Option Greeks: DELTA

Delta is a measure of the change in the option's price resulting from a change in the underlying stock price.

Delta is an estimate of how much the theoretical value of an option will change when the price of the underlying stock changes by $1, assuming all other variables are unchanged.

Delta is the only Option Greek that has a different value for Calls and Puts:

• Positive number for Calls (0 to 1)
• Negative number for Puts (-1 to 0)

Positive Delta means that the option's value will increase when the underlying stock price rise, and will decrease when the stock price drop

Negative Delta means that the option's value will increase when the underlying stock price drop, and will decrease when the stock price rise


Delta and the position in the market:

• Long Calls have positive Delta; Short Calls have negative Delta
• Long Puts have negative Delta; Short Puts have positive Delta

When you Long a Calls say at $1.00, with Delta say at 0.10, your option will be $1.10 when the underlying stock rise by $1 (assuming all other variables are unchanged).

When you Short a Calls say at $1.00, with Delta say at 0.10, your option will be $0.90 when the underlying stock rise by $1 (assuming all other variables are unchanged).

It is not so straight forward when you have a Spread, where you have a Short options and a Long options.  Take for example, the N225 Jul10 15500/15750 Call Bear Spread in the diagram below.
Call Bear Spread

N225 Jul10 15500 Call   0.1691
N225 Jul10 15750 Call   0.1215

While both of the Call options (15500 and 15750) are having positive Delta, The Call Bear Spread is having a negative Delta.  This is because in Call Bear Spread, you Short 15500 Call and Long 15750 Call.  The Short 15500 Call will have negative Delta and the Long 15750 Call will have positive Delta.

-0.1691 + 0.1215  = -0.0476

Thus, the Call Bear Spread is in fact having a negative Delta of 0.0476, as indicated in the Quote Panel above.  The Call Bear Spread position will gain 0.0476 value if the underlying stock price (N225) drop by 1 point (assuming all other variables are unchanged).

Option Greeks: VEGA

Since my main trading strategy is to sell Out of The Money (OTM) Credit Spread, as specified in my Trading Plan, the second Greek that I want to talk about is Vega.

OTM Options contains only Extrinsic Value.  There are 4 factors that determine Extrinsic Value:

1. Time left to expiration (Theta)
2. Volatility of the underlying stock (Vega)
3. Changes in interest rate (Rho)
4. Dividends of the underlying stock

Besides Theta, Vega is the second greatest influence on Extrinsic Value.  Interest rate and dividend are relatively insignificant.

Vega is an estimate of how much the theoretical value of an option will change when Implied Volatility (IV) changes 1%.  An increase in IV will increase an option's price, a decrease of IV would decrease an option's price.

Vega is expressed as a positive number in Option Chain.  And there is only 1 Vega value for both Calls and Puts at the same Strike Price.  See image below.

Thus, a 1% increase in IV would increase both the Calls and Puts option by the Vega value.  While all Calls and Puts has positive Vega, your position can have either negative or positive Vega.

Vega and the position in the market:

• Long Calls and Long Puts always have positive Vega
• Short Calls and Short Puts always have negative Vega

When you Long an option (Calls or Puts) say at $1.00, with Vega say at 0.10, your option will be $1.10 when IV increase by 1% (assuming there is no move in the stock price and Theta is 0). 

When you Short an option (Calls or Puts) say at $1.00, with Vega say at 0.10, your option will be $1.10 when IV increase by 1% (assuming there is no move in the stock price and Theta is 0).  While the option price increase by 0.10, your Short position actually lose value by 0.10.  That is the reason why Short Calls and Short Puts always have negative Vega.

When you have a Spread, you have both a Short options and a Long options.  Take for example, the N225 May08'14 +16250 -16000 Call Bear Spread in the diagram below.

                                               Vega

N225 Jun12'14 16000 Call    12.7140

N225 Jun12'14 16250 Call    10.1607

While both of the Call options (16000 and 16250) are having positive Vega, the Call Bear Spread is having a negative Vega.  This is because in Call Bear Spread, you Short 16000 Call and Long 16250 Call.  The Short 16000 Call will have a negative Vega and the Long 16250 Call will have positive Vega.

-12.7140 + 10.1607 = -2.5533

Thus, the Call Bear Spread is in fact having a negative Vega of -2.5533, as indicated in the Quote Panel above.  The Call Bear Spread position will lose 2.5533 value if IV increase by 1% (assuming there is no move in the stock price and Theta is 0). 

Let's put both Theta and Vega together to see the impact to this Call Bear Spread.  

• Vega is -2.5533
• Theta is  0.8185 

IV increase by 1%

If IV increase by 1%, the Call Bear Spread will lose 1.7348 value after 1 day (assuming there is no move in the stock price).

• -2.5533 + 0.8185 = -1.7348

IV decrease by 1%

If IV decrease by 1%, the Call Bear Spread will gain 3.3718 value after 1 day (assuming there is no move in the stock price).

• 2.5533 + 0.8185 = 3.3718

Therefore, there is an advantage to sell Credit Spread when the IV is high.  So, when IV drop from the high, the Credit Spread will gain value from both Vega and Theta.  However, if you sell Credit Spread when the IV is low, the increase IV will make the Credit Spread lose more value from Vega than the value gained from Theta.

Option Greeks: THETA

Since my main trading strategy is to sell Credit Spread, I will start with Theta, one of the Option Greeks.

Theta, a.k.a. time decay, is an estimate of how much the theoretical value of an option will decreases each day, assuming there is no move in either the stock price or volatility.

As mentioned in my previous post Selling Options, Time Decay is an unique feature in Options (not in Stock, Futures, Forex, etc).  All Options lose time value every day.  It loses time value at a faster rate as you get closer to the expiry date.

Theta is expressed as a negative number in Option Chain.  And there is only 1 Theta value for both Calls and Puts at the same Strike Price.  See image below.

While all Calls and Puts has negative Theta (they lose value each day), your position can have either negative or positive Theta.

Theta and the position in the market:

• Long Calls and Long Puts always have negative Theta
• Short Calls and Short Puts always have positive Theta

When you Long an option (Calls or Puts) say at $1.00, with Theta say at -0.10, your option will be $0.90 after 1 day (assuming there is no move in either the stock price or volatility).  Your Long position lose value by 0.10.  Thus, Long Calls and Long Puts always have negative Theta.  Remember all options lose time value very day.

When you Short an option (Calls or Puts) say at $1.00, with Theta say at -0.10, your option will be $0.90 after 1 day (assuming there is no move in either the stock price or volatility).  While the option price lose -0.10, your Short position actually gain value by 0.10.  That is the reason why Short Calls and Short Puts always have positive Theta.

It is not so straight forward when you have a Spread, where you have a Short options and a Long options.  Take for example, the N225 Jun12'14 +17500 -17250 Call Bear Spread in the diagram below.

N225 Jun12'14 17250 Call   -1.8672
N225 Jun12'14 17500 Call   -1.5954

While both of the Call options (17250 and 17500) are having negative Theta, The Call Bear Spread is having a positive Theta.  This is because in Call Bear Spread you Short 17250 Call and Long 17500 Call.  The Short 17250 Call will have positive Theta and the Long 17500 Call will have negative Theta.

+1.8672 - 1.5954 = 0.2718

Thus, the Call Bear Spread is in fact having a positive Theta of 0.2718, as indicated in the Quote Panel above.  The Call Bear Spread position will gain 0.2718 value after 1 day (assuming there is no move in either the stock price or volatility).

For selling vertical spread (credit spread), we will always have positive Theta.  Our vertical spread (credit spread) will gain value slowly each day.