Delta Hedging Explained: Options Trading Strategies

Summary

This video script offers an insightful introduction to Delta hedging, a strategy used in options trading to minimize risk. Delta measures an option's price sensitivity to the underlying asset's price changes, acting as a sensitivity meter. The script explains positive and negative Deltas, their impact on trading positions, and how to create a delta-neutral portfolio. It further discusses the dynamic nature of Delta, illustrating the need for continuous adjustments in a hedge to maintain neutrality. Examples provided demonstrate the process of dynamic hedging, emphasizing the importance of adjusting positions as market conditions evolve.

Takeaways

• 📈 Delta measures the rate of change in an option's price relative to the price change of the underlying asset.
• 🔍 High Delta indicates a price that is very sensitive to the underlying asset's movements, while a Delta near zero shows minimal sensitivity.
• 📊 Delta can be calculated using the formula: change in option price divided by change in stock price, providing a snapshot of price sensitivity.
• 👆 Instruments with positive Delta, such as long stock or long call, increase in value when the underlying asset's price rises.
• 👇 Negative Delta instruments, like short stock or long put, decrease in value when the underlying asset's price increases.
• 🛡️ Delta hedging is a strategy to minimize risk associated with an option position by offsetting it with an opposing position in the underlying stock.
• 🧩 A delta neutral portfolio has a total Delta of zero, making it insensitive to small changes in the underlying asset's price.
• ⏳ Delta changes over time and with stock price fluctuations, necessitating adjustments to maintain a delta neutral position.
• 📉 Static hedging involves setting up a hedge once and not adjusting it, which can lead to higher potential gains or losses.
• 🔄 Dynamic Delta hedging requires continuous adjustments to the hedge position as market conditions change, resulting in lower potential gains and losses.
• 📚 The example from 'Options, Futures and Other Derivatives' illustrates the process of maintaining a delta neutral portfolio through dynamic hedging over time.

Q & A

What is Delta in the context of options trading?

Delta measures the rate of change in an option's price with respect to the price change of the underlying asset. It's a sensitivity meter that indicates how much the option's price will move for a $1 change in the stock price.

How does a high Delta affect an option's price sensitivity to the underlying asset's movements?

If an option has a high Delta, its price will be very sensitive to the movements of the underlying asset. This means that even small changes in the stock price can lead to significant changes in the option's price.

What is the significance of an instrument having a positive Delta?

An instrument with a positive Delta will increase in price if the underlying asset's price goes up. Examples include owning a stock or buying a call option, where an increase in the stock price results in a profit.

What does a negative Delta imply for an instrument's price movement when the underlying asset's price increases?

A negative Delta implies that the security's price will drop when the underlying asset's price increases. This is typically the case with shorting a stock, shorting a call, or owning a long put.

Can you explain the concept of Delta hedging?

Delta hedging is a strategy used to minimize the risk associated with an option position. It involves taking an offsetting position in the underlying stock to counteract the Delta of the option, aiming to create a delta-neutral portfolio that is insensitive to small changes in the underlying asset's price.

What is the goal of Delta hedging?

The ultimate goal of Delta hedging is to create a delta-neutral portfolio where the total Delta equals zero, meaning the gains and losses from the option position and the underlying stock position offset each other, making the portfolio insensitive to small price changes in the underlying asset.

Why is it necessary to adjust a Delta hedge over time?

A delta-neutral position will only remain neutral for a short period of time because Delta changes over time as the stock price changes or as time to maturity passes. Therefore, adjustments are needed to maintain the delta-neutral status of the portfolio.

What are the two types of Delta hedging mentioned in the script?

The two types of Delta hedging mentioned are static hedging and dynamic hedging. Static hedging involves setting up the hedge once and leaving it, while dynamic hedging involves continuously adjusting the hedge position as market conditions change.

How does the Delta of an option change as the stock price changes?

The Delta of an option changes as the stock price changes in such a way that an in-the-money call option's Delta approaches 1, an at-the-money call option's Delta approaches 0.5, and an out-of-the-money call option's Delta approaches 0.

What is the difference between static and dynamic Delta hedging in terms of risk and return?

Static hedging has a higher upside and downside because the Delta will move away from zero as time passes and the stock price changes. Dynamic hedging, on the other hand, results in lower upside and downside due to continuous adjustments that keep the Delta close to zero, reducing exposure to price changes in the underlying stock.

Can you provide an example of how dynamic Delta hedging works?

In the provided example, if you sold short 100,000 call options with an initial Delta of 0.522, you would adjust the hedge every week based on changes in the stock price and Delta to maintain a delta-neutral portfolio. As the stock price changes, you would buy or sell shares of the underlying stock to offset the Delta of the short call options.

Outlines

00:00

📈 Introduction to Delta and Its Role in Option Trading

This paragraph introduces Delta, a critical 'Greek' in options trading that measures an option's price sensitivity to changes in the underlying asset's price. Delta acts as a sensitivity meter, indicating how much the option's price will move for every $1 change in the stock price. It's explained that a high Delta suggests a high sensitivity to the stock's movements, while a Delta near zero indicates minimal price movement even with significant stock price changes. The paragraph also differentiates between instruments with positive and negative Deltas, such as long stock, long call, short put for positive, and short stock, short call, long put for negative. The concept of Delta hedging is briefly mentioned as a strategy to offset risk associated with option positions.

05:02

🔄 Dynamic Nature of Delta and Hedging Strategies

This section delves into the dynamic nature of Delta, explaining that a delta-neutral position is temporary and requires adjustments over time as the stock price and time to maturity change. It uses graphs to illustrate how Delta changes with time and stock price, showing that in-the-money, at-the-money, and out-of-the-money options all have varying Deltas that move towards 1 or 0 as expiration nears or as the stock price changes. The paragraph contrasts static hedging, where a hedge is set and left unchanged, with dynamic Delta hedging, which involves continuous adjustments to maintain a delta-neutral position, leading to lower exposure to price changes but also lower potential gains or losses.

10:03

📉 Practical Example of Dynamic Delta Hedging

The final paragraph presents a practical example of dynamic Delta hedging using a scenario from John Hull's textbook. It describes a situation where an investor has sold 100,000 call options and must maintain a delta-neutral portfolio over 20 weeks. The investor starts with an initial Delta of 0.522 and adjusts the hedge weekly in response to stock price changes, buying or selling shares of the underlying stock to offset the Delta of the short call options. As the stock price fluctuates, the Delta changes, requiring the investor to sell shares to maintain neutrality. Towards expiration, as the option becomes deeper in-the-money, the Delta approaches one, necessitating a large number of shares to offset the position, highlighting the need for continuous adjustment in a dynamic hedging strategy.

Keywords

💡Delta

Delta is a measure of the rate of change in an option's price in response to a $1 change in the price of the underlying asset. It serves as a sensitivity meter in options trading, indicating how much an option's price will move with the underlying stock. In the video, Delta is central to understanding how to hedge option positions, as it helps traders gauge the potential impact of stock price movements on their options.

💡Option Trading

Option trading involves buying or selling options contracts, which give the holder the right, but not the obligation, to buy or sell an underlying asset at a set price before a certain date. The video discusses Delta in the context of option trading, emphasizing its importance for managing the risk associated with options positions.

💡Sensitivity Meter

In the script, the term 'sensitivity meter' is used metaphorically to describe Delta. It highlights how Delta quantifies the sensitivity of an option's price to changes in the underlying stock's price, which is crucial for making informed trading decisions.

💡Underlying Asset

The underlying asset is the stock, commodity, or other financial instrument on which an option contract is based. The video script explains how Delta measures the change in an option's price with respect to changes in the price of the underlying asset, which is essential for Delta hedging strategies.

💡Longing a Stock

In the context of the video, 'longing a stock' refers to owning or having a long position in a stock, which is expected to increase in value. The script mentions that if the stock price goes up, the person longing the stock makes a profit, which is an example of a positive Delta instrument.

💡Longing a Call

Longing a call option means buying a call option, giving the holder the right to buy the underlying stock at a set price. The video script explains that if the stock price goes up, the value of the call option increases, illustrating a positive Delta position.

💡Shorting a Put

Shorting a put involves selling a put option, where the seller has the obligation to buy the underlying stock at the set price if the buyer exercises the option. The script mentions that if the stock price goes up, the person shorting the put benefits, as they keep the premium and the put becomes less likely to be exercised.

💡Delta Hedging

Delta hedging is a strategy used to minimize risk associated with an option position by offsetting it with an opposing position in the underlying stock. The video script provides an example of how to achieve a delta-neutral portfolio by buying shares of the underlying stock to counteract a short call option position.

💡Delta Neutral Portfolio

A delta-neutral portfolio is one where the total Delta of all positions equals zero, making the portfolio insensitive to small changes in the underlying asset's price. The video script explains that while achieving delta neutrality can reduce risk, it requires continuous adjustments as Delta changes over time.

💡Static Hedging

Static hedging involves setting up a hedge once and leaving it unchanged. The video script contrasts static hedging with dynamic hedging, noting that static hedging has a higher potential for both gains and losses due to the unchanging nature of the hedge as market conditions evolve.

💡Dynamic Hedging

Dynamic hedging is the continuous adjustment of a hedge position as market conditions change. The video script describes dynamic hedging as a way to maintain a delta-neutral position by frequently buying or selling shares of the underlying stock to offset changes in the option's Delta.

💡Black-Scholes Option Pricing Model

The Black-Scholes model is mentioned in the script as a method to price options and calculate Deltas over time. While the script does not delve into the specifics of the model, it is used to illustrate how Delta changes as time passes and stock prices fluctuate.

Highlights

Delta measures the rate of change in an option's price with respect to the price change of the underlying asset.

Delta is a sensitivity meter for how much an option's price will move for a $1 change in the stock price.

High Delta indicates high sensitivity to the underlying asset's movements, while near-zero Delta indicates minimal movement.

Instruments with positive Delta include long stock and long call, while negative Delta includes short stock and short call.

Delta hedging is a strategy to minimize risk associated with an option position by offsetting it with an opposing position in the underlying stock.

A delta neutral portfolio has a total Delta of zero, making it insensitive to small changes in the underlying asset's price.

Delta changes over time and with stock price changes, requiring adjustments to maintain a delta neutral position.

Static hedging involves setting up a hedge once and leaving it, while dynamic hedging involves continuous adjustment as market conditions change.

Dynamic hedging aims to keep Delta close to zero, reducing exposure to price changes in the underlying stock.

The Black-Scholes option pricing model is used to demonstrate how Delta changes over time and stock price.

In-the-money call options approach a Delta of one, while out-of-the-money call options approach zero as time to maturity decreases.

As stock price increases, Delta for call options increases from zero towards one, and for put options it decreases from one towards zero.

Maintaining a delta neutral portfolio requires buying or selling shares to offset the Delta of the short call options.

The total number of stocks traded to maintain a delta neutral position approaches the number of short call options as expiration nears.

An example scenario from 'Options, Futures and Other Derivatives' illustrates the process of dynamic delta hedging over the life of options.

The video provides educational content on finance and options trading, including tutorials and explanations of Greek options.

Transcripts

before we can dive into Delta hedging

we're going to go over a brief intro to

the most popular option trading Greek

Delta so what is Delta Delta measures

the rate of change in an options price

with respect to the price change of the

underlying asset Delta is a bit like a

sensitivity meter that tells you how

much will your options price move for a

$1 change in the stock that underlies it

so if your option has a high Delta then

its price will be very sensitive to the

movements of the underlying asset

whereas if its Delta is near zero it

will hardly move at all even when the

stock price changes a lot the bottom

formula tells us that Delta is equal to

the change in price of an option divided

by the change in the price of a stock

this formula is like a snapshot for the

options price sensitivity at any given

moment in time now let's look at a few

instruments with positive Delta and a

few instruments with negative Delta so

what does it mean if an instrument has

positive Delta that means that if the

underlying assets price goes up this

instrument's price should also go up a

few uh instruments in this category

could be longing a stock so that would

be owning a stock right if I own a stock

and its price goes up I've made money

longing a call so if I bought a call

option on this stock as price goes up I

profit or shorting a put so if I sell a

put the price goes up that's good for me

because I sold away the put so I'll get

to keep the premium and the person who

bought the put for me cannot exercise it

against me whereas on the flip side of

that negative Delta means that this

Security will have a price drop when the

underlying assets price goes up so if I

short a stock meaning I sell the stock

short its price goes up that hurts me I

lose money and the same thing is going

to happen with a short call and a long

put so if I have a position on this left

side in this positive Delta area if I

need to hedge that position I could take

an offsetting position from one of the

positions on the right side in the

negative Delta category and vice versa

let's dive into an example imagine that

there is a call option underlying a

stock this call option has a Delta of

0.5 the call option currently has a

price of

$4 now if the stocks price goes up

$1 then the call option should go up by

50 and the final call option price will

be

$44.50 however if the Stock's price had

fallen by $1 then the options value

would also Fall by 50 and the new option

price would be just

$3.50 what is Delta hedging so when you

own an option position you are exposed

to risk that the underlying asset moves

in an adverse way and you lose money so

Delta hedging is a strategy used to

minimize the risk associated with an

option position for example if you have

an option position with negative Delta

which means that if the stock price goes

up you will lose money

what you could do to offset that is you

could take a long position in the

underlying stock by buying shares of

that underlying stock and then if the

price goes up you'll make money on the

shares you just purchased while your

option Position will lose money but

those values should theoretically offset

one another so this Delta hedging

strategy involves offsetting the Delta

of the option with an opposing position

in the underlying stock the ultimate

goal is to create a delta neutral

portfolio now this would be a portfolio

where the total Delta of the whole

portfolio is equal to zero because you

perfectly offset the Delta of both

positions this portfolio would be

insensitive to small changes in the

price of the underlying asset so if

there was a small change in the stocks

movement your portfolio should see 0 of

gain or loss because the gains and

losses of both positions perfectly

offset one another now let's look at an

example where we have shorted 2,000 call

options and each of these call options

has a Delta of

.6 we can find our total position Delta

by taking the Delta multiplied by the

quantity this gives us a position Delta

of

1,200 now how could we offset this

position to make our portfolio complete

delta neutral where the total Delta is

zero well we could do that by just

buying shares of the underlying stock

and how many shares would we need to buy

we would need to buy 1,200 shares

because an underlying stock has a Delta

of one so if we buy 12200 the position

Delta of our long shares will be $1,200

and both of these positions will offset

for a total Delta of zero so shorted

those call options we were exposed to

price rises in the underlying stock and

we had a non- Del neutral portfolio so

what did we do we bought shares and then

our portfolio became deltra neutral with

a total Delta of zero so now we're good

right we're safe that's incorrect

because Delta changes over time a delta

neutral position will only remain

neutral for a short period of time and

as time passes or as the stock price

changes the Delta of a call option or

put option will also change so as that

Delta changes now the amount of shares

that we had purchased will not perfectly

offset the Delta of our underlying

position and we will once again be

exposed to Delta let's take a look at

two graphs that'll really drive home the

point of how Delta changes as the time

passes or the stock price changes here I

have created a graph to show how Delta

changes over time I have used the black

schs option pricing model to price out

these Deltas don't worry too much about

how that works but understand that I

have held the stock price consistent the

risk-free rate consistent and the

volatility consistent over time and I

have plotted the Delta 4N in the money

call a Delta for an at the money call

and a Delta for the out of the money

call on this graph

we can see that on the leftmost part of

the xaxis this is our time to maturity

in years is 10 and then as we move to

the right we go all the way to zero so

we can see that when there's still 10

years left to maturity all of these call

options have Deltas that are pretty

close together they're all with about

point2 of each other and then as time to

maturity passes we can see that they Dev

devate from each other massively and the

in the money call option approach is one

the out of the money call option

approach is zero and the in at the money

call option approaches 0.5 as we get

down to the expiration date and here we

can see a chart that shows how Delta

changes as stock price changes so once

again we're going to hold all of the

inputs constant including the strike

price risk-free rate volatility and the

time to

expiration and we're just going to

change the stock price so the strike

price is 50 and what you'll see here is

that when the stock price is around zero

the call option is far out of the money

and the Delta is zero whereas the put

option is far in the money and the Delta

is near to ne1 and then as we increase

the stock price and the stock price gets

close to the strike price when the stock

price is 50 we should see a call Delta

at about 0.5 and a put Delta at about .5

and then as we increase our uh stock

price all the way to 100 the call option

becomes far in the money and that Delta

is near one and that put Delta is near

to zero so this is just to illustrate

that we could lock in a Delta hedge but

as the price changes or as the time to

maturity passes we might have to adjust

that hedge to make sure that our

portfolio

stays delta neutral that brings us to

the point of static hedging versus

Dynamic hedging so a static hedge will

be one where we offset our option

position with a certain number of

purchases or sales of the underlying

stock and then we just set it and forget

it we just set up our hedge once and we

leave it forever this has a higher

upside because our Delta will move away

from zero as time passes and the stock

price changes and it will also have a

higher downside because basically the

fact that we have this Delta exposure

can drive us to achieve either huge

gains or huge losses where the opposite

of this would be dynamic Delta hedging

and this involves continuously adjusting

the Hedge position as the market

conditions change and as time passes so

this means that we will keep buying or

selling shares to keep our Delta as

close to zero as possible and because

our Delta is so low we will be very

little have very little exposure to

price changes in the underlying stock

and therefore we will have lower upside

and lower downside if we do Dynamic

Delta hedging versus just static hedging

now let's take a look at a dynamic

hedging example scenario which I took

out of the John Hall famous t textbook

options Futures and other derivatives in

this example we're going to be playing a

role assuming that we have sold short

100,000 call options and we want to

maintain a delta neutral portfolio on

these 100,000 call options they're set

to expire in 20 weeks and they have an

initial Delta of

0.522 we're going to adjust this Hedge

every week to make sure that our Delta

stays as close to zero as possible so

we're chasing this delta neutral

position throughout the life of the

options however each week the stock

price is going to keep changing which is

going to affect the Delta and so we need

to determine how many shares do we need

to buy or sell of the underlying stock

in order to maintain a delta neutral

portfolio so we are short 100,000 call

options and we need to make sure that we

can offset that position by buying

shares of the underlying stock to make

our portfolio Delta equal to zero so

that it is a delta neutral portfolio

we're going to start in week zero where

the Delta is.

522 how many shares do we need to

purchase to offset the Delta of our

short 100,000 call position well it will

just be equal to the Delta of the stock

or sorry the Delta of the option . 522

multiplied by the 100,000 options gives

us a total number of stocks we need to

trade of

52,2 but let's say next week the stock

price Falls to

4812 because the stock price fell we are

going to see a decrease in the value of

delta to

0458 that gives us a total change in

Delta of a decrease of

0.64 so now we know that to maintain our

delta neutral position we need to sell

6,400 shares of the stock that we had

purchased this week bringing our total

stocks that we own to

45,800 next week week two we see the

stock price fall yet again which means

that Delta is also going to fall and now

Delta

is4 so we can see there's another change

in Delta where it decreased by 058 so we

need to sell more shares which brings

down our total number of stocks traded

but let's fast forward into the future

the stock price starts rising and rising

and rising and by the time we're getting

to week 19 or 20 the stock is so far or

this call option is so far in the money

by expiration

that the Delta is close to one now to

offset this position we're going to need

a total number of stocks almost equal to

the number of call options that we are

short and we can see that our total

stocks traded approaches 100,000 as we

get closer to expiration on this in or

in the money call option thank you so

much for watching this video check out

Ryan oconnell finance.com where you can

get help with Finance to tutoring and

also be sure to check out some of my

other videos on the Greek options which

you can find here and here

[Music]