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I'm currently studying the pricing of autocallable options, especially snowball (accumalated coupon) and phoenix (accumlated coupon, but the coupon may also be autocalled if the underlying price touches the lower barrier) type with down-and-in put option embedded (The underlying asset could be single asset or a basket of assets), but I cannot find any materials talking about this topic.

I'm confused about the following questions:

  1. What are we pricing in this product in reality? The option premium given the coupon rate or the coupon rate that set the option premium to be zero?

  2. How to price the option? If Monte Carlo simulation is the only way for pricing, or we can find PDE and solve it numerically, or there are some other better ways?

  3. How is the coupon much higher than the other fixed-income products? And how to implement the hedging strategy for this kind of products?

Thanks!

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  1. Typically structures like this are traded as notes. They will be sold at a face value of 100%, where that is normally the combination of a zcb (ie 1y usd, say 97.5%), expected coupon (say +10%), short Knock In put (also knocked out by the autocall feature, say -8%), and some profit for the issuer (in this case, 100%-97.5%-10%+8%=0.5%). Sometimes these are traded is "swap format", where there is no notional exchange, instead libor+spread is paid on the notional (normally). Essentially, the short components are set so that they can fund some coupons.
  2. Montecarlo is normally the best way, the payoffs are very frequently tweaked, so you need the flexibility a "generic montecarlo" offers you to quickly add in these features as potential clients make up their minds on what they want.
  3. The coupons are higher when you are giving up something more likely to happen. The reality is that investors are somewhat unbothered by the volatility of the underlying, despite this being what sets the value of the Knock In put you nearly always sell in this family of structures. If it's traded on something like eurusd then you're looking at a single digit vol handle - that KI put is worth very little. If we trade it on natgas on the other hand, it's worth a lot, so you get a better coupon. In these cases, the barrier on the fx phoenix is probably going to have to be around 95% to get the same coupon as a 50% barrier on natgas. A 95% barrier is not terribly palatable to investors though, so it's not going to sell too well, so you lower the coupon and push the barrier farther away, to make it more attractive. To hedge them, you dump them into the rest of your portfolio and hedge the residual. Unfortunately, you'll not be able to hedge some of the risks with you end up with from your portfolio.
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  • $\begingroup$ Thanks! So the coupon rate is determined so that the price of the product is close to the face value? And currently I'm focusing on pricing this kind of product by solving PDE, but I don't know how to convert the features into boundary conditions, especailly the phoenix type. Do you have any ideas? $\endgroup$ – HenryLiu Aug 24 '19 at 12:40
  • $\begingroup$ I'm not aware that you can price these using pdes, since you have the final payoff being conditional on not having breached the autocsll barrier. $\endgroup$ – will Aug 24 '19 at 12:46
  • $\begingroup$ You may refer to this paper: link However, in the paper it does not consider the case where there exists a down-and-in put feather, instead, they simplify the situation. And I'm wondering how to transfer this feather into the boundary condition. I think only snowball type can be included, as the phoenix type is much more complicated. What's your opinion? $\endgroup$ – HenryLiu Aug 25 '19 at 15:57
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Recently because of some personal reason, I tried to price Snowball Autocall using MC and PDE, assuming single underlying.

12 months Snowball, Monthly autocall observations, Daily Put Down & In. Payoff:

  1. if Autocall, then 100% principal + autocall coupon
  2. if Knock in and No Autocall, then client lose because of short put
  3. if No autocall and No Knock in, them principal + bonus coupon.

so if you want to price it using PDE, one simple way I used is to price these 3 components and then combine it into one which is the fair price of Snowball. For 1) and 3), it's easy to deal with the boundary; for 2), since it's knock-in, we can price it using normal product - normal product with knock-out; for example, for simple down and in put, you can price a) a put, as well as b) a put with down and out, then a - b is what you want.

let me know if you need more information. I can share my code and simple report if you want.

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  • $\begingroup$ Did you account for the auto-call feature when pricing the barrier option as well? As you write this down & in put is conditional on no prior auto-call. If yes, then what benefit did you get from splitting the valuation into its components since the down & in put already needs to handle all the complexity of the auto-call feature? $\endgroup$ – LocalVolatility Feb 24 at 11:15
  • $\begingroup$ For your first question, yes, this put down and in is conditional on no prior autocall. As I say, splitting the payoff into 3 components then it's easy to handle the boundary. for 1), upbarrier => autocall coupon; for 3) upbarrier and downbarrier => zero; for 2), it's the same but a little bit more work. $\endgroup$ – wxu Feb 24 at 11:25
  • $\begingroup$ Even if the payoff is the combination of 1) and 3), (here we don't look at the short put), how do you deal with the downbarrier please? if we look at 3) only, then for downbarrier, we can simple set the option value to be 0; BUT if we look at the combination, then how to deal with the downbarrier since there might be autocall coupon in the future dates so option value is not 0? Hence, I just split it and price in this way; Luckily, I got same price as I did using Monte Carlo. I did this since it's an question after an interview. Need to solve ASAP. Happy to discuss if it can be solved directly $\endgroup$ – wxu Feb 24 at 11:30
  • $\begingroup$ If you have a new question, please post it as a new question. But maybe best not to put your interview questions on the internet. $\endgroup$ – Bob Jansen Feb 24 at 13:35
  • $\begingroup$ I don't have a question... I am just answering a question $\endgroup$ – wxu Feb 24 at 13:52

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