Volatility Arbitrage - How does it work? - Options Trading Lessons

Summary

In this informative video, Patrick Boyle delves into the world of volatility trading, explaining the Black-Scholes model's role in pricing options and the real-world challenges it faces. He discusses how traders use delta hedging to manage risk and profit from volatility, highlighting the importance of understanding implied versus realized volatility. Boyle also explores the concept of volatility arbitrage, where traders buy low and sell high on volatility based on their forecasts, emphasizing the need for continuous re-hedging to capture profits. The video provides valuable insights for those interested in options trading and financial derivatives.

Takeaways

• 📚 Patrick Boyle introduces the topic of volatility trading and its relation to option pricing, specifically the Black-Scholes model.
• 💡 The Black-Scholes model assumes continuous and riskless delta hedging, which is not feasible in the real world due to trading limitations and market behavior.
• 💼 Real-world trading involves less frequent hedging, and traders often hedge after significant market moves, leading to deviations from the Black-Scholes model's predictions.
• 📉 The underlying assets do not always behave as the Black-Scholes model expects, with trading not being 100% continuous and asset prices experiencing jumps.
• 🌡 Volatility, or the standard deviation of the market, is not stable over the life of the option, which is a key assumption in the Black-Scholes model.
• 💰 Due to the challenges in perfect hedging, options are often sold at a premium to compensate for the risks and costs involved in trading.
• 🔄 Sellers of options are the counterparty with nearly unlimited downside, so they require additional compensation for selling options.
• 🛍 The price of an option is related to the cost of creating it, similar to any other product, and must cover the costs of production, including the risks involved.
• 🔄 Volatility arbitrage involves trading a delta-neutral portfolio to take advantage of differences between implied and forecasted realized volatility.
• 🤔 Volatility traders do not have a directional opinion on the market; they aim to profit from their view on volatility rather than the movement of the underlying asset.
• 📈 The profit in volatility trading comes from the continual rehedges required to maintain a delta-neutral position, which can result in gains if the realized volatility aligns with the trader's forecast.

Q & A

What is the main topic of Patrick Boyle's video?

The main topic of Patrick Boyle's video is volatility trading, specifically how option traders trade and profit from the volatility of the underlying asset's price on which their option is based.

Why is the Black-Scholes model important in the investment industry?

The Black-Scholes model is important because it provides a theoretical framework for pricing options. It suggests that if traders could continuously and risklessly delta hedge, the model would perfectly price options.

What are some real-world issues with the Black-Scholes model?

Some real-world issues include the inability to trade continuously at every microsecond, the fact that underlying assets don't behave as the model assumes (e.g., asset prices jump on news), and that volatility is not stable over the life of the option.

Why do volatility traders and market makers charge a premium above the Black-Scholes price?

Volatility traders and market makers charge a premium to compensate for the costs and risks associated with imperfect and riskless delta hedging, as well as for the administrative and IT expenses involved in trading options.

What is the relationship between the price of an option and implied volatility?

The price of an option is closely tied to the implied volatility used in its calculation. Higher implied volatility generally leads to a more expensive option, and vice versa.

What is the role of a volatility arbitrage trader?

A volatility arbitrage trader attempts to profit from differences between the implied volatility of an option and their forecast of future realized volatility. They aim to buy volatility when they believe it is low and sell when they think it is too high.

How do traders manage the directionality of options through hedging?

Traders manage the directionality of options by delta hedging. This involves buying or selling the underlying asset to maintain a delta-neutral position, thereby isolating exposure to volatility rather than direction.

What is the significance of gamma in delta hedging?

Gamma represents the rate of change of delta for a 1% change in the price of the underlying asset. It is crucial in delta hedging because it dictates how often and by how much the trader needs to adjust their position to maintain delta neutrality.

How can a trader realize a profit from a volatility trade?

A trader can realize a profit if the realized volatility of the underlying asset is closer to their forecast than to the market's forecast (implied volatility). Profits are extracted through the continual rehedges required to maintain a delta-neutral portfolio.

What happens if the underlying asset's volatility is less than the implied volatility?

If the underlying asset's volatility is less than the implied volatility, the trader who is long volatility (and has bought options) will likely lose money, as they would not make back the premium paid for the options through hedging.

What is the opposite outcome for a trader who is short volatility?

If a trader is short volatility and the underlying asset's volatility is less than the implied volatility, they would keep the entire premium received from selling the options, as there would be no significant market movements requiring hedging.

How does the concept of 'Delta hedging' relate to the profitability of a volatility trade?

Delta hedging is directly related to the profitability of a volatility trade. If the market moves less than expected, the trader makes back less of the premium paid. If it moves more, they make more than the premium spent, potentially generating significant profits.

Outlines

00:00

📚 Introduction to Volatility Trading and Black-Scholes Model

Patrick Boyle introduces the topic of volatility trading, explaining how option traders capitalize on the volatility of the underlying assets. He mentions that the video is part of a series on dynamic hedging and provides a link to the playlist. Boyle discusses the Black-Scholes model, which theoretically prices options based on the assumption of continuous and riskless Delta hedging. However, he points out the discrepancies between the model and real-world trading, such as the inability to hedge continuously and the unpredictable behavior of asset prices. He also explains that due to these real-world challenges, options are often sold at a premium to compensate for the risks and costs involved in Delta hedging.

05:00

🔍 Volatility Arbitrage and Delta-Neutral Trading Strategy

This paragraph delves into the concept of volatility arbitrage, a strategy used by traders to exploit the difference between implied and forecasted realized volatility. Boyle clarifies that this is not a true arbitrage due to the element of forecast involved. Traders aim to profit from their views on volatility without having a directional bias on the market. They look for options where the implied volatility diverges from their forecasts and engage in Delta hedging to maintain a delta-neutral position, which isolates them from directional market movements. The profit or loss from these trades is realized through the continuous adjustment of the Delta position, which can result in gains if the market's realized volatility aligns with the trader's forecast.

10:02

📉 Examples of Volatility Trading Outcomes

Boyle provides two examples to illustrate the outcomes of volatility trading. In the first scenario, a trader is long volatility but the market remains stagnant, resulting in a loss of the entire premium paid for the option. Conversely, in the second example, the market experiences extreme volatility, leading to substantial profits from the hedging activities, far exceeding the initial premium spent. These examples underscore the importance of accurate volatility forecasting and the impact of market movements on the profitability of volatility trading strategies. The video concludes with an invitation for viewers to engage with the content, subscribe for more, and consider a recommended book on the subject.

Keywords

💡Volatility Trading

Volatility trading refers to the practice of speculating on the future volatility of a financial asset's price. It is central to the video's theme, which discusses how traders can profit from the volatility of the underlying asset of an option. The script explains that traders look for discrepancies between implied volatility (the market's forecast of future volatility) and their own forecasts of realized volatility to make trades.

💡Black-Scholes Model

The Black-Scholes Model is a mathematical formula used to calculate the theoretical price of European-style options. It is mentioned in the script as a foundational concept for understanding how options are priced and the assumptions it makes about continuous trading and riskless hedging, which are not always applicable in the real world.

💡Delta Hedging

Delta hedging is a strategy used by traders to manage the risk of price movements in an option's underlying asset. The script explains that traders adjust their positions in the underlying asset to maintain a delta-neutral position, which is crucial for volatility trading as it allows traders to focus on volatility rather than directional price movements.

💡Implied Volatility

Implied volatility is the market's expectation of a likely movement in a security's price, derived from the price of options on that security. The script discusses how traders compare implied volatility to their own forecasts to identify trading opportunities, as it directly affects the price of options.

💡Realized Volatility

Realized volatility is the actual volatility experienced by the price of an underlying asset over a certain period. It is contrasted with implied volatility in the script, where traders aim to profit from differences between the market's expectation (implied volatility) and the actual future volatility (realized volatility).

💡Volatility Arbitrage

Volatility arbitrage is a trading strategy that exploits the difference between implied and realized volatility. The script describes how traders engage in this practice by buying or selling options based on their forecasts of future realized volatility compared to the market's implied volatility.

💡Option Premium

The option premium is the price paid by the buyer to the seller for the rights granted by the option. The script explains that sellers of options charge a premium to compensate for the risk and costs associated with selling options, which is a key factor in volatility trading.

💡Riskless Hedging

Riskless hedging is a theoretical concept where a trader can perfectly offset the risk of an option position by taking an opposite position in the underlying asset. The script points out that in reality, riskless hedging is not always possible due to trading limitations and market imperfections.

💡Underlying Asset

The underlying asset is the security or financial instrument on which an option is based. In the context of the script, the price movements of the underlying asset are what traders are speculating on when they engage in volatility trading.

💡Gamma

Gamma in options trading measures the rate of change of an option's delta relative to a 1% change in the price of the underlying asset. The script uses gamma to illustrate how delta hedging can generate profits or losses, depending on the actual volatility experienced by the underlying asset.

💡P&L (Profit and Loss)

P&L refers to the financial result of a trade or investment, showing the profit or loss realized over a specific period. The script uses P&L to demonstrate the outcomes of volatility trading strategies, highlighting the potential gains or losses depending on whether the trader's volatility forecast is accurate.

Highlights

Introduction to volatility trading and its significance in options trading.

Explanation of the Black-Scholes model and its relevance in pricing options.

Discussion on the limitations of the Black-Scholes model in real-world trading.

Real-world traders do not hedge continuously as assumed by the Black-Scholes model.

Volatility traders and market makers charge a premium to sell options to compensate for risks and costs.

Comparison of option selling to selling insurance policies, emphasizing the need for fair compensation.

Explanation of Delta hedging and its role in volatility trading.

Introduction to volatility arbitrage as a type of statistical arbitrage.

Objective of volatility arbitrage: exploiting differences between implied and forecasted volatility.

Traders do not have a directional opinion on the market; they focus on volatility.

Long volatility means buying options and hedging Delta; short volatility means selling options and hedging Delta.

Importance of Delta-neutral positions in volatility trading.

Explanation of Gamma and its impact on Delta-neutral positions.

Example scenarios illustrating profit and loss based on market movements and hedging strategies.

Conclusion on how volatility trading works and its practical applications.

Transcripts

hello my name is Patrick Boyle welcome

back so today we're going to learn about

volatility trading and we're going to

learn about how option traders trade and

how they try and profit from the

volatility of the price of the

underlying that their option is based

upon if all of this is new to you that

this video is part of a longer series

that I'm doing on dynamic hedging and if

you want to watch that whole series I've

put it in a playlist that is linked to

right there so anyhow today we're just

talking about volatility trading and how

that works so firstly we have to look

back at the idea of the black Scholes

model and how we price options and kind

of why the black Scholes model is

actually useful and interesting and why

it matters - to people in the investment

industry so the black Scholes model

tells you that if traders were able to

riskless Lee Delta hedge continuously in

the manner described in in the manner

that we're gonna describe in today's

class that this model would perfectly

price options okay now the problem is

that there are of course some real-world

issues with the black Scholes model so

in the real world traders to not always

hedge continuously right you can't trade

at every microsecond and in fact often

they just do it daily maybe to close a

day or hourly or often they'll just wait

til there's a big move and hedge you

know

so the real world is a little bit

different than the world described by

the black Scholes model equally the

underlying asset doesn't behave exactly

the way it is described in the black

Scholes model trading is not a hundred

percent continuous asset prices jump on

big news or on announcements or even

just when the market is closed overnight

it's reasonable to expect the market to

gap up or down by the

so volatility our standard deviation is

not stable over the life of the option

and that's of course an important part

of the black Scholes model is that idea

and so because of these difficulties

with perfectly and riskless Li Delta

hedging options volatility traders and

market makers usually are going to

charge a small premium to sell options

above what might be the perfect black

Scholes price and this is essentially

that they need to be compensated for the

costs of what they're doing right

because how it often works in the

options world is that there's lots of

people who sort of like the idea of

buying options they like the idea you

know buying a put option in order to

insure their portfolio it's a little bit

like buying an insurance policy on your

house or your car makes people

comfortable

someone has to sell that and you know

when we early on in this video series we

described the payoffs of being long and

short options I imagine lots of people

who are new to this think well gosh you

know I I can understand why you would

buy an option but it seems unreasonably

risky to sell an option and it it sort

of is unless you're over paid for them

right so essentially sellers of options

they don't have to sell options they can

they can do other things with their day

you know they're really going to only

sell options if they feel that they're

being offered enough money to compensate

them for doing the kind of work that

we're about to describe today that

involves Delta hedging that auction and

trying to hopefully you know hedge it

out and end up with a small profit

leftover so our sellers charge this

premium because they're the counterparty

would unlimited our nearly unlimited

downside in the options payoff and so

for that reason they're just not really

going to get involved a little bit like

an insurance company they're not going

to sell you an insurance policy it fair

fair value they're gonna work out the

fair value of you

current policy and charge you a little

bit more in order to make it reasonable

for them to you know to go to all of

this work and the work isn't just the

risk there's kind of there's all the

sort of paperwork and IT expenses

associated with that and that has to be

encapsulated in this price as well so

that leads us to the idea that actually

an option is like almost any other

product that you might buy the price of

it kind of just relates to the cost of

creating it right like when you buy a

pair of shoes

how much does issue cost well it

shouldn't cost less than the leather and

the stitching and the you know the labor

and whatever else that goes into it

otherwise people wouldn't want to make

them and so volatility traders

volatility arbitrators to a certain

extent kind of manufacture options for

people to buy so let's look a little bit

at this idea of volatility arbitrage or

what volatility traders do and see see

how it might make sense for someone to

do this so in finance volatility

arbitrage is a type of statistical

arbitrage that's implemented by trading

a delta-neutral portfolio that I've

explained in earlier videos of an option

and it's under lire

the objective is to take advantage of

differences between the implied

volatility of the option and I have a

video on unemployed volatility if you

need to watch that but their objective

is to take advantage of differences

between the implied volatility of the

option and their forecasts of future

realized volatility of the options under

lire now of course the problem in there

is it's not really an arbitrage you know

earlier when I explained what arbitrage

was this clearly isn't an arbitrage just

because it's their forecast of

volatility and that may or may not be

right you know will

have to find out over time whether that

works in volatility arbitrage traders

attempt to buy volatility when they

believe it to be low and sell volatility

when they think it is too high usually

they don't have a directional opinion on

the market so they're not trading in

order to profit from the price at the

underlying moving up or moving down

they're simply trying to profit based

upon their view on volatility so how

does this work will the trader looks for

options where the implied volatility is

either significantly lower or higher

than their forecasts realized volatility

for the underlined so they're basically

when I say they look for ones where

implied volatilities I essentially that

kind of means options that are too

expensive because as you hopefully know

from our earlier videos the price of an

option is very much tied to the implied

volatility used in the calculation now

because the trader is not trading

directionally they don't care if these

are calls or puts okay so an owl Atilla

tea trader is either they don't want to

be long or short volatility which means

long or short options now they don't

care if their puts are calls because

they're gonna hedge out the

directionality they're just going to be

exposed to this volatility portion of

the option so if you buy options and

help hedge the Delta your long

volatility if you sell options and hedge

the Delta your short volatility so

basically if your long option to your

long volatility if your short options

your short volatility but you also have

that directional component and you're

able to get rid of that directional

component through Delta hedging so over

the holding period our trader will

realize a profit on the trade if the

underlines realized fall is closer to

our traders forecast than it is to the

markets forecast which was the implied

volatility and the profit is extracted

from the trade and this is the important

point the profit is extracted from the

trade through the continual rehashing

required to keep our portfolio Delta

trouble so as you can see up here on the

screen right now we've got our payoff

diagrams of puts and calls and you can

be long or short them and if you're long

a call or long put your long volatility

but then you need to hedge at the Delta

and if you're sure to call or shorter

put you are short volatility but of

course you need to hedge out the Delta

once again as described I'm not on that

slide so how do you extract the value

well once you have a delta-neutral

position and I've kind of explained

Delta and Delta neutral trading in an

earlier video would you have this

delta-neutral position if the market

moves you find that you have to buy and

sell the underlying in order to stay

delta-neutral and that's because of

gamma gamma is the amount the Delta

changes for a 1% change in the price of

the underlying now if this this hedging

is going to generate profits and losses

if the underlying realizes the same

volatility as was implied

then your hedging will cost you the

amount of the premium you received or

generate profits equal to the premium

paid out hopefully that makes sense so

let's look at an example now in this

example I'm using this idea of 16%

implied fall and that's just because

I've reverse engineered that from a 1%

daily swings in the underlying would

equal 16% implied fall so if we bought a

call with 16% implied volatility and

sold the underlying against it to be

delta-neutral if the market never moved

again between initiating this position

our Delta would never change right and

if our Delta doesn't change we find that

we're never hedging now if we're never

hedging we can't generate profits or

losses right so we paid we bought a call

so where long volatility we're expecting

it to move more than 16 percent standard

deviation or

1% today and what we find is that it

doesn't move at all and what that means

is that we lose the entire premium right

because we don't make anything back at

all from our hedging now someone else

who sold us that option will have

received the full premium that we paid

them and the price of the underlying

won't have moved at all and so they will

will never have to rehash and thus they

will have managed to keep the entire

premium so we were in that example long

volatility and wrong about the

volatility we're extremely wrong so

let's look at the opposite of that say

the same example we bought a call 16

percent implied volatility sold the

underlying against it in order to be

dealt a neutral to 0.5 Delta option and

instantly what happens is the price of

the underlying falls straight to zero

right no soon aren't you have you bought

the call and hedged yourself than the

price of the underlying falls to zero

now at 0 the the Delta of this option

will also be 0 right so we were short 50

shares we have to buy all 50 of them

back right because we no longer need to

have that position now we'll imagine

that we do that and instantly the price

rockets and it doesn't rock it a little

bit it goes up like a top you know it

goes to houses we'll say if it started

at a hundred it goes to a thousand so we

recalculate our Delta and what do we

find we find that the Delta now is

around one and so what we have to do we

have to sell 100 shares and so we'll

imagine if this just kept on happening

so we were expecting the underlying to

swing one percent a day and within a

single day we've got these massive

thousands of percents of percentages of

swings right and every time it makes

these big swings it keeps fluctuating

between zero and a thousand and every

time it does that we're either buying or

selling the underlying and this is of

course generating us huge profits right

where we're hedging our options about

that we're not really

you know losing money on the option

because we keep rehashing but not only

that we're making huge profits from the

hedging and this is because the price is

moving way more than expected so in our

last example it moved way less than its

expected in fact it didn't move at all

and we lost all of the money that we

made in premium and in this example it

moved way way way more than was expected

and we're making way way way more back

than we spent on premium to begin with

so hopefully you understand with this

example how volatility trading works so

essentially if it swung around about 1

percent a day and we diligently rehash

their Delta us as described in my

earlier video on Delta hedging you would

find that you make back the amount of

money that you spend in options premium

but when it moves less you make back

less and when it moves more you make

much more than you spent in options

premium so that's really what it means

to be long volatility and then obviously

the person at the other side of each of

those trades will say with short

volatility and they'll have really the

exact opposite PNL assuming that they

don't sorta hedge identically or if they

do hedge identically to us they'll have

the exact opposite P&L to us so in the

first example they'll they'll have kept

the entire premium and in the second

example they'll have lost a ferocious

amount of money because of these large

swings so hopefully that video was

helpful if you'd like if you liked it

and you must have to watch almost 30

minutes of it please hit the like button

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interested in the book that all of this

is based on it's called trading and

pricing financial derivatives

derivatives and it's linked to in the

description below so have a great day

and tune in again for more of these

videos and do comment below if you've

any questions about this talk to you

later bye