Option theta and time value

Question

Hello!

I'm trying to get my head round a Schweser mock question (vol 1, exam 2 am question). the question is essentially:

You bought a put 5 months ago, premium = $2.81, strike is $30; share price at the time was $42. If the put's premium has increased to $3.18 from $2.18 now you are closer to expiration which is now 18 days away, what has most likely occurred to prompt this rise in premium? I was torn between the answer of A and B:

A) 'the price of the underlying has decreased to $26.82'

b) 'underlying stock had a negative earnings surprise'

Correct answer is B). I get that the time value of the option is 0 at expiration which is what would be the reason for the premium being $3.18 if the strike is $30 and the underlying $26.82. But I can't get my head around what the formula would be for the answer B to be correct, i.e. you are not at expiration date, the premium is $3.18 and therefore the stock price must be ABOVE $26.82.

would the formula be:

Intrinsic Value = stock - strike - premium

And where is the theta? Is the theta negative? Or positive making the put option more valuable? I'm trying to work out how the stock must be above $26.82 and isn't below this value...

Sorry I appreciate the above is a bit of a jumble

mikey · Answer

An option's premium is made up of:

Intrinsic value: how much it's worth if the option holder exercises their option right now

For call options: Price of underlying asset - Strike price
 	For put options: Strike price - Price of underlying asset

Time value: additional value investors are willing to pay due to the potential upside it has left - because the option could further increase in value before expiration.

Option Premium = Intrinsic Value + Time Value

You're on the right track. If the premium = $3.18, strike = $30, underlying = $26.82 then the put option should be at expiry since it implies time value is 0.

A negative earnings surprise would lower the price of underlying (drives intrinsic value up) as well as increase volatility (drives time value up), so would increase option premium.

Looking at options A and B, it sounds like the kind of question that asks for the "most likely" answer, and means it.

Zee Tan · Answer

Just jumping in on the theta part of your question - theta is the rate of change in the value of an option as time passes, i.e. the time decay of an option.

Whether theta is negative or positive depends on how time (t) is defined:

e.g. If t = 1,2,3... theta is usually negative (value declines as t increases)
 	e.g. If t = 30,29,28... theta is usually positive (value declines as t declines)

Check out this explanation on theta by @sophie here: https://300hours.com/f/cfa/level-2/t/option-theta-is-it-always-negative/