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The second part of my tutorial on dynamic hedging.

Hello youtube welcome to today’s video this is the second one on dynamic hedging of options which is possibly the most important thing you can learn about options once you understand this topic you should really have a good understanding of options oh and stay tuned until the end where you’ll learn how you can win a free copy of my book that all these lessons are

Based upon from our prior videos on the options greeks you’ll remember that delta is the amount the options price changes for a one unit change in the price of the underlying asset you can see the formula for delta on the screen right now the delta of a portfolio is the weighted sum of the deltas of the portfolio constituents you are delta-neutral when this is

Equal to 0 delta neutral portfolios are of interest to traders because there are a way to hedge out the risk of an option or a portfolio of options if for example you sell one european call option which covers a hundred shares of stock and the options delta is 0.6 how can you get your trade to be delta neutral the answer is that in order to neutralize the delta

Of that option we need to hold 0.6 times 100 shares of stock or 60 shares and that would make us delta-neutral if you were to dynamically hedge the above call option you would sell the call and buy its delta at times the number of shares covered by the option each time the price of the underlying stock changes the delta of the option will change to as the delta

Of the option changes you’ll find yourself buying and selling stock if the realized volatility of the stock over the period covered by the option is equal to the implied volatility of the call option you sold you’ll find that your losses from this constant buying and selling of the underlying stock will exactly offset the premium that you took in when you sold

The call option when we look at the payoff diagrams of a call option we concede that it looks a little bit like the payoff of being a stock with a stoploss or also known as a stop order in place if the stock price goes up we get a return somewhat like that of the underlying stock and if the price falls a lot it looks like we get stopped out with an option if the

Price rises again we find ourselves with the payoff of being along the stock again for the replicating portfolio to work it must trade in such a manner if you look at how delta changes as the stock price moves up and down you will see that roughly speaking and at the money call has a delta of around 0.5 so owning the option is a bit like owning half of a share

Times the number of shares covered by the option as the underlying goes up in price the delta increases and it becomes like owning more and more of the stock as it gets deeper and deeper into the money as the price of the stock falls the delta also falls and you find yourself owning less and less of the stock in your dynamic hedging as the option moves out of the

Money unlike being long a stock with a stop-loss as the price falls you do not dump all of your stock in one go you sell it in small increments over time as the price is moving down to maintain your appropriate delta hedge ratio equally as the stock price rises you find yourself buying more and more stock in small increments to maintain your appropriate hedge

This example helps to give you some insight into gamma in particular for an at the money option very close to expiration suppose you wish to replicate and at the money call option on expiration day and the option has a strike price of $50 and the underlying is trading right at $50 in order to replicate the payoff of the option you buy a hundred shares of stock

Every time the price of the underlying ticks above 50 and sell a hundred shares every time it ticks below 50 as you can see in an example like this gamma is at its highest for out the money options on expiration day delta quickly takes between 1 and 0 wood up and down moves in the underlying because of this high gamma on expiration day for out the money options

A huge amount of the trading in the underlying stock can be options traders delta hedging their options positions with no real long-term view as to the long term prospects of the company that the option is based upon for this reason on expiration day you will often see stocks becoming pinned to high open interest option strikes tune in tomorrow for a video on

Delta hedging a call option where we will work through an example if you’ve made it this far please hit the like button i mentioned at the start of the video that i would tell you how to win a free copy of my latest book trading and pricing financial derivatives which is linked to in the description below all you have to do is to be a subscriber to this channel

And to watch yesterday’s video on dynamic hedging our link to that here and click the like button on that video see you tomorrow and have a great day bye

Transcribed from video

Dynamic Hedging (Part 2) By Patrick Boyle