# Options traders: How is delta determined?

I get what delta is, the change in the price of the option given a change in the price of the underlying, but how is it determined?

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It’s the first derivative of the option price

you can google the formula if you want

ltlurker -

It’s the first derivative of the option price

you can google the formula if you want

LOL, you’re just saying what the definition of delta is. That by no means explains how it’s determined. Of course it is the rate of change of the price of the option relative to the rate of change to the underlying.

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ABCTT_GROUNDnLB -
ltlurker -

It’s the first derivative of the option price

you can google the formula if you want

LOL, you’re just saying what the definition of delta is. That by no means explains how it’s determined. Of course it is the rate of change of the price of the option relative to the rate of change to the underlying.

You clearly don’t know who you’re taking to, lol.

He’s asking how it’s determined and I’m telling him it’s the first derivative of the option value, which is exactly what it is and how it is calculated.  I don’t know what calculus he understands. He can easily look the formula up.  If he doesn’t understand it he can come back and I’ll teach him.

ltlurker -
ABCTT_GROUNDnLB -
ltlurker -

It’s the first derivative of the option price

you can google the formula if you want

LOL, you’re just saying what the definition of delta is. That by no means explains how it’s determined. Of course it is the rate of change of the price of the option relative to the rate of change to the underlying.

You clearly don’t know who you’re taking to, lol.

He’s asking how it’s determined and I’m telling him it’s the first derivative of the option value, which is exactly what it is and how it is calculated.  I don’t know what calculus he understands. He can easily look the formula up.  If he doesn’t understand it he can come back and I’ll teach him.

You either have no understanding of calculus or the English language.

Literally the first thing he says is knows what delta is. Then you go on to tell him (poorly) what it is.

A statement like “the first derivative of the option value” doesn’t even properly describe delta, since it’s an incomplete statement. While it is true that every option has a first derivative in relation to the underlying price (delta), it also has a first derivative relating to other factors like, length to expiry (beta).

Then, for what he actually wants to know, you just say “google it”.

Brilliant champ.

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You'll are sleeping on the camel toes

nek -

I get what delta is, the change in the price of the option given a change in the price of the underlying, but how is it determined?

Typically it's determined by bumping spot and revaluing.

Whoever said "Google the formula", there isn't "a" formula. I guess you mean black scholes but you don't know he's using that model; the vast majority of pricing is not done BS.

An easy approximation is that is the probability of being in the money, so for example if there's 20% chance of being ITM, your delta is about 20% of the underlying equivalent. Doesn't hold with skew.

Also lol@ "you must not know who you're talking to".

Its determined by recalcing the price of the option after the stock price has moved. The stock price drives the option price.

Dont let other explanations overcomplicated things....

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ABCTT_GROUNDnLB -
ltlurker -
ABCTT_GROUNDnLB -
ltlurker -

It’s the first derivative of the option price

you can google the formula if you want

LOL, you’re just saying what the definition of delta is. That by no means explains how it’s determined. Of course it is the rate of change of the price of the option relative to the rate of change to the underlying.

You clearly don’t know who you’re taking to, lol.

He’s asking how it’s determined and I’m telling him it’s the first derivative of the option value, which is exactly what it is and how it is calculated.  I don’t know what calculus he understands. He can easily look the formula up.  If he doesn’t understand it he can come back and I’ll teach him.

You either have no understanding of calculus or the English language.

Literally the first thing he says is knows what delta is. Then you go on to tell him (poorly) what it is.

A statement like “the first derivative of the option value” doesn’t even properly describe delta, since it’s an incomplete statement. While it is true that every option has a first derivative in relation to the underlying price (delta), it also has a first derivative relating to other factors like, length to expiry (beta).

Then, for what he actually wants to know, you just say “google it”.

Brilliant champ.

First derivative of options price with relation to time to expiration is theta not beta.  Options greeks don't usually beta as a label.

Look up blacke scholes model op.

BailmeOut -
ABCTT_GROUNDnLB -
ltlurker -
ABCTT_GROUNDnLB -
ltlurker -

It’s the first derivative of the option price

you can google the formula if you want

LOL, you’re just saying what the definition of delta is. That by no means explains how it’s determined. Of course it is the rate of change of the price of the option relative to the rate of change to the underlying.

You clearly don’t know who you’re taking to, lol.

He’s asking how it’s determined and I’m telling him it’s the first derivative of the option value, which is exactly what it is and how it is calculated.  I don’t know what calculus he understands. He can easily look the formula up.  If he doesn’t understand it he can come back and I’ll teach him.

You either have no understanding of calculus or the English language.

Literally the first thing he says is knows what delta is. Then you go on to tell him (poorly) what it is.

A statement like “the first derivative of the option value” doesn’t even properly describe delta, since it’s an incomplete statement. While it is true that every option has a first derivative in relation to the underlying price (delta), it also has a first derivative relating to other factors like, length to expiry (beta).

Then, for what he actually wants to know, you just say “google it”.

Brilliant champ.

First derivative of options price with relation to time to expiration is theta not beta.  Options greeks don't usually beta as a label.

Look up blacke scholes model op.

Yes, slip of the mind. Beta addresses the volatility premium. Good catch.

Beta is usually to define how much a stock moves with broad market.  Not sure what you are refering to.  Maybe vega?  The change in price vs the change in implied vol?

Chuck Norris determines the Delta.

You're all speaking Greek to me

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ryans -
nek -

I get what delta is, the change in the price of the option given a change in the price of the underlying, but how is it determined?

Typically it's determined by bumping spot and revaluing.

Whoever said "Google the formula", there isn't "a" formula. I guess you mean black scholes but you don't know he's using that model; the vast majority of pricing is not done BS.

An easy approximation is that is the probability of being in the money, so for example if there's 20% chance of being ITM, your delta is about 20% of the underlying equivalent. Doesn't hold with skew.

Also lol@ "you must not know who you're talking to".

You are correct that bs is not commonly used for pricing American options. There are still formulas used to calculate delta in those other models.

bumping the underlying can yield an approximation, but accounting for variations in volatility (for sure), time and rates (possibly) in addition yields a much more accurate number.

asking how it is calculated is obviously a simplistic question, which is why my answer was simplistic.  Regardless of model, delta is still the first derivative of the option price (in relation to the underlying price - since I left out that obvious factor in my original post).

ive written multiple option pricing and risk models for proprietary use and discussed this in other threads.  Hence the comment you obviously don’t know who you’re talking to.

And the first order greeks are delta(price), Theta (time), Vega (vol), Rho (rates).

Psi (dividend) and lambda (percentage price) are also possible, but in practice are not. Dividends don’t change often enough and elasticity is more of a position management.

ltlurker -
ryans -
nek -

I get what delta is, the change in the price of the option given a change in the price of the underlying, but how is it determined?

Typically it's determined by bumping spot and revaluing.

Whoever said "Google the formula", there isn't "a" formula. I guess you mean black scholes but you don't know he's using that model; the vast majority of pricing is not done BS.

An easy approximation is that is the probability of being in the money, so for example if there's 20% chance of being ITM, your delta is about 20% of the underlying equivalent. Doesn't hold with skew.

Also lol@ "you must not know who you're talking to".

You are correct that bs is not commonly used for pricing American options. There are still formulas used to calculate delta in those other models.

bumping the underlying can yield an approximation, but accounting for variations in volatility (for sure), time and rates (possibly) in addition yields a much more accurate number.

asking how it is calculated is obviously a simplistic question, which is why my answer was simplistic.  Regardless of model, delta is still the first derivative of the option price (in relation to the underlying price - since I left out that obvious factor in my original post).

ive written multiple option pricing and risk models for proprietary use and discussed this in other threads.  Hence the comment you obviously don’t know who you’re talking to.

BS isn't used for European options either by anyone serious. Its decades old and doesn't capture skew.

There aren't formulas in all the other models; many are not closed form depending on the payoff

"bumping the underlying can yield an approximation, but accounting for variations in volatility (for sure), time and rates (possibly) in addition yields a much more accurate number."

He asked how it is determined. Bump and reval is how it is determined. There's no need to account for changes in time etc if you're looking at pure delta, and plus your BS formula will not do so; it's a partial deriv with no concept of correlation or backbone.

You were douchey to that guy for no reason. What you said wasn't right and you came back pulling rank while saying lots of wrong stuff.

I wasn’t being douchy nor pulling rank on the OP.  Nothing I’ve  said is wrong either.

youre the one who assumed bs (I only spoke of it in reference to your post)and also the one who assumed  it wasn’t  used still in pricing European options(it is, btw, but not in its 1973 noble prize winning form)

Bump and reval is great for looking at a SINGLE option.  It is computationally expensive in any real world application and a major drawback to Monte Carlo simulations. If you’re a professional and that’s what your software does, you are light years behind me.

i answered his question (the only person to so) in the most direct (and correct) way possible, with an offer to educate him in any further question he has after finding his answer.

Now im being douchy.

ltlurker -

I wasn’t being douchy nor pulling rank on the OP.  Nothing I’ve  said is wrong either.

youre the one who assumed bs (I only spoke of it in reference to your post)and also the one who assumed  it wasn’t  used still in pricing European options(it is, btw, but not in its 1973 noble prize winning form)

Bump and reval is great for looking at a SINGLE option.  It is computationally expensive in any real world application and a major drawback to Monte Carlo simulations. If you’re a professional and that’s what your software does, you are light years behind me.

i answered his question (the only person to so) in the most direct (and correct) way possible, with an offer to educate him in any further question he has after finding his answer.

Now im being douchy.

Either you're talking MC in which case bump and reval is the only appropriate method, or you're taking CF in which case it's not computationally expensive. Either way what you're saying is not right.

You keep throwing stuff out there that doesn't make sense. Seems that you haven't worked for a major firm for a while/ever or you're just very clumsy in your wording today.

I still think "you must not know who you're talking to" is the douchiest thing I've ever seen on here.