Hi all,
With regard to delta, will the delta of an option always underestimate the price effect of decreases in the underlying, and overestimate the price effect of increases in the underlying? I’m just trying to generalize this convexity rule - if it applies equally to calls AND puts is it safe to say this property is inherently “good” for call options and “bad” for put options?
Thx - only a few more weeks of this hell.
Delta is directional exposure. Convexity (gamma) is volatility exposure (delta’s exposure to a change in underlying).
Delta
Whether delta is good or bad depends on 1) the up or down movement of the underlying and 2) whether you are short or long this exposure.
Up Market, Long Call or Short Put -> Long Delta -> “good”
Down Market, Long Call or Short Put -> Long Delta -> “bad”
Up Market, Long Put or Short Call -> Short Delta -> “bad”
Down Market, Long Put or Short Call -> Short Delta -> “good”
Gamma
As you said, convexity is the difference between the delta approximation and the actual price of the option.
For calls, delta underestimates the price increase in up moves and overestimates the loss in down moves. For puts, delta underestimates the price increase in down moves and overestimates the loss in up moves moves.
This is a desirable property for both long calls and puts , however you have to pay a premium.
Whether gamma is good or bad depends on 1) the volatility of the underlying and 2) whether you are short or long this exposure to volatility.
Volatile Market, Long Call or Long Put -> Long Gamma -> “good”
Stagnant Market, Long Call or Long Put -> Long Gamma -> “bad”
Volatile Market, Short Call or Short Put -> Short Gamma -> “bad”
Stagnant Market, Short Call or Short Put -> Short Gamma -> “good”
“For calls, delta underestimates the price increase in up moves and overestimates the loss in down moves. For puts, delta underestimates the price increase in down moves and overestimates the loss in up moves moves.”
Can you explain why this is desirable? I think I’m simply overthinking as I’m usually very comfortable with options material. Assuming a long call position, isn’t underestimating price increase in up moves seen as a negative from my vantage point if I’m the call holder?
you dont want to overhedge
Its very similar to bonds. The option price - underlying relationship of a long call (or put) option is convex (a curve) while delta is a straight line approximation of the the price (a tangent line). For extreme movements in either direction, the curve is much higher than the straight line. In other words, the actual price is much higher than the approximated price using a straight line. This is desirable because, the more convex the relationship - the more the actual price exceeds the delta approximated price … for a long call, you benefit alot from up moves in the underlying (increases more than a straight line), but if the market moves down, the option price decreases at a lesser rate than a straight line.
Howdy.
For puts, yes.
For calls, it’s the opposite.
(Draw two pictures and it’ll be obvious.)
these last two drilled it home, thanks gents
My pleasure.
(As a general rule, I like drawing pictures.)
The graphs of call and put both exhibit positive convexity similar to option-free bonds
The delta underestimate the true value of both call and put.
Call option: Overestimate the impact of decline in stock price, and underestimate the impact of higher stock price
Put option: Overestimate the impact of higher stock price and underestimate the impact of lower stock price.
delta is the first derivative of an option wrt stock price. gamma is the second derivative of an option wrt stock price. gamma is always positive. now let’s look at how delta works. assume we are long.
for calls, if stock price goes down, call price goes down (first derivative is positive - s goes down, call goes down). if you don’t add gamma to this the delta is overestimating the loss. if stock prices goes up, the call value goes up as well, if you don’t add the gamma then it underestimates the gain
for puts, if stock price goes down, put prices goes up (delta of put is negative). without the gamma it underestimates the increase. if stock price goes up, put decreases in value but without the positive gamma we are overestimating the loss.
this comes from the taylor series saying the value of a function at a specific point is an infinite sum of the terms calculated from the values of the function’s derivatives at that point. the function is the value of the option, the points are the values of the stock. delta is only using the first derivative. the gamma term is the second
I’m pretty hopeless with these questions. They are either going to ask the tricky version or the straight forward one. If it’s the straight forward ill put that answer. If it’s not, I’ll guess. I think the key is not to waste time on these problems.
Gross!
For those of you without a degree in mathematics (or engineering or physics): draw a picture! It will be obvious; trust me.
S2000 do you have an example of these pictures that explain delta?
Let me figure out how to get pictures in here and I’ll get back to you.
would be amazing thanks.
Here you go:
http://www.s2ki.com/s2000/topic/1024332-puts-and-calls/
It’s a roundabout way to get you the pictures, but it works.
Man . . . I go to all the trouble of posting pictures and nobody looks at them.
Thanks Bay Street, I found it helpful!
I’d look at it S2000 but it requires sign up
Delta call and delta put graphs were part of LII. I actually had to go back and revisit those. Yes, the link up there requires a signup, but many thanks, S2000magician. (I guess you don’t need to understand 1st and 2nd derivatives to answer a few questions on this.)