I am pretty new in quantitative finance, and I am interested by the hedging of autocalls. Could you, please explain which financial products should be traded (specify the way, please) to delta hedge, gamma hedge and vega hedge an autocall? And why the latter strategies work?

Thanks in adcance

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    $\begingroup$ Not sure why this question is given a "-1", it's not straightforward to hedge an auto callable. Giving it a +1. $\endgroup$ – ilovevolatility Feb 23 at 15:11
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    $\begingroup$ Hello,thanks for your answer. Do you know some books that can help me to improve my understading of all the risks that matter to hedge an autocallble product? $\endgroup$ – user11798649 Apr 16 at 11:24
  • $\begingroup$ To understand autocallables you need to understand barrier options. So as a start if I were you I would study the pricing and hedging of barrier options. Here is also a link to a discussion of barrier option risk on this forum: quant.stackexchange.com/questions/37200/… $\endgroup$ – ilovevolatility Apr 16 at 12:13

Well, it's a topic which actually should have its own book dedicated. Unfortunately, existing literature is rare or not practical enough. Let me at least try to provide some key ideas and challenges you should consider when hedging this kind of structure.

First, let's start with the question: How not to hedge an autocallable? What is not going to work is that you flatten the market risk for a given risk factor set and the corresponding greeks by permanently using the spot and derivatives market. Why? Because sensitivities are so dynamic for an autocallable note that this approach would eat up all the margin you passed to investors in maybe 2-3 days. Of course, you can charge more in order to cover your hedging costs, but you are in competition and need to have an eye on external pricings in order to win deals.

Now, what are the challenges. We have Delta and Gamma risk towards the spot.

Delta: Directional (as an issuer you are short and hence need to buy/sell stocks or futures)

Gamma: Has sign changes around barriers and will explode around them. Will make hedging very difficult, if not impossible depending on moneyness. Of course, you would need to buy/sell options in order to risk manage your Gamma from the structure

Vega: This is a tough one. Besides the question what kind of Vega we are speaking about, what really matters is that you have exposure across the whole term structure and need to measure this exposure. However, the exposures on different Vega buckets are so dynamic that Vega can be concentrated around one bucket today but then, depending on spot movement, may shift to other buckets tomorrow. So once you have flatten Vega in one specific bucket, you may be forced to buy your hedge back and buy/sell Vega in other buckets. Now you see, that all means crossing (costly) bid-offer spreads while hedging your Vega

Dividends: Same as vega except for the fact that the dividend market is clearly more illiquid, especially for single stocks. Typically, you will buy (exchange traded) dividend futures but then again, the quotes are so wide (if they exist at all) that you do not want to cross the spread permanently. But you will have to, because dividend sensitivity is as dynamic as Vega risk. It will change as spot moves. If no dividend futures exist, you can, e.g., try to flatten the risk via synthetics (calls and puts).

2nd order derivatives (Vanna, dividend sensitivity w.r.t to spot): These second order mixed partial derivatives are incredibly important as they will provide insight in how your (hard to hedge) Greeks Vega and Div sensitivity will change with spot. Therefore, traders will have a look at different scenarios: What will be my Vega if spot moves by +2%? What about dividend sensitivity then? You will, e.g., observe very intense convexity in your sensitivity towards dividends once spot moves significantly. How can you hedge this 2nd order Greek? Well, you could try to buy dividend options but there is actually no market for dividend options on single stocks. Alternatives? You could try an overlay hedge via Dividend Options in the Eurostoxx

There are so many other risks factors I even did not mention (third derivatives, EQ-IR correlation etc.). If you want to incorporate all risk factors and potential hedging costs, the fair value of the note would probably be infinity

Last but not least: Watch out for market directionality which is an issue for Index Autocallables rather than single stocks. As every issuer has the same risk position w.r.t Eurostoxx, they often need to start buying/selling Vega at the same time in order to hedge their books. In this case, you will have a hard time to find a reasonable quote in the interbank market as everyone needs to do the same thing (probably you will see very large bid-offer spreads). That's why Banks have a very critical impact to the volatility term structure of the Eurostoxx. This actually is a very famous example for what we call "Liquidity is never there when you need it most in hedging"

I know my answer is not a recipe, simply because there is no recipe to hedge this highly structured and dynamic risk product. It will differ from desk to desk depending on internal risk limits and trader psychology etc. What is more important is that you have a look at different scenarios which will lead to sharp changes in your greeks and find a framework and level of risk you are comfortable with as a trader.

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