Replicating Autocall Coupons and Down-and-In Puts with Vanilla Options
Summary
The document breaks a single-asset autocall payoff into early-redemption coupon digitals and a maturity down-and-in put. It explains how call spreads with strikes around a digital barrier can approximate the coupon component. For an autocall seller, placing the spread just below the barrier makes the replication conservative: the spread can pay in a region where the digital pays nothing, while matching the digital outside that region.
For the down-and-in put, the note describes combining put spreads with an additional put at the barrier. Its example shows the portfolio matching the put payoff at selected levels while paying less within part of the barrier region, so it is cheaper and conservative for a seller who buys the put. The spread width controls this conservatism. These are payoff approximations, not exact replications across every level; the explanation omits pricing, path dependence before maturity, transaction costs, and practical hedging details.
Key ideas
- An autocall payoff can be separated into early-redemption digital coupons and a maturity down-and-in put.
- A digital coupon can be approximated with a call spread whose strikes lie close to the trigger barrier.
- A seller can position a call spread below the digital barrier to create a conservative coupon hedge.
- A down-and-in put can be approximated using put spreads and an additional put at the barrier.
- Wider put spreads make the illustrated down-and-in put hedge more conservative.
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Full text
# Autocall replication using vanilla options # Autocall replication using vanilla options How to replicate a single asset auto call through call spreads ? Single asset auto call: Definition and pay off profile is clear. Just want to know the method to replicate it through vanilla call spreads. ## Answer by Alex (score 3) https://quant.stackexchange.com/a/40205 You can only replicate the digital part with call spreads. To be clear, let's decompose the Autocall as: - the first part made of digital options (paying the coupons in case of early redemption) - the second part made of a down and in put (this is the part responsible for the fact that, at maturity, you benefit from a conditional capital protection as long as the underlying's final level is above the DIP barrier; otherwise, capital loss equal to underlying's loss Replication of the first part: The digitals can be replicated using call spreads. It can be shown that a digital is equal to a call spread with the width between the strike tending towards 0. The more aggressive you are, the tighter the width between the strikes of the call spread. From the seller's point of view of the Autocall, you are short the digitals. So, when building your replication, you want to price (sell) the digitals at a price slightly higher than the actual "true" price of the digital. You do that with the spread "on the left" of the digital barrier. Example: consider a digital option paying a 10% coupon if underlying > 100% ==> replication by the Autocall seller : 5 * call spread 98%-100% (if spot below 98%, then payoff = 0 just as for the digital; same thing if above 100%; between 98% and 100%, the call spread will pay something positive whereas digital pays 0 hence it is conservative from the seller's point of view). Replication of the second part: Via a combination of put spreads + put (I can develop that one if you'd like) A good reference for the above: Exotic Options and Hybrids: A Guide to Structuring, Pricing and Trading from Mohamed Bouzoubaa Edit: down and in put replication From the Autocall seller's point of view (who is buying the down and in put): it is replicated by a certain number of put spreads + one more put. For example, let's say you want to replicate an at-the-money down and in put with barrier at 70% - so, if the spot at maturity decreased by at least 30%, the DIP behaves like a vanilla ATM put, otherwise it pays 0 at maturity. You can replicate this with 10 put spreads 67%-70% (i.e long 70% strike puts, and short 67% strike puts) + long 1 put with strike 70%. - If at maturity the spot is at 71%, the DIP should pay 0 and the replicating portfolio pays 0 as well - if the spot is at 67%, the DIP should pay 33% and the replicating portfolio pays 10*3% (from the put spreads) + 3% (from the additional put) = 33% (so same as DIP, all good) - if at maturity the spot is between 67% and 70%, say 68%, the DIP should pay 32% but the replicating portfolio pays 10*2% (put spreads) + 2% (additional put) = 22% < 32% We see than in all cases, the replicating portfolio either pays the same amount or a smaller amount than the down and in put. Hence the replicating portfolio is a bit cheaper than the real DIP, hence it is conservative from the Autocall seller's (i.e. from the DIP's buyer) point of view. The larger the width between the 2 strikes of the put spreads (and the smaller the number of put spreads) (for example long 6 put spreads 65%-70% + long 1 put with strike 70%), the more conservative the replicating portfolio is.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.