Pricing Turbo Warrants as Resetting Barrier Options
Summary
The document considers whether a turbo warrant should be modeled as a down-and-out barrier option. The described contract becomes worthless when the underlying reaches a barrier, while its quoted price is tied to the difference between the underlying price and a financing level, adjusted by a ratio. The financing level accrues interest, causing both it and the barrier to rise over time.
The answer suggests viewing the product through the framework of cliquet or ratchet options: a sequence of forward-start options with periodically resetting strikes, where an early knock-out ends the later option exposures. It contrasts this upward reset with warrants whose strikes reset downward, while noting that cap-and-floor assumptions in other analyses may not fit. The entry offers a conceptual analogy, not a full valuation derivation. It gives no calibrated inputs, pricing results, or explicit Greeks, so further modeling would need to specify reset mechanics, barrier behavior, and contract terms.
Key ideas
- The warrant price is described as the underlying minus a financing level, adjusted by a ratio.
- Interest accrual raises the financing level and associated barrier over time.
- A resetting warrant can be viewed as a sequence of forward-start options.
- A knock-out can extinguish subsequent option exposures in this interpretation.
- The document provides a conceptual framework rather than a complete pricing model or Greeks.
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Full text
# Can "Turbo warrants" be priced using the Black & Scholes model?
# Can "Turbo warrants" be priced using the Black & Scholes model?
I am trying to model the pricing of an asset called a "Turbo warrant", which to me looks a lot like a Down-and-Out Barrier option with leverage. When the price of the underlying asset hits a certain barrier (B), the contract becomes worthless. The issuer of these Turbo warrants indicates that their price is calculated as follows: $$P = \frac{S - F}{ratio} $$
(Note: the ratio is used in case the price of the underlying asset is high, like in the case of Amazon stock which is around $3,000. The ratio is often 10 or 100)
But I wonder if this is the correct way to model the price of these options. I do not fully understand why the Black and Scholes model or a variant is not used (like is sometimes used with Barrier options), so that Greeks can also be calculated for these Turbos. Could someone explain?
Edit
To be entirely complete, the issuer of the Turbo charges an interest of around 2% on the financing level $F$, which is paid daily by increasing the level of $F$ and consequently $B$ everyday. So that:
$$ F(t) = F(0) (1+r)^t$$
## Answer by kurtosis (score 1)
https://quant.stackexchange.com/a/55893
This looks similar to a cliquet or "ratchet" option: an option with a strike price which resets occasionally. The Wikipedia definition of a cliquet is a bit too restrictive since one of the most common uses of such options was by Japanese firms which issued warrants and convertible bonds in the 1990s after the implosion of the Japanese real estate bubble. Also, beware since many analyses look at cliquet options with caps and floors.
The Japanese warrants and convertible bonds had strikes which could only reset downward (often to ATM or 10%-15% ITM). This increased the probability of expiring ITM. Here, your strikes reset upward. Both can be handled with the same perspective: treat the option as a series of forward-start options where early exercise extinguishes the later options.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.