Option Greeks

[srinu2singaraju]

Hi David,

I have attached an excel sheet on option greeks. Please let me know if any thing is wrong in that sheet.
Thanks in advance

srinivas

 

[liordp]

Hi srinivas

According to My understanding (and I'm not an expert at all ....) It seems to me that the time value is not negative all the time, for example if I sell a Put option with a short term maturity I will enjoy the depreciation of time so the impact can be possitive

Regard Vega dont u think that if i have a long position on put option higher volatility will improve my position because the probability to excercise ITM get higher and there is no cost to excrcise OTM or deep OTM

Regarding the negative Rho of short put option something look to me suspicious but i am not sure

hope that what i said make a little sense but again i am not sure
have a nice day

 

[srinu2singaraju]

Hi Convexity,

Thanks for your inputs.

Regarding the time value:- It can be negative. The seller of the option will enjoy the benefit of negative time value at the same time buyer will lose.
This is what my understanding.

For the rest of the things I am waiting for David’s reply.

Good day.

 

[David Harper CFA FRM]

Hi srinivas,

I edited and attached the XLS (please see below). Re: time to maturity, most of those are too conditional for universal increase/decrease.

For the Greeks, i inserted a percentage Greek which refers to the pure Greek partial first derivative, the measure without units. So, the long is then simply 1*percentage Greek and short is -1*percentage Greek. This is simply to parse out the potential confusion between meaning of long/short. So, for example, both gamma and vega are always positive (+), as the assigned Hull says and shows, but this really means "the unitless gamma and vega are always positive"
... then a short position has a negative position gamma; e.g., short 100 options of +3 gamma each has a negative position gamma = -100 quantity * +3 percentage Gamma = -300 position Gamma. See my point? the percentage Gamma is always (+), so the long position is always position positive but the short position is position negative.

... and I agree with everything Convexity says: I have "either" for all the thetas. If you look at the Greek PUT worksheets @
http://www.bionicturtle.com/premium/spreadsheet/4.b.7_greeks_put_option/
... it is mathematically not difficult to produce positive thetas. You will notice that even my default assumptions produces some positive slightly thetas at longer terms.

And this is true also; "Regard Vega dont u think that if i have a long position on put option higher volatility will improve my position because the probability to excercise ITM get higher and there is no cost to excrcise OTM or deep OTM" ... long positions in options (call or put) are long volatility

And this: "Regarding the negative Rho of short put option something look to me suspicious but i am not sure" is (IMO) conceptually tricky but correct, also:
percentage Rho of put option is negative, therefore
position rho of short option = negative quantity * negative % rho = positive position Rho

thanks Convexity, i think your observations are spot-on!

David

 

[srinu2singaraju]

Thanks David. Great explanation.
Now, I am clear on the concept of greeks. Your edited excel sheet is very good, no confusions....
I am happy...Thanks once again for your time.

Regards,
srinivas

 

[skoh]

Hi David,

In L1.T4. Valuation & Risk Models,
Option Greeks

For question 8.5, why does Rho (put) = -K*T*exp(-rT)*N(-d2) ? I am kind of confused by the computation of this formula, I mean like why -K?

Thanks in advance!

 

[David Harper CFA FRM]

Hi skoh, like the other Greeks (delta, vega, theta), it's the first partial derivative of the BSM, dp/dr. (I don't think it's difficult to retrieve, intermediate calculus, but i'm crunching on T6 notes today...). If you just want some intuition around the direction, then the minimum value (lower bound) formulas I find helpful:

• c = S - K*exp(-rT); lower bound of call. Notice that an increase in (r) tends to increase (c), which is consistent with rho as positive for European calls; i.e., dc/dr is positive
• p = K*exp(-rT) - S; lower bound of put. Notice that an increase in (r) tends to decrease (p), consistent with rho as negative for Euro puts; i.e., dp/dr tends to be negative. Using these does not get you to the dp/dr, don't get me wrong, but I think they are handy when you just want to recall the directional impact (higher rate --> higher call, lower put). Hope that helps,

 

[skoh]

I got it.Thanks David!