Structured products
What an autocall is really worth
A Phoenix note quotes a coupon of 7% a year and is sold as income. Price it and you find something different: most investors are repaid within a few quarters having collected two or three coupons, and the ones who are not repaid early are the ones holding a position that has already fallen a long way.
The structure is simple to state. Every quarter the underlying is observed. Above the coupon barrier a coupon is paid, and missed coupons are carried forward and paid in full the next time the barrier is met. Above the autocall barrier the note redeems early at par and everything stops. If it survives to maturity, capital comes back in full provided the underlying is above the capital barrier, and is indexed to the underlying otherwise.
That last clause is the whole product. The investor has sold a down-and-in put, and the coupon is the premium.
Loading the model
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What to look at
Drag the volatility up. The price falls. That is the single most counter-intuitive thing about the product for anyone used to options: the investor here is short volatility, because the put they sold is worth more when the market is nervous, and the coupon is fixed.
Drag the spot down towards 60. The value collapses far faster than the spot does. Between the coupon barrier and the capital barrier the note loses its income and keeps its downside, which is the worst place on the curve to be holding it.
Compare the mean and the median coupon. At the default settings the mean is around 7.6 points and the median around 3.5. The mean is pulled up by the minority of paths that survive for years and keep paying. A term sheet quotes the coupon rate, not this distinction.
Where this model stops
The underlying follows flat Black-Scholes: one volatility, one rate, a continuous dividend yield. That is enough to get the shape of the payoff right and to reason about the risk, and it is not what a desk quotes on.
The gap that matters is skew. The capital barrier sits far out of the money, precisely where index puts are most bid up, so a single flat volatility systematically understates how expensive that downside is. A flat-vol model makes an autocall look better than it is. The options page shows the skew this model is ignoring, measured from a live option chain.
Full source, including the eleven tests that check the engine against closed-form prices, at github.com/Nicolas8330/structured-products-pricer.