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I understand the structure of the autocall, how they're priced and their contingent coupons. What I'm not completely clear on is the difference between a "vanilla" Autocall and a Phoenix Autocall. From what I gathered reading some papers and bank brochures is that an Autocall accumulates the coupons and pays them at maturity while the Phoenix Autocall pays them periodically whenever the barrier condition is observed. Is this correct or am I missing something?

Thanks.

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For "Classic Autocall" or "Athena", the coupons are indeed accumulated and paid on the event of autocall, either pre-maturity or at maturity (but for the later it will not be called autocall). So only one barrier level (without considering the down-and-in put), the one of the autocall, or we could say the autocall barrier and coupon barrier are equal.

For Phoenix, they have typically two barriers (without considering the down-and-in put), the one of the autocall and the one of the coupons. For example, it might be the case that we receive a coupon without autocall at each observation date. One precision, for Phoenix, coupons can be also accumulated and paid at first coupon barrier trigger if they have "memory effect". In that case, they will be accumulated as Athena but their payment will not be made at the condition of an autocall.

Can you share some books/paper you know about autocall pricing ?

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  • $\begingroup$ Thanks for the answer ! You said "but for the later it will not be called autocall" what would it be called then? And yes of course, I started by reading Bouzoubaa's "Exotic Options and Hybrids", there's a whole chapter on Autocalls then looked for Longstaff-Shwartz Monte Carlo method for Autocalls. I then looked at some Python implementations the following one is the most "functional" that I found (using Monte Carlo with Heston stochastic volatility model): mikejuniperhill.blogspot.com/2019/11/… $\endgroup$
    – Metrician
    Oct 14, 2020 at 17:22
  • $\begingroup$ This paper was interesting too (especially the papers referenced in it): math.uni-frankfurt.de/~harrach/publications/StableDiffs.pdf $\endgroup$
    – Metrician
    Oct 14, 2020 at 17:25
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    $\begingroup$ Thank you for the references ! It will just be called "Maturity". My point was just that the coupon(s) can also be paid at maturity for both products. Usually we think of the coupons for an Athena as something that can be paid in the event of autocall, but it can be also at last observation date (maturity). $\endgroup$
    – Pierre_G
    Oct 15, 2020 at 15:16

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