Options trading part 2: delta hedging

You have learned in school, on television, or YouTube how to visualize atoms, protons, neutrons, electrons, etc.

This model is entirely inaccurate, yet we use it because it helps us visualize the specifics of these abstract subjects.

Consider everything in this article to be an oversimplification to assist you with more advanced reading about options trading

Abstract subjects

Options Delta Δ

Every options contract has a delta

between 0 and 1

or 0 and -1

Delta Probability

A call option with a delta of 0.3Δ has an approximately a 30% chance of finishing “in the money” (ITM).

Aput option with a delta of -0.3Δ has an approximately a 30% chance of finishing “in the money” (ITM).

Out the money (OTM) “Delta” example

steeper when it’s “out the money.”

In the money (ITM) “Delta” example

“In the money (ITM)” — delta 1Δ

At the money (ATM) “Delta” example

“At the money” call option: Δ Delta of 0.5
Put option diagram

Our “delta Δ” is 0 when we are out “Out the money.”

Our “delta Δ” is -0.5 when we are out “At the money.”

Our “delta Δ” is -1 when we deeply “In the money.”

Put option Δ Delta

“Call option” contracts always have a positive delta Δ

“Put option” contracts always have a negative delta Δ

Call option — delta Δ

“Out the money” call option contract it’s near 0 Δ

“At the money” call option contract it’s near ~0.5 Δ

“In the money” call option contract it’s near ~1 Δ

The “delta Δ” starts relatively low, close to zero
The “delta Δ” achieves maximum velocity from the “strike price.”
as the option becomes more and “more in the money” and reaches a limiting value of 1
Delta profile put option “At the money” (ATM) -0.5Δ
Delta profile put option “Out of the money” (OTM) ~0Δ
Delta profile “put option” far “in the money” (ITM) -1Δ
Put option “At the money” (ATM) delta -0.5Δ
Put option “At the money” (ATM) delta -1Δ

Delta Δ on the option chain (Deribit example)

If you don’t have an account on Deribit, you can sign up and receive a 10% discount on fees for trading futures & options: https://www.deribit.com/reg-572.9826

Click to zoom in
Click to zoom in
Click to zoom in
Click to zoom in

A call option “in the money” has a “delta Δ” greater than 0.5.

Option contracts that are “out of the money” have lower “delta’s Δ,” while option contracts that are “in the money” have higher “delta’s Δ.”

Trading platform: Delta exchange

If you’re seeking to signup and want a 10% discount

You can use my referral link

https://delta.exchange/?code=rnr

What is Delta Hedging? Δ

The appeal of options trading is the “leverage” they provide.

Since 1 option contract controls 100 shares of the underlying asset, buying a call option contract exposes the gains and losses of 100 shares at a fraction of the price of 100 shares.

That is the “multiplier” (standardized at 100)

amount of options * multiplier = amount of shares5 * 100 = 500 shares
amount of options * multiplier * stock price = notional value5 call options * 100 * 700 = $350 000

How to delta hedge my options contracts?

amount of options * multiplier * delta = amount of shares to sell 5 * 100 * 0.5 = 250 shares 
amount of shares * price = notional value
250 * 700 = $175 000

Earning money with delta-neutral trading with options trading

Delta hedging a call option & making money on it

0.5 * 100 = 50 shares
-50 + 70 = 20 shares or delta 0.2Δ
0.5 – 0.7 = -0.2Δ
-50 (sell shares)
-20 (sell shares)
+20 (buy shares)
+20 (buy shares)
______
-30 shares short
The call option is delta is 0.5Δ which is equal to +50 shares long-30 + 50 = 20 shares long (delta 0.2Δ)

What was the point of doing this?

Deribit positions show the total amount of delta etc

If you don’t have an account on Deribit, you can sign up and receive a 10% discount on fees for trading futures & options: https://www.deribit.com/reg-572.9826

Deribit

Delta value convention

“delta” of a call option falls within a range of 0 to 100 Δ

“delta” of a put option falls within a range of -100 to 0 Δ

The underlying contract (ie spot) always has a delta of 1 or, using this convention, a delta of 100 Δ.

How to delta hedge a put option & earn money

-0.5 * 100 = -50 shares
+50 (buy shares)
______
+50 shares long
The put option is delta is 0.3Δ which is equal to 30 shares short50 - 30 = 20 shares long or delta 0.2Δ
50 - 20 = 30 shares
30 shares and 50 shares short exposure which leaves us to -20 shares short exposure
+50 (buy shares)
-20 (sell shares)
___
+30 shares long
The put option is delta is 0.5Δ which is equal to 50 shares short50 - 30 = 20 shares long or delta 0.2Δ
+50 (buy shares)
-20 (sell shares)
+20 (buy shares)
____
50
The put option is delta is 0.7Δ which is equal to 70 shares short50 - 70 = 20 shares short or delta -0.2Δ

What was the point of doing this?

In this case, I would need to short BTC-perp since my delta is net positive

If you don’t have an account on Deribit, you can sign up and receive a 10% discount on fees for trading futures & options: https://www.deribit.com/reg-572.9826

But that’s for part 3 of the options trading article.

ByBit exchange

ByBit Options (Discount on fees and $100 deposit bonus): https://www.bybit.com/register?affiliate_id=6776&group_id=1653&group_type=1

Trading platform: Delta exchange

If you’re seeking to signup and want a 10% discount

You can use my referral link

https://www.delta.exchange?code=medium

Conclusion

The tail that wags the dog

You can continue reading options trading part 3: Gamma/Curvature risk

Final words

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derivatives trader

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