Greek video for option pricing and trading

(Last Updated On: August 24, 2015)

Greek video for option pricing and trading

A series of videos for newbies understand all this

Call options range between 0 -1.0 put option range is between -1.0 to 0.

Delta on call option is 0.35 so for every $1.00 change in stock, there is a $0.35 change in the options.

Stock at $20, call option=$2. Change In stock to $21 call options should go up $2.35.

Put option delta is -0.65, $1.00 = -%0.65 decrease in put option, if stock is $20, put option is $2, if stock goes up to $21, put option goes to $1.35


Supplied example:

stock (S) = 10, K= 10, volatility=30%, r=4%,T=1,div yield=0.

Black Scholes=$1.38


Delta = N(d1) (normdist(d1)) or normdist(.28)

Plot: call options vs stock price so delta is slope to the tangent line of this curve

Plot of DELTA of call option vs stock price. This asymptotic to 1.0 (never will be 1.0) which is more in the money. As it approaches 0, it is out of the money.

Knowing delta means you can set up a hedge:

SHORT # of call options=100 <- same as writing 100 options

If you multiply the 100 by .61 delta, you could a LONG # of share of 61. This becomes a riskless hedge in a moment of time. For long, 61*$10/share=$612 value of long shares.

Short # of call options is 100 * 1.38 or value of short options is $138.

Portfolio (stock – options) = $612-$138=$474

For trading, new stock price drops to $9. You would lose $1 per share. Hedge LONG # of share =61 but value of long shares $63 (unhedged). Value of short options is $54. You short those so you profit. Hedge value is $8. Option_delta.xls

More stock option Greeks



Volatility=30% (annualized)


T=1 (expires in 1 year)

Div yield=0

Black Scholes=$13.75

Plot of call option vs time to expire

Non-linear Plot call option vs stock price but option goes up since you are in the money.


Delta = change in options price with respect to stock price

Greeks are first derivative. These measure sensitivity of price change in options.

Delta is 0.6, if stock price changes by small amount, option price will change based on amount of delta (or 60%)

Plot could be DELTA of call option vs time to expire

Plot DELTA of call option vs stock price: As stock price increases delta increases (which is bounded by 0 to 1), option price is more in the money such that delta converges to 1. As stock price decrease,  options become progressively out of the money as delta decreases.

Gamma is second derivative. Gamma (or first derivative of delta) is change in delta with respect to: change in stock in price

In plot of Gamma of call option vs stock price where delta will peak when at the money. This is when delta is changing the fastest when was steepest at the money. The delta will converge to 1 where it becomes more stable.


Vega is change in options price with respect to change in volatility. In plot of vega of call option vs stock price, it will peak at the money.

There are more including Theta for time decay

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