough, the time value of even european call options can be negative.

Question 52

how can we use a call option to represent a firm’s value?

Answer 52

Cal loption with strike price equal to the firm’s debt outstanding.

If the firm were to liquidate, the option would be worth the difference between the value of the assets and the value of the debt.
If the debt exceeds the assets, the equity holders receive nothing. This is exactly the same as with the regular call options on stock.

Question 53

elaborate on representing debt with options

Answer 53

First of all, this is purely from a mechanics point of view. We consider the financial effect of various parties, and consider how this can be represented by options.

If we assume equity holders ‘could’ be held liable for damages, if the assets are worth less then the debt, they would be in loss. However, due to the way shit works, they are not liable. Therefore, the mechanics of this event would be the same as owning the assets and the put option. The put option is worthless if the assets clear the debt. However, if the assets do not clear the debt, the put option offset the losses, thus making the equity holders at 0.
From the debt holders, the short position on the put illustrate what happens if the assets does not clear the debt. The put option is exercised, and the creditors loose money.

Question 54

elaborate on representing the value of the debt of a firm with put options

Answer 54

The goal is to represent the value of the debt. The debt is inherently risky because there is a probability of default.

First, we find the value of the debt if there were no chance the firm would fuck up. We call this part “risk free debt”.
Then we need the value of the fuck up.
This is where we use the put option. The put option excels at this, becuase it relates fuck-up value with stock price movement. The put represent what the creditors LOOSE if the firm fucks up, as a function of the degree of fuck up.

So, we can consider it as saying “The value of the debt of a firm is equal to the value of the debt if it were risk free, less the value of the put should the firm fuck up”.

Question 55

elaborate on valuing debt using call option

Answer 55

The creditor sell a call option to the firm. The call option have stirke price equal to the debt outstanding.

IF the firm fuck up, the assets are worth less than the debt. I nsuhc a case, the firm gain nothing on the call option they bought.

Question 56

What is the exiting outcome of using put options to value corporate debt?

Answer 56

By re-arranging the equation, we can see how we can eliminate the bond rating, essentially creating risk free securitiy:

risk free debt = risky debt + put option on firms assets

This put option is known as a credit default swap. NB: The puts on the firm’s assets is not publicly traded. It require a third party. This put is only for conceptual understanding of how the mechanics of the credit default swap works.

Question 57

Key working in the CDS?

Answer 57

Eliminate the bond rating from corporate debt.

Question 58

Elaborate on the credit default swaps

Answer 58

As noted before, it is a way to insure ourselves against the risk of buying risky debt. Risky debt is simply corporate debt. By buying the risky corporate debt and also buying the conceptual asset put, we obtain the riskfree debt.

In real life, the conceptual asset put is purely conceptual. what actually happens is that you pay a third party periodic payments to hedge the bond. If the bond defaults, you will receive the conceptual asset put money from the third party. If the bond does not default, you do not get this.

Question 59

precisely define CDS

Answer 59

position that removes the credit risk of a corporation