802 wrote:Am I correct to say that the Greeks (specifically Delta) suggest that price of option will go up/down by the same amount whichever way the stock price goes?

you are right... in this example, if V moves up or down by $1, the option values of the 80 Call and Put will increase or decrease by ~$0.50 ($1 x 0.5) since their deltas are 0.50

802 wrote:If that's the case, can we not just sell both, and just earn some petty cash from Theta?

this means you choose

c) establish both Short 80 Call and Short 80 Put.this is similar to selling a straddle. a Long straddle is Long Call and Long Put of the same strike of the same underlying which expire at the same month. if you recall my earlier description, it was mentioned that you are expecting V to not stay close to $80 but in fact expect V to move away from $80, just that you are not directional bias; ie, you think it could move up or down.

if this is the case, Selling a straddle may not be such a great idea, although, if V does not move sufficiently, this strategy could still be a profitable one. that is, as long as V's price movement stays within the breakeven points.

but let's nonetheless discuss this position from the Greek's perspective...

Short V 80 Call (Delta : - 0.50, Gamma : - 0.07, Theta : +0.04 and Vega : - 0.09)

Short V 80 Put (Delta : +0.50, Gamma : - 0.07, Theta : +0.04 and Vega : -0.09)

Short 80 Call (A) + Short 80 Put (B)Delta of A + Delta of B = - 0.5 + 0.5 = 0

Gamma of A + Gamma of B = -0.07 + -0.07 = -0.14

Theta of A + Theta of B = +0.04 + 0.04 = +0.08

Vega A + Vega B = -0.09 + -0.09 = -0.18

in summary, the new Greeks profile for this option position is as such (Delta= 0, Gamma= -0.14, Theta= +0.08, Vega= -0.18)

Deltawhat has happened is that with a 0 delta, this position becomes very insensitive to V's price movement. whether V moves up or dow, the option value does not change. this position best reflects a trader's intention for V to be stagnant. if the trader is expecting V to move away from $80, then the Delta of this position is not showing that desire.

GammaGamma at -0.14 means that if V rises by $1 dollar, the overall position's Delta will become -0.14 {0+ (-0.14)} and if V drops by $1, the new Delta will be +0.14 {0 - (-0.14)}. these are not desired effects.

what you want is when V rises in value, the option's Delta must gain + delta and not become -ve delta. remember when you Long a Call, it is +ve delta and you want this +ve delta to get to +1.00 delta, which will happen when the underlying rises so much that it makes your Long Call get very deep In-The-Money... but if underlying rises in value, yet the Delta gets smaller or more negative, this option will defeat itself into a losing option.

ThetaTheta is doubled as a result of selling this straddle. very good indeed. with every passing day, this new position yields $8 (100 x 0.08) of premium into the account.

Vega Vega is the amount of change to the option value per 1% increase or decrease in Implied Volatility of the options. if after establishing this short straddle, IV rises by 1%, this new position will lose $18 (100 x $1 x -0.18) and gains $18 if IV drops by 1% (100 x -$1 x -0.18). but IV rise and falls depending on several factors; such as the implied demand or lack of for the options, earnings news, M&A activities, new product launch, etc...

so, does it mean, it is better to be Short Vega (hope that IV will fall) or Long Vega. there is no right or wrong answer here. this is where the "art" of trading options come in.... if one believes that IV will drop off, then, logically, one will choose to Short Vega (which means, open Short option positions) and conversely, if one is expecting a increase in IV, then Long option position (which yields Long Vegas) maybe a considering factor.

yet there is one characteristic about underlying price movement that is intricately tied to IV. there is an inverse relationship. recall when SPX index falls, VIX rises and when SPX rises, VIX falls. similarly, if V's price drop off sharply and quickly, IV of V's options will explode upwards. now, envisage this scenario, V's price drop suddenly and intensely, you should be happy with that Short 80 Call. but in reality, even though directionally correct (Short Call represents non-bullishness outlook). such Short 80 Call can generate significant losses due to -0.09 vegas (Short 80 Call has a -0.09 Vega)

With Short 80 Put, you want V to rise in price and if it actually does, IV of V's options will likely decrease. A Short 80 Put has a -ve Vega which benefits when IV is lower... double winner here...

Hence between a Short Call or a Short Put, all things equal, I prefer a Short Put position.