2 - Basic Option Valuation Flashcards
What percentage is the assumed risk free rate, if none given?
5%
For time to expiration, for option valuation how many day in trading year?
365
what six factors impact option price?
- time
- underlying asset
- volatility
- interest rates
- exercise price
- dividends
How do you determine the compounding frequency? how do you replicate real-time using compounding?
The unit measurement of time, i.e. interest paid yearly, monthly, daily.
the more frequent the compound, the closer you are to replicating real time (continuous compounding).
what is the formula for continuous compounding/discounting?
- continuous compounding= e^(rt)
- continuous discounting= e^(-rt)
do you use continuous or discrete compounding in the exam?
Always continuous
what is the formula for discrete compounding and discounting?
- compounding= (1+r)^t
- discounting= (1+r)^-t
What is the minimum value of a call?
0
Call=Max (0, S-X)
In Call=Max (0, S-X), how does the formula adjust for US or EU call?
EU must adjust for time value of X as it can’t be exercised at any time
Call=Max (0, S-PV(X))
can time value be negative? explain (put/call)
yes, if you long a put, you want the price to decrease. when value gets close to zero the extra time has no value (for EU option)
can’t be negative for a call, max low/min value = 0
what is the formula for intrinsic value? call and put?
S-X
X-S
S=stock price at the time
if an option is out of the money, but has a market value greater than zero, what explains this? what two things affect this?
time value
EXAM QU
- time to expiration
- money-ness i.e. deep in/out of the money minimises time value, at the money= maximises time value
if an option has a longer time to expiry, how will this affect its price?
increases the time value/speculative value
closer to maturity option value is equal to 0 or the intrinsic value - time value disappears
what is the maximum value of a call option? explain?
stock price at time of expiry
stock is perpetual while options expire so it must be less than the underlying, if the call is equal to the stock it must have infinite maturity
as expiration gets closer, what happens to the value of a call option?
decreases
if the call has a lower exercise price, what happens to the value of the call option?
the call option is worth more - the lower the strike the higher the cost of the call
if a call has a lower strike and is selling at a lower price, you can long that call and sell at the higher price with the higher strike (risk free profit)
if there is high interest, volatility and extended time to expiration, how is the value of the call impacted?
higher value of call
if there is a high dividend paid, how is the value of the call impacted?
lower value of call
why does the payment of a dividend decrease the value of the call?
because it decreases the value of the stock
Call = S - X
which is more valuable a EU or a US call option?
US, option to exercise early i.e. before a dividend/call value decrease
What might be a reason for not exercising a US call option early?
call value = intrinsic value + time value
when you exercise you only gain intrinsic value, might be worth waiting as stock price has unlimited upside potential.
how do calls save you money?
gives you the right but not the obligation to buy, can invest money and earn interest instead, the higher the interest rate the higher the value of the call - because you can earn higher levels on interest on money you didn’t spend.
why are calls worth more when there is a higher level of volatility?
- no downside risk
- higher risk increases the chance that the call will be in the money
what is the absolute minimum value of a put?
zero
if a put is trading for more than it’s intrinsic value, what is the cause of this? what increases this feature?
time/speculative value
The longer the time to expiry the larger the time value
what’s the absolute max value for a put? how do EU and US options differ?
stock price
- EU= PV(S)
- US= (S)
what is the value of a put at expiration? does this apply to US and EU options?
put = max(0, X-S)
Yes at expiry EU don’t need PV valuation
Two put options with exactly the same features differ only in time to expiry, which one will have greater time value?
the one with a longer time to expiry, time value decays closer to expiration
when is time value maximised/minimised for a put option?
max - at the money
min- deep in/out of the money
how does a closer expiration date affect the overall value of the put? for US
a US put is worth less when expiration is closer
how does the exercise price impact the value of a put?
the higher the exercise price the more valuable the put
put = X -S
how do differences in exercise price impact call and put prices? assume they are the same in all other aspects
- the difference in call prices will be less than or equal to the difference in exercise prices
- difference in put price will not be greater than the difference in exercise prices
How do dividends affect put value?
paid dividends decrease stock value and therefore increase put value
P = X -S
how does a dividend payment affect the likelihood of early exercise of a put option?
it decreases it, as it decreases stock value and therefore makes the put worth more
is an EU put worth less than a US put?
yes, but not always due to dividends and unlimited upside potential of stock
what are the benefits of a put over a call option?
- there is a price floor for stocks
- dividends have a good effect on the value of puts
how does interest rates affect the value of puts? explain
higher i = lower put value
puts delay sale of stock, you do so at the cost of i
how does volatility impact the value of a put? explain
higher the volatility the higher the value of the put, because there is no downside risk and it’s more likely that the put will become in the money.
which 3 factors are good for the value of a put and which one factor is bad?
Good - high volatility, high level of time to expiration, high level of dividends
Bad- high interest rates
which 3 factors are good for the value of a call and which one factor is bad?
Good - high volatility, high level of time to expiration, high interest rates
Bad- high level of dividends
what is the formula for the put call parity?
P + S = C + PV(X)
if a call is at the money is it worth more or less than a put for the same stock with similar maturity? how would you explain your answer?
It’s worth more
C = P + S - PV(X)
since S=X at the money
C= P + r
you can earn interest on calls
in the real world what are some reasons why the put call parity may not hold?
- risk free rate used
- dividend payments
- bid/ask spread§
can the put call parity be used on US options?
only if options are held to expiration
A friend of yours tells you she holds a call option that is very deep-in-the-money. She tells you she’s going to exercise it now and cash in on her winnings. Is this a wise move to make?
C = intrinsic value + time value
by exercising you receive only intrinsic value (loose time v), by selling call you receive both intrinsic and time value.
A friend of yours tells you he holds a put option that is very deep-in-the-money. He tells you he’s going to exercise it now and cash in on his winnings. Is this a wise move to make?
Put deep in the money - i.e. stock close to $0, time value can be negative in this case as any time left may allow stock to recover - so yes he should exercise
You notice two call options on the market that are costing the same. However, the expiration dates are different. If everything else is the same, how can this be the case?
usually the one with the longer expiration date would be more expensive.
same price can only mean there is no time value - which can only occur when there is no volatility and they are deep out of the money
Your friend is about to offer an American call option on the market. However, she decides to be a little different and set no maturity date for the option. What would be the maximum and minimum value you would pay for this option?
option with no maturity date = stock
Will an option’s time value be greatest when the stock price is near the exercise price, when the option is deep-in-the-money, or deep out-of-the-money?
when the stock price is near the exercise price, any movement will change value of option
in- t value close to 0
out- t value doesn’t exist
Is it possible to have two calls (or puts) similar in all respects, except the exercise price, having the same market price?
yes, when the options are deep in or out of the money
