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Calc Option Price


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Calc Option Price

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  #1 (permalink)
 bchip 
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Hi all

I understand there might not be an easy answer to this but hoping
there might be some experience one can share.

I'd like to work out what that option price would be (% wise) if the SPY moved 10 points.
So basically I'm doing a bit of testing on a system and I enter a trade on SPY options.
(eg) I buy at $6 and the market moved 10 points I should then be able to sell at $12 ?

I understand that theres a lot of considerations like the expiry period and volatility at the time, but if I limit it to 2 or 3 weeks expiry in the future, I buy ATM option and the market moves 10 points...
Is there any kind of general rule of thumb that a 10 point should result in a 100% most of the time?

With a very small test, I can see that if the SPY did move
- 15 points up and I owned a call then every time its done a 100% return..
- with a 10 point move 80% of the time it did a 100% return.

Can I expect the SPY futures (on a 2 week expiry, ATM option) to move 100% if it goes in my favour on a call option?

I've taken a sample of 5 trades in the last year and found the following results
(1 option is ATM, the other OTM to compare...seems ATM is better)

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 AllSeeker 
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This is not regarding SPY, I trade my local index options so I would talk about it since no one has yet replied..most people here are future traders so I will take a shot at your question from my noobiesh perspective

You can't define "if underlying moves this much option should move this much" with set number, there are too many variables in that formula, IV and actual supply and demand etc, which you also mention.

You can however, pin down an proximate range for this movement depending on what are different IV values.

For example, in NIFTY options ATM strike, if Nifty moves around 30 points AND IV is in normal range of 17-22, you can expect your option to gain 10-12 points approx, its never an exact even in this case. But just a thumb rule.

If IV range is lot higher than this then option premiums can be much more volatile in gain or loss of premium, we retail traders generally don't pay much attention to it and when price goes sideways, make serious losses and wonder "why premiums vanished so much even though underlying moves only this much", its the IV, which has probably dropped now and silently killing all the gains

What I'm trying to say here is that don't get into that trap.

I hope someone with much more technical explanation comes by too but till then, this will be it.

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 bchip 
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LastDino View Post
This is not regarding SPY, I trade my local index options so I would talk about it since no one has yet replied..most people here are future traders so I will take a shot at your question from my noobiesh perspective

You can't define "if underlying moves this much option should move this much" with set number, there are too many variables in that formula, IV and actual supply and demand etc, which you also mention.

You can however, pin down an proximate range for this movement depending on what are different IV values.

For example, in NIFTY options ATM strike, if Nifty moves around 30 points AND IV is in normal range of 17-22, you can expect your option to gain 10-12 points approx, its never an exact even in this case. But just a thumb rule.

If IV range is lot higher than this then option premiums can be much more volatile in gain or loss of premium, we retail traders generally don't pay much attention to it and when price goes sideways, make serious losses and wonder "why premiums vanished so much even though underlying moves only this much", its the IV, which has probably dropped now and silently killing all the gains

What I'm trying to say here is that don't get into that trap.

I hope someone with much more technical explanation comes by too but till then, this will be it.

Thanks. Yes I understand I wont have an exact formulae but something that help give me an idea.
Pointing out the importance (and risk) of the IV definitely helps, as it means my formulae wont be as simplistic as x% = 10p,
but x% = points + IV will be give me a fair idea if my trading strategy might work or not.

Thank you.

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 SMCJB 
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There are ways to calculate it precisely, and they are called option 'greeks'. If you believe in the Black Scholes model - probably okay for retail traders - not okay for professional market makers - there are even closed form formula's.

First order greeks, explain how the option price changes relative to one of the inputs changing
  • Delta measures the rate of change of the theoretical option value with respect to changes in the underlying asset's price
  • Vega measures the rate of change of the theoretical option value with respect to changes in implied volatility
  • Rho measures the rate of change of the theoretical option value with respect to changes in the risk free interest rate
  • Theta measures the rate of change of the theoretical option value with respect to changes in time to expiration.

So the quick estimation of how much the option will change is Delta * Underlying Price change. Given that ATM options have an approximate delta of 50% and ATM option will move 50% the amount the underlying price moves - if everything else stays constant.

In reality its not that simple. As the option moves in or out of the money the delta changes, as volatility changes the delta changes, as time passes the delta changes.

That leads to Second Order greeks, which explain how a first order greek changes relative to one of the inputs changing. In this case the three important second order greeks effecting delta are
  • Gamma measures the rate of change in the delta with respect to changes in the underlying price.
  • Charm measures the rate of change of delta over the passage of time.
  • Vanna measures the rate of change in the delta with respect to changes in volatility.

Lots of resources out there on this type of stuff

https://en.wikipedia.org/wiki/Greeks_(finance)

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 bchip 
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SMCJB View Post
There are ways to calculate it precisely, and they are called option 'greeks'. If you believe in the Black Scholes model - probably okay for retail traders - not okay for professional market makers - there are even closed form formula's.

First order greeks, explain how the option price changes relative to one of the inputs changing
  • Delta measures the rate of change of the theoretical option value with respect to changes in the underlying asset's price
  • Vega measures the rate of change of the theoretical option value with respect to changes in implied volatility
  • Rho measures the rate of change of the theoretical option value with respect to changes in the risk free interest rate
  • Theta measures the rate of change of the theoretical option value with respect to changes in time to expiration.

So the quick estimation of how much the option will change is Delta * Underlying Price change. Given that ATM options have an approximate delta of 50% and ATM option will move 50% the amount the underlying price moves - if everything else stays constant.

In reality its not that simple. As the option moves in or out of the money the delta changes, as volatility changes the delta changes, as time passes the delta changes.

That leads to Second Order greeks, which explain how a first order greek changes relative to one of the inputs changing. In this case the three important second order greeks effecting delta are
  • Gamma measures the rate of change in the delta with respect to changes in the underlying price.
  • Charm measures the rate of change of delta over the passage of time.
  • Vanna measures the rate of change in the delta with respect to changes in volatility.

Lots of resources out there on this type of stuff

https://en.wikipedia.org/wiki/Greeks_(finance)

Thanks Ive tried the BlackScholes before and can never seem to get it right
Didnt really seem to keep track with the market much.
Things get really complicated if your backtesting with it as well. That's why Im hoping for a simpler solution like
(eg) Delta usually at 50 with ATM, so 50% of 10 point move means it will go up up $5 per premium,
ATM usually trades at (14 day) $9...so usually a 10point would mean 14/9 = 50-70% move
(obviously give or take for a bit of volatility).

Here are my inputs though with the BS Model
BS Model provided by: https://aaronschlegel.me/black-scholes-formula-python.html

If on VISA I have the value of underlying 180, strike 185 call option with a 14 day expiry the BS Model returns a value of 102...
Currently its trading @ $4.15


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 SMCJB 
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You've got 14 years to expiry!

14 days to expiry is either 14/250 = 0.056 years but more probably 14/365 = 0.038 years.

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 bchip 
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SMCJB View Post
You've got 14 years to expiry!

14 days to expiry is either 14/250 = 0.056 years but more probably 14/365 = 0.038 years.


Thanks, that does help.
Answer now comes to around ~ 4.80 which is a lot closer

(considering this is for a european option and theres supply and demand) think it gets pretty close.

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 SMCJB 
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I don't know where the implied vol / how they calculate them but the shape of the skew is strange to me.
Specifically $177.5 at 43%, 180 at 39%, 185 at 40.5%, 190 back down to 39.5%.
They could be based upon last print vs current market which means they could be off a few points.

For what its worth with 180.21, 185, 0.38, 1% and 40.86% I get 3.743

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Mozart2112
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Intrinsic and extrinsic value. At expiration whatever intrinsic value (In the money) there is that's the value of your option.

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