What is Delta Hedging || Dynamic Delta Hedging like a Quant || Profit & Loss Options Trading

Today we look at hedging options from a quant’s perspective. In this video we look at the difference in Profit and Loss (P&L) with three different strategies: dynamic delta hedging, static delta hedging and no delta hedging.
Delta hedging is a way to reduce directional risk of the underlying to your options positions by transacting in the money markets (bank account) and the underlying (stocks/futures/etfs/index). By continually adjusting in the underlying and bank account, we can effectively replicate the changes in payoff of the ‘new’ option contract. Essentially instead of betting on the direction at one time spot (on entry) we are now making a series of bets at different levels.
Hopefully in this video the importance and relevance of realized volatility becomes apparent and hence why market marking firms like Optiver are so keen on forecasting realized volatility as accurately as possible.
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00:00 Intro
00:22 What is Delta Hedging?
01:40 Importance of Realized Volatility
02:00 Real world examples
03:56 Full worked example: Short CBA Nov 102 Call
06:40 Looking at P&L over 1000 trades
07:45 P&L distributions for different hedging strategies
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[@deepdivestocks]

Fantastic recap of hedging and its applicability in real-world trading.

[@christianhjerrildblom5972]

Your videos are amazing, I'm currently doing a Bsc in mathematical finance and these videos are so inspiring to me. Keep up the good work!

[@kaiwang2924]

Thanks for the excellent video, you make it so easy to understand!

[@alexandert6172]

Briliant explanation

[@bbqchickenlemon]

you've taught me more than my prof with a PHD ever could

[@dzi333]

Well this is actually very well explained in the literature of the subject, like Natenberg.

[@pzhangd]

THanks, I learned a lot

[@ghostwhowalks5623]

This is super-useful! Silly Q - how do you control the change the hedge frequency from say monthly to weekly (daily etc.).....do you keep the number of steps constant and only change the time step; "dt"? Thanks!

[@IStillHaveDialUp]

Another great video

[@fminc]

Thanks for your work, great channel. (ha ha ha, you slipped when you explained the short at 1:30, but thats all good, well explained as such).

[@vwedeagboro-jimoh6556]

This is mint!

[@gusinthecloud]

awesome

[@Lukas-cm2b]

you made it look very easy that with hedging you almost not lose any money eg the low P5, but if the price dips 50% then your long shares are in 50% loss so i am not really sure about that profit distributions.

[@Freewill888]

Hi Jonathan, I happen to find your channel and would like to know whether you upload a video subsequent to understand market maker to explain how they predict the realized volatility. If you do can you let me know which video is it? Thanks!

[@wetradealerts2594]

Hey! I have a question. On your code, the number of weeks is set to 11. The option had an expiry of appx 2 months and you had converted that to years and divided by 11 to get each time step. My question is, if i take smaller time steps and delta hedged, lets say instead of 11, I delta hedged every day, lets say instead of 11, i put 100. Will the P/L distribution of delta hedge flatten out and be close to 0 ?

[@olivermohr417]

How do you model the delta in your simulation? You can simulate a random walk with a previously set volatility, but then you need market volatility to calculate the delta on each step. Which vol do you use there?

[@poorbadger]

How were you calculating P5, P95, mean - via Monte Carlos Analysis?

[@maurohalpern]

I am just buying low volatility and selling hi volatilty at same time using different stocks of a list.....very profitable; for me makes more sense "hedging" each leg of my cheap options with expensive ones, not using the stock itself

[@junchenggeng2949]

when you calculated the original stock pnl, why is 102.59-102 instead of 102.69-102 @5:59

[@yassinetac6646]

Hi thanks a lot for the very useful content. I am considering studying a certificate in it quant operations and it is a lot about making a Python api bot to automatiquely rebalance hedging. My question is:how do banks make money from that? What can be the monthly or annual outcome of using dynamic hedging? Thanks

[@konradwk622]

did you end up getting the certificate, or create the api. Cheers from a year ago haha

[@martinluther3712]

Hi, could someone tell me the name of the chair you use?

[@carrotblog1746]

set the speed to 0.75 is much better :))

[@davidececk9668]

Can you help me understand what Is p5 and p95 ? Thank you great work 👍

[@QuantPy]

No problem, glad you enjoy the videos. I’m just referring to percentiles of a distribution. In this case p5 is 5th percentile and p95 is 95th percentile. Think of it in terms of a ranked list of values.

[@_el_yeyo]

I assume the simulations are based on Black Scholes for the profit calculations?

[@QuantPy]

Yes apologies if I didn’t make that clear, but feel free to adapt the code with whatever mode you want.

[@josephwehby9313]

Is there an advantage or disadvantage to rebalancing your deltas daily versus weekly?

[@QuantPy]

I'll point you in the right direction here, as I can't give financial advice. You'll be interested to know that there are a number of studies that show that fixed time discrete delta hedging (day/week) is suboptimal. Recommend jumping on Google Scholar and reading 'A Note on Hedging: Restricted but Optimal Delta Hedging, Mean, Variance, Jumps, Stochastic Volatility, and Costs' by Hyungsok Ahn and Paul Wilmott (2009).

[@josephwehby9313]

@@QuantPy thank you. I’ll check it out. Keep up the great content

[@MrLisaFischer]

Oh lord, why do I find Option trading so difficult. Where can I obtain introductory lessons on Options trading, all that Gamma and stuff😵

[@junwang0525]

what if a stock is paying dividend

[@mathieusaussez7345]

Short selling is you sell when the price is high to buy it low

[@defface777]

Gamma scalping...

[@investwithvincent6329]

as per row 1, what's the formula to get "3" ?

[@investwithvincent6329]

ok... i see that 3 represents the change from the delta value in row 1 to row 2 and so fourth

[@janegoodall1837]

At 4:28 you state you have to immediately buy 54 shares to be delta neutral. But The very first adjustment you make in week 1 is entering a short position making the account -3 of the stock? But if you bought 54 shares immediately when you sold the call, wouldn't you still be long 51 shares of the stock? If the delta changes by 3 week 1. Then how come when you start with 54 shares its not 54 - 3, but 0 - 3?

[@QuantPy]

You are exactly right. When we first entered the position (Short Call), we had a delta of -54, therefore we also bought 54 shares to offset this directional risk. In the table you are referring to there, I am only showing the adjustment process so we can calculate, adjustment cashflow and interest on adjustment separately to the initial positions we put on. You can then add the ending results of the Short Call and initial 54 shares purchased back in at the end to get the final PnL. That is what I showed here. Hopefully that's clear, if not I encourage you to read Option Volatility & Pricing by Sheldon Natenberg

[@investwithvincent6329]

as per row 1, what's the formula to get "1.16" ?

[@QuantPy]

Please refer to code on my website. Link in description 👍

[@tutumumu8428]

Assuming you sell a call(short) and at the same time you delta hedge it with stock. if the stock price drop say significantly, do you keep the premium at expiration or will the hedge offset the premium and you end up with 0 impact ?

[@QuantPy]

Please watch the video all the way to the end, I attempt to explain the difference in hedging strategies. What you’ve described is a static hedge.

[@tutumumu8428]

@@QuantPy I watched the video till the end. Assuming IV does not change and ignoring the interest, will the call writer collect the premium at expiration assuming the stock price drop by more than the primium collected? Logically no as the stock purchased will lose value and offset the the premium collected. I would like to confirm if my understanding is correct. Thank you in advance.

[@QuantPy]

In summary, it’s probabilistic. In the video I show the Monte Carlo like analysis of the different PnL outcomes that can occur. If you statically hedge once, there are definitely scenarios as you’ve described if you write a call, and buy the stock, if the price goes down dramatically you can lose you entire premium. However the edge is, over a large number of trades using delta hedging your premium (that you’ve collected at IV) if there is a positive difference between realised and implied volatility then you decrease your variance around your expected value.

[@tcurson1]

It may have been better to use underlyings with better liquidity, like the S&P500 ETF. Also if you sell a call then buy 50 shares, then the market goes up a ton in a week, buying the x shares to delta hedge, then having the market go down, etc is just locking in loads of losses. At this point just sell a call against your short put

[@QuantPy]

Thanks for your comment. By delta hedging you’re offsetting the changes in the price of the option with respect to the underlying. And yes, you can also do this by offsetting delta changes by buying/selling other derivatives

[@strawberrymilk836]

The code doesn't work anymore

[@esmailpirasteh3098]

Lost me on the second put option example

[@Footprints1111]

It’s just another strain of Corona. 😂