chapter 14 Flashcards
define financial option
a contract that gives its owner the right (but not the obligation) to purchase or sell an asset at a fixed price at some future date
define call option
a financial option that give sits owner the right to buy an asset
define put opinion
gives the owner the right to sell the asset
define option writer
the seller of an option contract
define what it means to exercise an option
when a holder of an option enforces the agreement and buys or sells a share of stock at the agreed upon price
define strike price
the price at which the holder buys or sells the share of stock when the option is exercised is
define american options
most common kind, allow their holders to exercise the option on any date up to and including a final date (expiration date)
define option expiration date
the last date on which an option holder has the right to exercise the option
define european option
allows their holders to exercise the option only on the expiration date - holders cannot exercise before the expiration date
what’s an option contract
An option contract is a contract between two parties. The option buyer, also called the option holder, holds the right to exercise the option and has a long position in the contract. The option seller, also called the option writer, sells (or writes) the option and has a short position in the contract. Because the long side has the option to exercise, the short side has an obligation to fulfill the contract.
when is an option exercised
only when investors make a positive payogg
define option premium
the market price of the option - the upfront payment
why is there an option premium
to compensate the seller for the risk of a negative payoff in the event that the option holder chooses to exercise the option.
how to read an option
The first two digits in the option name refer to the year of expiration. The option name also includes the month of expiration, the strike or exercise price, and the ticker symbol of the individual option (in parentheses).
define open interest
the total number of contracts of a particular option that has been written
define an option that’s at the money
describes options whose exercise prices are equal to the current stock price
why is it that much of the trading occurs in the options that are closest to being at the money
bc of not much time that EV will add value
define an option that’s in the money
describes an option whose value if immediately exercised would be positive
Call options with strike prices below the current stock price are in-the-money, as are put options with strike prices above the current stock price.
define an option that’s out of the money
describes an option that if exercised immediately, results in a loss of money
Call options with strike prices above the current stock price are out-of-the-money, as are put options with strike prices below the current stock price. Of course, a holder would not exercise an out-of-the-money option.
define an option that’s deep in the money
describes options that are in the money and for which the strike price and the stock price are very far apart
define an option that’s deep out of the money
describes options that are out of the money and for which the strike price and the stock price are very far apart
are stock option contracts always written on 100 shares of stock
yes,
which is more valuable a right to buy or sell when the call options with lower strike prices have higher market price
is it valuable to have a longer period to exercise
or having a put option with a higher strike price
call options with lower strike prices have higher market prices—the right to buy the stock at a lower price is more valuable than the right to buy it for a higher price. Conversely, because the put option gives the holder the right to sell the stock at the strike price, for the same expiration puts with higher strikes are more valuable. On the other hand, holding fixed the strike price, both calls and puts are more expensive for a longer time to expiration. Because these options are American-style options that can be exercised at any time, having the right to buy or sell for a longer period is more valuable.
define hedge
to reduce risk by holding contracts or securities whose payoffs are negatively correlated with some risk exposure
define speculate
when investors use securities to place a bet on the direction in which they believe the market is likely to move
how to hedge with options or speculate with options
a stock index put option can be used to offset the losses on an investor’s portfolio in a market downturn. Using an option to reduce risk in this way is called hedging. specifically, to hedge with options is to reduce risk by holding option contracts whose payoffs are negatively correlated with a risk exposure. Options also allow investors to speculate, or place a bet on the direction in which they believe the market is likely to move. By purchasing a call, for example, investors can bet on a market rise with a much smaller investment than investing in the market index itself.
how to consider the option payoffs at expiration
we must determine an option’s payoff at the time of expiration. When we consider the payoff at expiration for an option owner, we ignore the initial cost of purchasing the option. Similarly, when we are considering the payoff at expiration for an option writer, we ignore the initial amount received when the option was sold to the buyer.
what’s the formula for the call value at experiation
C = max(S-K, 0)
where C = value of the call option
S = stock price at expiration
K = exercise price
the call’s value is the max difference between the stock price and strike price and zero
what’s the formula for the value of the put value at expiration
p = max(K-S, 0)
does a short position on a call option have a limit to downside
no, they have unlimited downside risk
what’s the relationship between a deeper out of the money the put option and beta
the deeper out-of-the-money is, the more negative it’s beta and lower its expected return. As a result, put options are generally not held as an investment, but rather as insurance to hedge against other risk in a portfolio.
The put position has a higher return in states with low stock prices; that is, if the stock has a positive beta, the put has a negative beta. Hence, put options on positive-beta stocks have lower expected returns than the underlying stock.
define straddle
a portfolio that is long a call and a put on the same stock with the same exercise date and the strike price
why is straddle strategy used
This strategy is sometimes used by investors who expect the stock to be very volatile and move up or down a large amount, but who do not necessarily have a view on which direction the stock will move. Conversely, investors who expect the stock to end up near the strike price may choose to sell a straddle.
define a protective put
a long position in a put option held on a stock you already own
define portfolio insurance
a protective put written on a portfolio rather than a single stock. when the put doesn’t itself trade, it’s synthetically created by constructing a replicating portfolio
how does the value of strike price and stock price affect option prices
the value of an otherwise identical call option is higher if the strike price the holder must pay to buy the stock is lower. Because a put is the right to sell the stock, puts with a lower strike price are less valuable.
For a given strike price, the value of a call option is higher if the current price of the stock is higher, as there is a greater likelihood the option will end up in-the-money. Conversely, put options increase in value as the stock price falls.
can a european option be worth more than an american one
no. option’s price cannot be negative. Furthermore, because an American option carries all the same rights and privileges as an otherwise equivalent European option, it cannot be worth less than a European option. If it were, you could make arbitrage profits by selling a European call and using part of the proceeds to buy an otherwise equivalent American call option. Thus an American option cannot be worth less than its European counterpart.
what’s the max payoff for a put option
occurs if the stock becomes worthless (if, say, the company files for bankruptcy). In that case, the put’s payoff is equal to the strike price. Because this payoff is the highest possible, a put option cannot be worth more than its strike price.
what’s the max payoff for a call option
the lower the strike price, the more valuable the call option. If the call option had a strike price of zero, the holder would always exercise the option and receive the stock at no cost. This observation gives us an upper bound on the call price: A call option cannot be worth more than the stock itself.
define the intinsic value
the amount by which an options is in the money or zero if the option is out of the money
the value it would have if it expired immediately
can an american option be worth less than its intrinsic value
no
define time value of an option
the difference between the current option price and its intrinsic value
no negative value for american option as it cannot be worth less than it’s intrinsic value
what’s the downside of a short position in s a put vs call option
because the stock price cannot fall below zero, the downside for a short position in a put option is limited to the strike price of the option. A short position in a call, however, has no limit on the downside
can the profit from purchasing an option and holding it to expiration be negative?
yes bc the payoff at expiration might be less than the initial cost of the option
in the money option vs out of the money option relationship with loss cost and potential profit/loss
the further in-the-money the option is, the higher its initial price and so the larger your potential loss. An out-of-the-money option has a smaller initial cost and hence a smaller potential loss, but the probability of a payoff is also smaller because the point where profits become positive is higher.
what’s the risk of call options
as a consequence, the risk of a call option is amplified relative to the risk of the stock, and the amplification is greater for deeper out-of-the-money calls. Thus, if a stock had a positive beta, call options written on the stock would have even higher betas and expected returns than the stock itself.
put position on positive beta stocks
he put position has a higher return in states with low stock prices; that is, if the stock has a positive beta, the put has a negative beta. Hence, put options on positive-beta stocks have lower expected returns than the underlying stock.
why are put options generally held as insurance rather than as an investment
The deeper out-of-the-money the put option is, the more negative its beta, and the lower its expected return. As a result, put options are generally not held as an investment, but rather as insurance to hedge against other risk in a portfolio.
define straddle
a portfolio that is long a call and a put on the same stock with the same exercise date and the strike price
why is a straddle used
this strategy is sometimes used by investors who expect the stock to be very volatile and move up or down a large amount, but who do not necessarily have a view on which direction the stock will move. Conversely, investors who expect the stock to end up near the strike price may choose to sell a straddle.
define portfolio insurance
a protective put written on a portfolio rather than a single stock. when the put doesn’t itself trade, it’s synthetically created by constructing a replicating portfolio
what are the two different ways to construct portfolio insurance
(1) purchase the stock and a put or (2) purchase a bond and a call. Because both positions provide exactly the same payoff, the Law of One Price requires that they must have the same price
define put-call parity
the relationship that gives the price of call option in terms of the price of put option plus the price of the underlying stock minus the present value of the strike price and the present value of any dividend payments
what are the different formulas of the put-call parity
S + P = PV(K) + C
C = P + S - PV(K)
Let K be the strike price of the option (the price we want to ensure that the stock will not drop below), C the call price, P the put price, and S the stock price
what’s the formula if there’s put-call parity with dividends
S+P = PV(K) + PV(Div) + C
C = P + S - PV(K) - PV(Div)
strike price vs call and put option value
For a given strike price, the value of a call option is higher if the current price of the stock is higher, as there is a greater likelihood the option will end up in-the-money. Conversely, put options increase in value as the stock price falls
the value of an otherwise identical call option is higher if the strike price the holder must pay to buy the stock is lower. Because a put is the right to sell the stock, puts with a lower strike price are less valuable.
why is it that a put option cannot be worth more than its strike price
The maximum payoff for a put option occurs if the stock becomes worthless (if, say, the company files for bankruptcy). In that case, the put’s payoff is equal to the strike price
why is it that a call option cannot be worth more than the stock itself
For a call option, the lower the strike price, the more valuable the call option. If the call option had a strike price of zero, the holder would always exercise the option and receive the stock at no cost
define intrinsic value of an option
the amount by which an option is in the money, or zero if the option is out of the money.is the value it would have if it expired immediately.
why is it that an american option cannot be worth less than its intrinsic value
If an American option is worth less than its intrinsic value, you could make arbitrage profits by purchasing the option and immediately exercising it.
define time value of an option
the difference between an option’s current price and its intrinsic value. Because an American option cannot be worth less than its intrinsic value, it cannot have a negative time value.
option prices and expiration dates - american options vs european options
an option with one year until the expiration date and an option with six months until the expiration date. The holder of the one-year option can turn her option into a six-month option by simply exercising it early. That is, the one-year option has all the same rights and privileges as the six-month option, so by the Law of One Price, it cannot be worth less than the six-month option: An American option with a later expiration date cannot be worth less than an otherwise identical American option with an earlier expiration date. Usually the right to delay exercising the option is worth something, so the option with the later expiration date will be more valuable.
What about European options? The same argument will not work for European options, because a one-year European option cannot be exercised early at six months. As a consequence, a European option with a later expiration date may potentially trade for less than an otherwise identical option with an earlier expiration date. For example, think about a European call on a stock that pays a liquidating dividend in six months (a liquidating dividend is paid when a corporation chooses to go out of business, sells off all of its assets, and pays out the proceeds as a dividend). A one-year European call option on this stock would be worthless, but a six-month call would be worth something. Now think about a European put option on the stock of a company that has gone bankrupt (and will not be reorganized). The stock price, S, is effectively zero and will not change. With a three-month European put, you would exercise in three months and get the exercise price, K, at that time. Since there is no risk, the current value to you of that put is the present value of K determined using the risk-free interest rate, , and discounting for one-quarter of a year.
option price and volatility
The value of an option generally increases with the volatility of the stock. The intuition for this result is that an increase in volatility increases the likelihood of very high and very low returns for the stock. The holder of a call option benefits from a higher payoff when the stock goes up and the option is in-the-money, but earns the same (zero) payoff no matter how far the stock drops once the option is out-of-the-money. Because of this asymmetry of the option’s payoff, an option holder gains from an increase in volatility.
Recall that adding a put option to a portfolio is akin to buying insurance against a decline in value. Insurance is more valuable when there is higher volatility—hence put options on more volatile stocks are also worth more.
why is the price of any call option on a non-dividend paying stock always exceeds its intrinsic value
where PV(K) = K - dis(K)
C = S - K + dis(K) + P
where S - K = intrinsic value
dis(K) + P = time value
In this case, both terms that make up the time value of the call option are positive before the expiration date: As long as interest rates remain positive, the discount on a zero-coupon bond before the maturity date is positive, and the put price is also positive, so a European call always has a positive time value. Because an American option is worth at least as much as a European option, it must also have a positive time value before expiration.
why is it never optional to exercise a call option on a non-dividend paying stock early
you are always better off just selling the option. It is straightforward to see why. When you exercise an option, you get its intrinsic value. But as we have just seen, the price of a call option on a non-dividend-paying stock always exceeds its intrinsic value. Thus, if you want to liquidate your position in a call on a non-dividend-paying stock, you will get a higher price if you sell it rather than exercise it. Because it is never optimal to exercise an American call on a non-dividend-paying stock early, the right to exercise the call early is worthless. For this reason, an American call on a non-dividend-paying stock has the same price as its European counterpart.
what are the 2 benefits to delaying the exercise of a call option
First, the holder delays paying the strike price, and second, by retaining the right not to exercise, the holder’s downside is limited.
what’s the implication of non-dividend paying stocks for european calls
for non-dividend-paying stocks, European calls with later expiration dates will also be more valuable than their equivalent European call options with earlier expiration dates.
what’s the put-call parity relationship for a dividend-paying stock
C = S - K + dis(K) + P = PV(Div)
can the price of the american option exceed the price of a european option
If PV(Div) is large enough, the time value of a European call option can be negative, implying that its price could be less than its intrinsic value. Because an American option can never be worth less than its intrinsic value, the price of the American option can exceed the price of a European option
why is it generally valuable to exercise a call option early for stock that pays dividends
When stocks pay dividends, the right to exercise an option on them early is generally valuable for calls. For puts, the right to exercise early is generally valuable whether or not the stock pays dividends
To understand when it is optimal to exercise the American call option early, note that when a company pays a dividend, investors expect the price of the stock to drop to reflect the cash paid out. This price drop hurts the owner of a call option because the stock price falls, but unlike the owner of the stock, the option holder does not get the dividend as compensation. However, by exercising early and holding the stock, the owner of the call option can capture the dividend. Thus the decision to exercise early trades off the benefits of waiting to exercise the call option versus the loss of the dividend. Because a call should only be exercised early to capture the dividend, it will only be optimal to do so just before the stock’s ex-dividend date.
what’s the formula for the put-call option parity for dividends on put option
P = K - S + C - dis(K) + PV(Div)
where K - S = intrinsic value
C - dis(K) + PV(Div) = time value
Because the time value of a put includes the present value of the expected dividends paid during the life of the option, dividends reduce the likelihood of early exercise. The likelihood of early exercise increases whenever the stock goes ex-dividend (due to the expected drop in the stock price).
why is equity considered a call option
a share of stock as a call option on the assets of the firm with a strike price equal to the value of debt outstanding.
If the firm’s value does not exceed the value of debt outstanding at the end of the period, the firm must declare bankruptcy and the equity holders receive nothing. Conversely, if the value exceeds the value of debt outstanding, the equity holders get whatever is left once the debt has been repaid
how can debt be represented using options
debt holders as owning the firm and having sold a call option with a strike price equal to the required debt payment. If the value of the firm exceeds the required debt payment, the call will be exercised; the debt holders will therefore receive the strike price (the required debt payment) and “give up” the firm. If the value of the firm does not exceed the required debt payment, the call will be worthless, the firm will declare bankruptcy, and the debt holders will be entitled to the firm’s assets
how to view corporate debt
as a portfolio of riskless debt and a short position in a put option on the firm’s assets with a strike price equal to the required debt payment.
what’s the formula of risky debt
risky debt = risk-free debt - Put Option on Firm Assets
When the firm’s assets are worth less than the required debt payment, the put is in-the-money; the owner of the put option will therefore exercise the option and receive the difference between the required debt payment and the firm’s asset value
This leaves the portfolio holder (debt holder) with just the assets of the firm. If the firm’s value is greater than the required debt payment, the put is worthless, leaving the portfolio holder with the required debt payment.
define credit default swaps (CDS)
when a buyer pays a premium to the seller (often in the form of periodic payments) and receives a payment from the seller to make up for the loss if the underlying bond defaults
