Deltas

Correct me if i'm wrong.

For the Call side, if delta is 0.2, if the underlying price increases by $1, the option price increases by 0.2 (20 cents). If the underlying price decreases by $1, the option price decrease by 0.2 (20 cents)

On the Put side, delta always have a minus sign. Assuming delta of 0.3, if the underlying price decreases by $1, the option decrease by 0.3 (30 cents). If the underlying price increases by $1, the option price increases by 0.3 (30 cents)

 

Correct for Call's incorrect for Puts.
The sign of the delta provides the clue.

 

So for Put side, i got it back to front? If underlying price go up by $1, the option price reduce by the delta stated?

 

Correct!

 

In your first example the call delta of .20 is called 20 Delta. It is like being long 20 shares of the underlying. Long one 20 delta call and short 20 shares gives you a delta neutral position. Long volatility.

 

Delta carries the weight of that (delta) number of shares and therefore indeed Delta = 20 (often shown as 0.20) will gain as much as 20 shares. And $1/share would make it the $20 profit as you pointed out.

TIP of the Day:
negative Option Delta = Number of shares you’d need to hedge/offset that option (or option combo).

 

Delta is the change in the option price when the price of the underlying changes by $1.

Beware:
Some textbooks additionally interpret abs(Delta) as a proxy for probability that the option will expire in-the-money.
This is mathematically wrong.
That wrong interpretation is unfortunately used even by wikipedia: https://en.wikipedia.org/wiki/Greeks_(finance)#As_a_proxy_for_probability

 

Be cautious about focusing *too* much on delta. Other Greeks, namely vega and theta, have substantial impact in option pricing

 

Eliminate unwanted delta. Isolate the other 1st and 2nd order greeks to simplify your risk.

 

You may want to use the average delta over the move in the stock.
After a stock moves the ending delta will be different from the starting delta.
The ending delta is the gamma times the stock price change plus the call delta.

endingDelta=gamma*stockChange+delta
averageDelta=average(endingDelta,startingDelta)

The new trade price is the trade price plus the average delta times the stock price change.

newOptionPrice=averageDelta*stockChange+tradePrice`

Here's an example:


If ZS stock goes from $128.53 to $127.53, you can estimate the new call value and new put value by using the average deltas, 0.9187 and -0.0813, not the starting deltas 0.9218 and -0.0782, times the change in the stock price.