Chapter 20 - Financial options Flashcards
Define a financial option
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.
Call vs put
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.
Who makes the option?
the option writer
What is a warrant?
A warrant is a call option where the writer is the firm itself
What is the strike price?
The strike price is the price at which the asset will be bought or sold at the poitn of option exercise.
Another word for strike price?
Exercise price
What position do we say that the option buyer has?
Has a long position
What position do we say that hte option seller has?
A short position
Does the option writer have a right to do anytihng+
they ahve the obligation to fulfill the agreement if the long position side choose to exercise his right to buy or sell
why do people sell/write options?
They get the option premium, which is the price of the contract
What is the largest and oldest exchange for options?
Chicago Board Options Exchange (CBOE).
By convention, when do options expire?
Third friday of eahc month. More pooular stocks have more frequent expliraitons.
What is Open int?
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.
recall ATM options
At the money. Strike price/exercise price is equal to the current share price.
What is the volume?
the amount of contracts traded the specific day
how many shares per contract
100
ITM
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.
using an option to reduce risk is called…?
Hedging
Can we use the law of one price to detemrine the value of an option?
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.
elaborate on the curve that describe the options worth as a function of share price
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.
Does the short or long position have obligations?
The short position is the writer of the option. therefore, he has the obligation to follow, should the long position exercise his right.
How does the losses of the option writer relate to the profits of the buyer?
The are the opposite. except for the option premium.
What can we say about the downside of taking a short position on a call option?
you can be infinitely fucked because there are no limit upwards
is there a relationship between the strike price and returns?
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.
What can we say about the returns of options vs the underlying
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
what can we say about the signs of option betas?
Call options have positive betas
Put options have negative betas (relative to the underlying)
What is the outcome of put options having negative betas (if the underlying has positive beta)?
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
define a straddle
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.
Define a butterfly spread
Makes money when the strike price and stock price is close together. Sort of the opposite of a straddle.
What is a protective put?
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.
What is portfolio insurance?
Holding protective puts on the enitre portfolio
how can we do portfolio insurance without using puts
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.
A straddle makes money when…?
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.
In one sentence, when does butterfly spreads make money
Butterfly spreads make money whenever the strike price is close to the stock price at expiration.
You’re essentially betting that volatility is low.
elaborate on butterfly spreads
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.
elaborate on portfolio insurance
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.
how can we perform portfolio insurance without protective puts?
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.
If we buy a protective put at strike price 45, and hold the stock as well, how does the payoff picture look?
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.
What can we say about protective put vs bond+call?
If they are constructed so that they yield the same results, they must be worth the same according to the law of one price.
Since we know that protective puts and bond+call have the same price when structured the same, what is the relationship between them?
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).
Elaborate on put-call parity
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.
What happens with put-call parity if there are dividends involved?
Subtract PV(div) just like we subtract PV(K) already
When does put call parity apply?
European options with the same expiration and strike price
What is worth more, american or european option?
The european cannot be worth more because the american option provides more flexibility.
What is the maximum value of a put option?
its strike price
Max value of call option
The stock itself
What is intrinsic value of an option?
Its value if it expired immediately.
Define the time value of an option
The time value of an option is the difference in value between the option’s current price and the instrinsic value
Elaborate on exercising options early
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.
elaborate on early exercise of put optins
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
What happens when the stock pays a dividend
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.
how can we use a call option to represent a firm’s value?
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.
elaborate on representing debt with options
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.
elaborate on representing the value of the debt of a firm with put options
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”.
elaborate on valuing debt using call option
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.
What is the exiting outcome of using put options to value corporate debt?
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.
Key working in the CDS?
Eliminate the bond rating from corporate debt.
Elaborate on the credit default swaps
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.
precisely define CDS
position that removes the credit risk of a corporation
