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These classes are all based on the book Trading and Pricing Financial Derivatives, available on Amazon at this link.

Hello youtube welcome back so in today’s video we’re going to learn about creating neutral portfolios of options this is the 8th video of my series on the options greeks if you need to learn more about the greeks make sure you watch some of those videos first assuming that you already know about the various options greeks like delta gamma theta and vega today

We’re going to learn about how options traders create neutral portfolios and why they might want to do that as we’ve seen in an earlier video by using a stock and an option a trader can create a delta-neutral portfolio if the trader wishes to further reduce sensitivities to other factors such as gamma they could do this by adding another option to the portfolio

A portfolio of a stock and a single option could never be gamma neutral once the trader adds an additional option and constructs a delta gamma neutral portfolio they would still be affected by other factors such as interest rates and volatility in general for each group they wish to hedge they would need to add at least one additional option to the portfolio in

The real world it’s very difficult if not impossible to hedge out all of your greeks it may be very difficult to find the correct option to hedge the portfolio and even if it could be found liquidity and transaction costs could be so high that putting together such a portfolio would make no economic sense in practice professional options traders flatten out their

Delta as if they wish and then they had the portfolio once or twice a day after that they just monitor their other greeks and take corrective action as necessary the greeks are additive in a linear manner this means that the total delta exposure for all of the options of a given underlying can be found by adding the delta of each individual option for example if

You are short 200 shares long 5 calls with a delta of 0.5 and short two puts with a minus 0.2 delta you have a net delta equivalent to 90 shares how we do that is we say minus 2 because the underlying has a delta of 1 so you’re short 200 shares that gives you a delta of minus 200 then plus five times a hundred that’s because each option covers 100 shares so five

Call options times a hundred times the delta of the call option which was 0.5 then minus two times 100 times minus 0.2 and that is to put options that were short with a multiplier of a hundred for a hundred shares minus point to being the delta of that put option and we sum that all up and that comes to 90 and so owning that portfolio gives you a risk exposure

As if you were long 90 shares of the underlying so for small moves in the price of the underlying you’d expect your profit and loss your p&l to change as if you were long 90 shares i hope that makes sense this approach works for delta gamma anti-de the net position of row may also be obtained by summing the row of each option only if all options have the same

Maturity net position greeks for vega vanna and volga can be complicated as each different strike and expiration will have a different volatility see my other video that’s coming out very shortly on the volatility surface and hopefully that will explain not to you four options with the same expirations and similar strikes these greeks can be summed so why might a

Trader want a neutral portfolio a market maker might find themselves buying and selling a variety of options based on customer demand they don’t necessarily wish to find themselves taking the other side of all of their customers trades and so will aim to hedge they do this by neutralizing their greeks other traders may just want exposure to a specific greek and

So they will put on a portfolio that gives them that precise exposure that’s really all on neutral portfolios for this week thanks very much for watching this video if you made it this far please hit the like button and possibly share with a friend if you want to see more content like this please subscribe oh and tune in to tomorrow’s video on dynamic hedging

Where you’ll learn how to win a free copy of my newest book trading and pricing financial derivatives have a great day bye

Transcribed from video

Creating Neutral Portfolios – The Option Greeks By Patrick Boyle