relationship between delta, theta, and gamma
- Thread starter ajsa
- Start date
Hi asja,
Right, theta is almost always negative; i.e., the option is losing money as "time marches on"
As that relationship follows directly from the Black-Scholes PDE, I don't have an intuition for it...
FYI, I did build a learning XLS @
http://www.bionicturtle.com/premium/spreadsheet/4.b.10_delta_theta_gamma_hull_17.7/
if you scroll over to column T, you'll see where I illustrated the equality...
if the delta = 0, then you have the inverse relationship between theta and gamma.
(to me, what complicates an attempt to inuit this is the non-intuive nature of theta-vs-time: yes, it's negative, but it may dip, etc ... if not for theta's strangeness, then the intuition would follow directly from the delta-vs-time plot as gamma is the slope of the tangent..)
...or, maybe there is an intuition and I am not aware...
David
Right, theta is almost always negative; i.e., the option is losing money as "time marches on"
As that relationship follows directly from the Black-Scholes PDE, I don't have an intuition for it...
FYI, I did build a learning XLS @
http://www.bionicturtle.com/premium/spreadsheet/4.b.10_delta_theta_gamma_hull_17.7/
if you scroll over to column T, you'll see where I illustrated the equality...
if the delta = 0, then you have the inverse relationship between theta and gamma.
(to me, what complicates an attempt to inuit this is the non-intuive nature of theta-vs-time: yes, it's negative, but it may dip, etc ... if not for theta's strangeness, then the intuition would follow directly from the delta-vs-time plot as gamma is the slope of the tangent..)
...or, maybe there is an intuition and I am not aware...
David
Hi asja - Hull is (i think) just expressing the mathematical truth of the relationship...it would be more natural indeed for him to say "if theta is large and neg then gamma tends to be large and positive" i.e., as gamma is always positive for a long call/put option...
but, on the other hand, this can apply to a short position ... but this is why I like Carol Alexander's terminology; e.g.,
position greek = percentage greek * quantity of options
so when Hull shows, e.g., -3000 gamma , that is not a "percentage" gamma as gamma is always > 0
rather, that means: -3000 position gamma = + percentage (per option) gamma of 0.3 * -10,000 options(negative for the short position)
so, it's a long way of saying percentage theta (ie.., per option) is almost always neg and percentage gamma is always positive, but for a SHORT position, multiply by negative quantity, and you've got a position that is positive position theta and negative position gamma...
it's the position greeks we use to achieve delta or gamma neutrality
David
but, on the other hand, this can apply to a short position ... but this is why I like Carol Alexander's terminology; e.g.,
position greek = percentage greek * quantity of options
so when Hull shows, e.g., -3000 gamma , that is not a "percentage" gamma as gamma is always > 0
rather, that means: -3000 position gamma = + percentage (per option) gamma of 0.3 * -10,000 options(negative for the short position)
so, it's a long way of saying percentage theta (ie.., per option) is almost always neg and percentage gamma is always positive, but for a SHORT position, multiply by negative quantity, and you've got a position that is positive position theta and negative position gamma...
it's the position greeks we use to achieve delta or gamma neutrality
David
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