quiz 8
suppose that we set up a butterfly spread by trading the proper options with exercise prices of $200, $240, and $280. At what price of the underlying asset would we have the highest payoff?
$240 the butterfly spread consists of two long calls with differing exercise prices ($200 and $280 here) and two short calls with an exercise price exactly midway between the two long calls ($240). this results in a payoff structure that is highest at the exercise price of the short calls. so, the highest payoff occurs at $240.
suppose that an out of the money put option currently trades for $4. the option has an exercise price of $50, while the underlying stock price is $51. what is the time value of this option?
$4 the time value is the value in excess of the intrinsic value. since the option is out of the money, its intrinsic value is $0. hence, the entire $4 is time value.
you purchased an option on April 1st. its expiration date is May 18th. which of the following options could you exercise on May 11th? -American call on an S&P 500 ETF -American call on the S&P 500 -European call on Amazon's stock -European call on the S&P 500
American call on an S&P 500 ETF American options can be used prior to expiration, while European options cannot. Thus, the only option on this list can be used early on the 11th is the American call on an S&P 500 ETF
we know that _____-style options are generally more valuable than otherwise identical ________-style options.
American; European Since American options offer you the ability to exercise at expiration or before (while European options only offer exercise at expiration), they are more useful. Thus, an American option would be more valuable than an otherwise identical European option.
assuming the two are otherwise equivalent, a(n) ________-style option is generally more valuable than a(n) ______-style option.
American; European since American options offer you the ability to exercise at expiration or before (while European options only offer exercise at expiration), they are more useful. Thus, an American option would be more valuable than an otherwise identical European option.
In general, the value of a European option CANNOT be _________ the value of an American option written on the same security.
greater than a European option can only be used at expiration, while an American option can be used at expiration or any time before. thus, the American option provides the same right and more than the European version provides. Thus, the value of the European option should never be greater than the value of the American option
why might we prefer a protective put over a sell stop order?
guarantees a minimum price a protective put performs a similar role to a sell stop order. however, it has an advantage that it can guarantee a minimum price, as we are assured of being able to use the option and sell for at least the exercise price, this comes at a cost, as the protective put is significantly more expensive than the sell stop, since we have to buy the option and then pay a commission to use it.
according to our class discussion, what is an advantage of using a protective put versus a sell stop order?
guarantees a minimum sale price the protective put allows us to use the option if the stock price falls below the exercise price. however, we can also chppse not to use the option if the price stays above the exercise price. hence, it guarantees a minimum sale price. this is an advantage over a sell stop order, which must be processed after being triggered (often resulting in a slightly lower than expected price).
why might a pig farmer get involved in the pork belly option market?
hedging a pig farmer would most likely get involved in a pork derivative market to shed the risks associated with their product's prices. thus, they would be most interested in hedging.
A multinational manufacturing firm would most likely choose to use currency options or other derivatives for ______.
hedging this firm likely does not have currency trading as its core business. So, it would be better off packaging and selling that risk as a hedging strategy.
all else equal, the payoffs for a straddle will be ________ the payoffs for a strangle.
higher than a straddle consists of a call and put with the same exercise price, while a strangle consists of a call with a higher exercise price and a put with a lower exercise price. this necessarily lowers the payoff for a strangle at any particular price, meaning that the straddle's payoffs will be higher. this is the reason that straddles tend to be more expensive to set up.
which of the following would INCREASE the value of a European call option?
higher time to maturity since call options have potentially unlimited upside, a higher time to maturity will always increase the value of European call option
you have constructed a synthetic short stop position. you write a call with a strike price of $60, and you purchase a put option with the same strike price. which of the following is true of the potential payoffs of this position? (HINT: "unlimited" implies that the value can go to infinity, while "limited" implies a finite limit)
unlimited loss and limited profit you wrote a call, so your payoff is the negative of the call option holder's payoff. we know that calls are unbounded, so your loss is unlimited. at the same time, you bought a put. puts can only payoff a maximum of the exercise price, so you have limited profit.
which of the following is true of the two-state model?
uses a risk free portfolio the two-state model is an interpretation of the binomial model in which the typical replicating portfolio approach is replaced by a risk free portfolio approach. everything else is the same: the model is still discrete. and were are only 2 outcome in each period.
according to our discussion, which of the following inputs for the Black-Scholes model is MOST difficult to accurately observe?
volatility a common use for the Black-Scholes model is to use the current option price to calculate the implied volatility, as the volatility of the underlying asset can be difficult to accurately observe. the other inputs are relatively easy to find.
which of these is the most difficult Black-Scholes input to observe?
volatility the least observable input for the Black-Scholes model is in the stock's volatility
which of the inputs for the Black-Scholes option pricing model is most difficult to observe accurately?
volatility it is more difficult to find the stock's volatility than any of the other Black-Scholes inputs
which of the inputs for the Black-Scholes option pricing model are we least likely to be able to observe accurately?
volatility the only input that we can't observe for the Black-Scholes model is the stock's volatility
which of the following inputs are we most likely to want to "back out" go the Black-Scholes model?
volatility we would want to "back out" the stock's volatility, as it would eliminate many of the statistical issues we otherwise face with calculating it (i.e., how much data to use, what frequency, new information not being reflected in the data).
_______ is the term report for the number of a trades that have occurred on a specific option contract (same underlying asset, same expiration date, same exercise price) for a particular day.
volume open interest tells us the total number of an option contract that exist, but volume tells us ow many have been traded on a given day.
which of the following is NOT true of the writer of a call option? -has an obligation to sell if exercised -has a right to buy -hopes the option is not exercised -limited profit potential
when writing an option, we receive the option premium in exchange for being obligated to fulfill the opposite side of the trade if the buyer uses the option. this is all the profit that the writer can hope to receive. in this case, the call provides a right to buy, meaning that the writer would be obligated to sell. the writer receives no rights, so they do not have a right to buy.
a common use for the Black-Scholes formula is to compute the underlying security's ______.
implied volatility the underlying stock's volatility tends to be the only Black-Scholes input that is not easily observable/calculable. So, it is common to use the Black-Scholes formula (along with the option's price) to solve for the implied volatility.
which of the following combinations can be true at the same time? the option is both ________ and ________.
in the money; near the money "near the money" does not have a specific meaning other than the underlying stock price being close to the exercise price. hence, an option can be both in the money and near the money.
if the firm's dividend payout ratio increase, then the price of the put option will ______ and the price of the call option will _____.
increase; decrease increased dividend payouts imply a reduced stock price in the future. this would increase the value of the put and decrease the value of the call.
when looking at the CBOE, we saw that we generally had significantly more choice of expiration date when considering _______ options.
index available expirations are identical, regardless of whether we are considering calls or puts. however, we saw that index options offered considerably more expiration dates for trading
generally, _______ options are cash settled, while _______ options are settled through physical delivery.
index; individual stock it would be difficult to acquire all the individual securities in the appropriate weightings to physically deliver an index when the option is exercised, so index options are cash settled. individual stock options are physically delivered.
according to our discussion, the _______ of a call option is limited by the underlying stock price, while its _____ is mostly unconstrained.
intrinsic value; time value the stock price is the best possible call option payoff. the option payoff is its intrinsic value. however, this has little effect on its time value.
which of the following is NOT generally true of an option? -one option hedges one share or less -it is less risky than the underlying asset -its payoffs are equivalent to a leveraged position in the underlying asset -the option's beta is higher than the underlying asset
it is less risky than the underlying asset the two countervailing influences on the option's risk. it generally has a smaller variable of cash flows than the underlying asset. however, it is essentially a levered position in the underlying asset. thus, when considering returns, it is typically more risky than the underlying asset
which of the following is NOT a valid interpretation of the option's delta? -it is the dollar change in the option price per $ change in share price -it is the firm's value at risk -it is the number of the shares hedged by 1 option -it is the number of shares held in the replicating portfolio
it is the firm's value at risk the delta of an option is its hedge ratio. this value represents the dollar change in the option price per dollar change in the underlying stock price. hence, it can be used to determine the number of shares held in the replicating portfolio or the number of shares hedged abby 1 option. however, it is not the firm's value at risk, as that is a different measure.
an option that is "out of the money" has an intrinsic value that is ________ its time value.
less than since the option is out of the money, we know that its intrinsic value is 0. Hence, any value it has is time value. this means that its intrinsic value is less than its time value.
all else equal, a _______ should lead to a lower call option value.
lower interest rate increased volatility always increases option values. likewise, a longer time to expiration always increase the value of a call option. a lower dividend yield can be thought of as the equivalent of a higher stock price, which would lead to a higher call value. however, a lower interest rate would increase the present value of the exercise price, necessitating a decrease in the value of the call option to maintain parity.
which of the following factors might have differing effects on the value of a European put option?
more time to expiration since the upside on a put is limited, it is possible that more time to expiration can actually reduce the value of a European put option that is already heavily in the money. At the same time, a European put option that is at the money or out of the money would likely see a value increase from more time to expiration.
the writer of a call option has a(n) ________ the underlying stock if the option is executed.
obligation to sell a call option offers the holder the right to buy the underlying asset. this right is backed by the seller of the option. hence, the option writer has an obligation to sell the shares.
______ is the term for how many of a particular option contract exist in the market at a given time.
open interest open interest is the number of a particular contract that has been written. this is similar to the number of shares outstanding for a stock.
when calculating the option price using the binomial model, which of the following assumptions did we NOT make? -ability to invest in a risk free bond -only two potential outcomes -probability that the stock price increases -rates don't change throughout -we made all of these assumptions
probability that the stock price increases in using the binomial model, we assume that there are only two outcomes, but we never make any assumptions regarding what the probability of these outcomes is
the maximum value of a(n) _______ option is its exercise price.
put the best case a pit option is that the underlying asset becomes worthless. in this case, the payoff is the exercise price.
the binomial model uses a _________ portfolio to price option, while the two state model reinterprets it as a ________ portfolio.
replicating; risk-free the binomial model uses the underlying stock and a risk free asset to construct a replicating portfolio for the option. the 2 state model rearranges this equation to form a risk-free portfolio from the underlying stock and some number of the options.
the binomial option pricing model relies on a ______ portfolio approach, while the 2 state option pricing model relies on a _________ portfolio.
replicating; risk-free the binomial relies on the underlying stock and a risk free bond to construct a replicating portfolio for the option. meanwhile, the 2 state model uses the underlying stock and some number of the options to create a risk-free portfolio.
calculation the implied probabilities of an upward or downward movement for the binomial model requires us to assume that investors are _______.
risk neutral for most pricing models, we assume that investors are risk averse, but here, we actually assume risk neutrality: that investor only care about returns.
according to our class discussion, if i wanted to purchase an option that expires on a Monday or Wednesday, I would most likely need to purchase a _______.
short-term option on an index in general, more expirations are available and traded on short-term options. further, index options tend to have significantly more expirations available than options on individual stocks.
the replicating portfolio for a put option typically involves _____ the underlying shares and _____ cash at the risk free rate.
shorting; lending when calculating the delta and beta for the replicating portfolio for a put option, we will generally find a negative delta and a positive beta. this represents a purchasing negative stars of the underlying stock (which of our mathematical representation of shorting) and purchasing a bond. ultimately, when we purchase a bond, we are lending.
which of the option strategies that we discussed would we expect to offer the highest payoffs given that the underlying asset is experiencing high volatility?
straddle the butterfly spread has its highest payoffs in a fairly narrow spread between its exercise prices. hence, it performs best with low volatility. the others both have increasing payoffs with higher deviations in the stock prices. however, the straddle will offer the highest payoffs, as the call and put have the same exercise price (there is a "delay" in the strangle paying off in either direction due to the difference in exercise prices)
options expiring on Mondays or Wednesdays would most likely be written on what underlying asset?
the S&P 500 index Index options tend to have a significantly more available expirations available. In particular, Monday and Wednesday "weekly" tend to be exclusive to index options. Hence, the S&P 500 index is the most likely to have these option expirations available.
which of the following is NOT an assumption we made when using the binomial model? -that there was only two possible outcomes in each period -the amount by which the stock price changes in each state -the likelihood that the stock price increase in a given period -whether the option is American or European -we made all of these assumptions
the likelihood that the stock price increase in a given period when using the binomial model, we never make any assumptions regarding the probability that the stock prices increases or decreases.
in our discussion, we claim that the Black-Scholes model is an extension of the binomial model where ________.
the periods are infinitesimally small the Black-Scholes model is an extension of the binomial model where the periods are infinitesimally small. by shrinking the period length, we can add more periods in, which results in more potential outcomes. this makes the model more realistic. at some point, we take this to the extreme: each period is so small that we can no longer tell the difference. this causes us to switch to continuous time and leads to the Black-Scholes model.
which of the following is most likely to result from a decrease in interest rates?
the price of a European put option increases interest rates have a inverse relationship with bond prices. so, when interest rates fall, the price of the risk free bond used in the put-call parity relationship increases. in order for parity to be maintained, the call option's price must fall and/or the put option's price must rise. it is irrelevant in this case whether the options are American or European.
what was an assumption we did NOT make in calculating the option pricing using the binomial model? -a limited number of potential outcomes -borrowing/lending at the risk free rate -no transaction costs -the probability of the stock going up -we assumed all of these
the probability of the stock going up the binomial model makes several assumptions: two potential outcomes, no transactions costs, and borrowing/lending at the risk free rate are some of the biggest. however, at no point does it make any assumption regarding the probabilities of the stock going up or down.
which of the follow is NOT an assumption we made when using the binomial model? -expected return is the risk free rate -only two potential outcomes -the probability of the stock price increasing -no transaction costs -we assumed all of these
the probability of the stock price increasing while we assume that there are only two potential outcomes, we never actually assume anything regarding the probability of the stock price increasing
why would we use a protective put instead of a stop loss order?
the put sets a guaranteed minimum price both a protective put and a stop loss order perform the function of limiting losses. however, the stop loss order is subject to the activity on the limit order book, meaning that its execution price could differ from the stop price. the put option guarantees you the right to sell the share at the exercise price regardless of market conditions, guaranteeing a minimum price.
an implication of the binomial model is that the expected return on the option equals _________.
the risk free rate because the binomial model assumes risk-neutrality, investors only care about returns. in such a world, there are no risk premiums, as investors aren't disincentivized by risk. hence, the expected return of the option is the risk free rate. we use this idea explicitly in the calculation of implied probabilities
at expiration, the maximum value of a call option is _______.
the stock price the maximum value that a call option can have at any point in time is the stock price. prior to expiration, this is a soft limit, as the stock price could increase. however, at expiration, the stock price is fixed. thus, the maximum value is the stock price.
You are looking to purchase a call option on an individual stock that expires in 6 months. Based on our class discussion, which of the following best represents the set of option expirations you would have available to you?
the third friday for an individual stock, the only option expiration available beyond the first two to three months is the third friday of the month.
what is the maximum payoff of a call option at any given time?
the value of the stock the best case for a call would be that the exercise price is $0. in this case, its payoff would be equal to the stock price. Thus, the stock price is the maximum value of the call option.
when looking at the CBOE's listings of S&P 500 index options, we saw that options expiring over one year from today would generally have what expiration(s) available?
third Friday of the month even for index options, we are generally only able to trade options expiring on the third Friday of the month at such extended expirations.
which of the factors affecting option prices can potentially affect two European put options in opposite directions (increasing the value of one and decreasing the value of the other)?
time to maturity a put can only ever be as valuable as its exercise price. due to this limited upside, time to maturity can potentially affect two European puts in differing ways.
while the values they calculate are the same, the ________ model uses a risk-free portfolio approach, while the ________ model uses a replicating portfolio approach.
two state; binomial the two state model is identical to the binomial model. however, the two state model is set up to represent a risk free portfolio, while the binomial is set up to represent a replicating portfolio.
the ________ model uses a risk free portfolio, while the _______ model uses a replicating portfolio to value options.
two state; black-scholes the two state model is a reinterpretation of the binomial model using a risk free portfolio. the binomial model. and the black-scholes model by extension, uses a replicating portfolio approach.
according to our discussion, which of the following likely has the most available expirations at a given time? -American call on AAPL -American call on MSFT -European call on AMZN -European call on SPX500
European call on SPX500 the S&P 500 is an index (and the most popular index), so it will typically have more expirations available than any individual stock. so, there are likely to be many more expiration of the European put on SPX500 available than the others.
suppose you are considering a set of options on the same underlying stock that all have a $50 exercise price. the current price of the underlying stock is $10. all else equal, which of the following options is MOST likely to have its value decreased by a longer time to expiration?
European put generally, a longer time to expiration is always better for an option. however, a European put that is already heavily in the money (as the puts here are) doesn't have a very far left to increase. since the option is European, it can't be exercised early, leaving the option holder exposed to risk of loss for a longer period of time. Thus, it is the only type of option that may decrease with a longer time to expiration.
assuming all other terms are the same and the options are not expiring today, a(n) _________ option should be worth less than a(n) _______ option.
European; American all else equal, a European option is inferior to an American option, as it provides the same choice (use it or lose it at expiration) but without the added benefit of being able to use the option prior to expiration. hence, a European option should be worth less than an American option.
All else equal, increasing the ______ of a European call option will always increase its value. -interest rate -time to expiration -underlying stock price -underlying stock volatility -all of these
all of these all of these increase the value of a call option. a higher volatility or time to expiration is always beneficial to a call, as it provides more change for upside while the option's downside is limited. further, a higher underlying stock price increase the payoff of the call option. finally, a higher interest rate results in a decreased price for the risk free bond in the put-call parity relationship, forcing the call's value to rise to offset.
which of the following is NOT true of a put option for the perspective of the option writer? -best case outcome is that the option expires worthless -contract specifies a purchase price -expires at a future date -represents an obligation to purchase -all of these are true
all of these are true the option contract specifies an expiration date and a price at which the contract can be exercised. since the option holder has the right to sell, the writer has the obligation to purchase. given this, the writer hopes that the option will expire out of the money, resulting in them owing nothing. so, all of these are true
increasing which of the following would DECREASE the value of an American-style put option? Assume that all other aspects remain constant. -dividend payout -strike price -time to expiration -volatility -all of these would decrease the value of the put option -all of these would increase the value of the put option
all of these would increase the value of the put option for american style options, time to expiration and volatility always increase the value of the option. a higher strike price increases the value of a put option. finally, an increased dividend payoff would imply a lower stock price in the future. this would increase the value of the put. so, all of these would increase the value of the put.
according to our discussion, which of the following is NOT typically true of an index option? -American-style -cash-settled -more viable expirations than individual stock options -more volume than individual stock options
american-style index options are typically European, so it is not true that index options are American.
Most likely, an option on Apple's stock would be _______-style, and it would be __________.
american; physically settled generally, options on the stock of an individual company are American options. they are also typically physically settled.
which of the following is NOT always true of option values? -a call cannot be worth more than the underlying -a put cannot be worth more than its exercise price -an American option must be worth at least as much as an equivalent European option -an index option is worth less than a portfolio of the individual stock options
an index option is worth less than a portfolio of the individual stock options in theory, the values of an index option versus its constituent individual options should be equivalent, so its not always true that an index option is worth less than a portfolio of the individual stock options.
which of the following is NOT true of an option whose value decreases with a longer time to expiration? -at the money -European style -put option
at the money a longer time to expiration generally correlates to a higher option value. the exception is that a European put option that is already heavily in the money might be negatively affected. hence, an at the money put would still experience a positive effect from a longer expiration.
when pricing an option, the ______ model relies on a replicating portfolio, while the _______ model relies on a risk free portfolio.
binomial; two state the binomial model is built on a replicating portfolio, while the two state model rearranges this to create a risk-free portfolio.
the ______ model relies on a replicating portfolio approach to value an option, while the _________ model relies on a risk-free portfolio approach.
black-scholes; two state the black-scholes model is an extension of the binomial model into continuous time. hence, it still retains the basic structure of the binomial model, in that it uses a replicating portfolio. meanwhile, the two state model is a reinterpretation of the binomial model that uses a risk free portfolio to value the option.
A farmer looking to hedge the price risk they face when selling their crops would most likely choose to ________.
buy put options since the farmer is selling, their risk is that price decrease. they would like to guarantee a minimum price, which is best done by purchasing out options. a short call would provide a similar result in isolation (highest profit when prices decrease), but it would fail to offset losses from significant price drops.
the replicating portfolio for a call option generally consists of ______.
buying shares and shorting the risk-free bond for a call, we typically have a positive delta and a negative Beta. this presents purchasing shares of the underlying security and shorting the risk-free bond
which of the following options would have the most available expirations? -call on Apple (AAPL) with 1 month to expiration -call on S&P 500 with 2 months to expiration -put on Apple (AAPL) with 8 months to expiration -put on S&P 500 with 9. months to expiration
call on S&P 500 with 2 months to expiration index options typically have many more available expirations than options on individual securities with similar expirations. likewise, there tend to be more short term expirations available than long term. in this case, the S&P 500 option is similar enough to the AAPL option in expiration that there is a greater volume of expirations for the call on the S&P 500 with 2 months to expiration.
according to our discussion, which of the following delta hedges are we most likely to need to rebalance on a regular basis?
calls with a delta of 0.5 delta is the most volatility when its magnitude is closest to 0.5 and least volatility when its magnitude nears 0 or 1. here, we have a delta of 0.5, so calls with a delta of 0.5 would be the most volatile and need the most rebalancing
An option written on the S&P 500 would typically be ______.
cash-settled index options (like an S&P 500 option) are difficult to physically settle, so they would typically be cash-settled.
why might we choose a stop loss order versus a protective out?
cheaper both a protective put and a stop loss order perform the function of limiting losses while allowing for the stock to still increase. the put guarantees its execution price, making it the more effective choice. however, this means that it will be more expensive. so, the stop loss order is cheaper than the protective put.
for a near the money put option, the underlying stock's price is ________ the option's exercise price.
close to near the money does not have a specific meaning other than to say that the exercise price is close to the underlying stock price.
suppose you are given a quote on an option with the ticker symbol SPXW1910E2950, which currently trades at $15. according to our discussion, which of the following pieces of information do you NOT know without additional information? -call or put -expiration date -option premium -strike price -underlying stock price
underlying stock price an option's ticker symbol provides much of the information regarding the option - we know that underlying stock, the expiration date, whether it is a call or a put, and the exercise price of the option. further, we should easily be able to find the option premium as the price that the option currently trades at. the only thing that we don't know without more information is what the underlying stock price is.
based on our class discussion, the ________ is the most difficult Black-Scholes input to observe accurately.
underlying stock's volatility the volatility of the underlying stock is the toughest to accurately observe, as it requires us to make several assumptions about the historical data being used to calculate it. the option's standard deviation is not an input for the Black-Scholes model
you are entering into a synthetic long stock position. you buy a call with a strike price of $60, while you write a put with a strike price of $40. the underlying stock currently trades at $50. which of the following statements is true? -your payoff is negative when the stock is below $40 0r above $60 -your payoff is positive when the stock price is below $40 and above $60 -your payoff is positive when the stock price is between $40 and $60 and $0 otherwise -your payoff is positive when the stock price is greater than $60 and $0 otherwise -none of these are true
P = max (X - S, $0) C = max (S - X, $0) Total Payoff = max (S- $60, $0) - max ($40 -S, $0) given these, you would have a positive payoff any time the stock price is greater than the $60 strike price on the call and a negative payoff any time the stock is less than the $40 strike price on the put. your payoff would be $0 at any price in between $40 and $60. however, this does not match any of the given scenarios.
which of the following is true for an "out of the money" call option?
S < X for an option to be out of the money, it must have a negative payoff if it was used (a $0 payoff, since we wouldn't actually use it). for a call, this means that the underlying stock price must be less than the exercise price, or S < X.
which of the following must be true for an "in the money" put option?
S < X if an option is "in the money", it would be valuable if it was used today (whether it can be used for not). for a put option, this would mean that the exercise price (X) must e greater than the stock price (S). hence, S < X
at expiration, the payoff of an American put option should be _______ the payoff an equivalent European put option.
equal to as a rule, the value of an American option should be worth at least as much as a European option, as it offers the same ability to exercise at expiration, as well as the ability to exercise early. however, at expiration, this difference is irrelevant (there is no opportunity to exercise early), so their payoffs will be equal.
according to our class discussion, if we are looking to invest in a short term option (maturity shorter than 1 month) on the S&P 500, we would be able to choose from what expiration date(s)?
every Monday, Wednesday, and Friday, and the end of the month for a short term index option, we have expirations available on Monday, Wednesday, and Friday, as well as the end of the month