Greeks and price. Question.

[raf_bcn]

Hi

I want to make a question about Greeks. I think it is basic stuff but I have doubts.
I want to know if the change in the option's price is completly explained by the greeks.

If we take two otm consecutives strikes for SPY we can see that maybe the greeks doesn't explain the change .
Now Spy is at 246,50. See the difference in premium between two otm Spy Oct. calls, 248 and 249 .
248 call is 2,04 and 249 call is 1,55 so a 0,49 difference, 24%

Now imagine Spy moves 1 dllar up today in a few hours, so no change in volatility. The strike 249 will be 1 dollar closer to ITM. In fact will be where now is the 248 strike.
So we can suppose the 249 premium will be 2,04 that's an increase of 0,49 from 1,55 to 2,04.

So Spy goes up 1 dollar , 249 strike goes 0,49 up.

But the 249 strike greeks are, as you can see in the attached image 0,34 delta -0,03 theta 0,32 vega 0,05 gamma

I would like to ask What greek explains the change in premium value of 0,49. Maybe it is missing a greek.

Thank you

 

[stevegee58]

Option prices are driven by supply and demand. If demand is higher it drives up implied volatility which is one of the inputs to the option pricing formula be it Black Scholes or whatever. Higher IV = higher option price.
The greeks are derived from option prices, they don't drive price.

 

[Martinghoul]

When you say "no change in volatility", what do you mean precisely? Do you expect the vol of the 249 strike after the SPY moves up $1 to be the same as the vol of the 248 strike before the move?

I am reasonably sure that if you answer this question, you'll be able to explain whatever you need to explain.

 

[stevegee58]

I should clarify that if you calculate the IV *for each strike* you'll find the resulting curve is very bumpy. It reflects the supply and demand of the various strikes at that moment of time.
There isn't just 1 "volatility"

 

[raf_bcn]

Thank you for the responses

@stevegee58 @Martinghoul

Yes I assume that a $ 1 incresase will not chance volatility, since is only a 0,4% upside increase, what i think could cause a decrease in iv.
Correct me please.
If this increase is in 6 hours I assume The iv wouldn't change, or at least wouldn't explain the difference in premium.

Do you think a 0,4% increase in Spy in a day would cause an increment in volatility that could explain 0,15 in premium value?
Do you know which would have to be the new iv to explain that change in premium ? I don't know how to calculate that.

thank you.

 

[cdcaveman]

The true explanation of an options price is based on the demand and supply of the market... People forget that all the time when they're looking at all these seemingly complex derivatives... The Greeks can give you a little bit more dimension on what might be driving demand.. if Delta is. The underlying is driving the price. If implieds go up then a demand for premium is going up... But Delta Vega and theta are dominating forces.. rho and others are almost transient terms on small portfolios or single positions

 

[TradingDemystified]

Yes I assume that a $ 1 incresase will not chance volatility, since is only a 0,4% upside increase

Implied Volatility is a very difficult concept to grasp (at least it is for me) so I might be wrong here but the way I see it is that IV is not DIRECTLY related to its underlying price but rather to PERCEPTION of risk (i.e. a fear gauge) that is reflected in Option Premiums (Premia?) all along and across strikes and expirations, so you can't just evaluate the change in the underlying to determine what its IV will do. Having said that, many of IV's intricacies and nuances can be identified when you look at the Volatility Skew for the specific expiration. You can notice that different call strikes have different levels of IV, one way to interpret this (I know this isn't strictly by the book but rather based on years of experience) is that as the underlying price keeps going higher those are the futures values that the ATM volatility will have so the whole curve would be shifted down, making the IV as a whole for that underlying lower.
TL;dr: Even though the up move may be small, the change in IV may be larger relative to that move because it is the PERCEPTION of risk that is reflected in option prices and their IV

 

[JackRab]

Yes I assume that a $ 1 incresase will not chance volatility, since is only a 0,4% upside increase, what i think could cause a decrease in iv..

The IV in the strike, both the 248 and 249 will change because it basically rides up the vol curve. If you look at the current IV, the 248 is about 0.40 higher than the 249. When we move up 1 point, it means that the 249 vol will be the current 248 vol (all else stays equal). Vega is about 30 cents? So there will be a gain due to delta of about 34 + gain due to vega of about 12 = 46... delta gain is actually a bit more because the average delta is higher due to gamma.

The fun thing with options is that it's never as straightforward as you think...

 

[Martinghoul]

Thank you for the responses

@stevegee58 @Martinghoul

Yes I assume that a $ 1 incresase will not chance volatility, since is only a 0,4% upside increase, what i think could cause a decrease in iv.
Correct me please.
If this increase is in 6 hours I assume The iv wouldn't change, or at least wouldn't explain the difference in premium.

Do you think a 0,4% increase in Spy in a day would cause an increment in volatility that could explain 0,15 in premium value?
Do you know which would have to be the new iv to explain that change in premium ? I don't know how to calculate that.

thank you.

It's actually rather simple and you don't need to worry about all the mystical supply/demand stuff...

Delta and gamma will give you an approximation of the change in the value of the option for a given change in the underlying. Roughly, assuming all else equal, for a $1 move in SPY, you can approximate the change in the option's value by delta * $1 + 0.5 * gamma * ($1^2) (those are the terms of the Taylor series that count).

The key point here, as I mentioned previously, is that the approximation above assumes nothing about the changes in volatility. In your calculation, where you expect the 249 strike to be where the 248 strike used to be, you are making an implicit assumption about the change in the strike vols. If you take that into account by adding vega * change in vol to the approximation above, you'll arrive at a number which is going to be mighty close to the 0.49 that you were expecting.

 

[ironchef]

If you have some technical or math training, you will understand the following:

Delta is the first derivative and gamma the second. Together these two greeks should almost account for the theoretical outcome. If you are mathematically inclined, you can add third derivative... and get the exact theoretical answer. Of course IV will change when price of the underlying changes and mess up your theoretical answer.