Delta Hedging Explained: Options Trading Strategies
Summary
TLDRThis 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
📈 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.
🔄 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.
📉 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.
Mindmap
Keywords
💡Delta
💡Option Trading
💡Sensitivity Meter
💡Underlying Asset
💡Longing a Stock
💡Longing a Call
💡Shorting a Put
💡Delta Hedging
💡Delta Neutral Portfolio
💡Static Hedging
💡Dynamic Hedging
💡Black-Scholes Option Pricing Model
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]
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