A Put on the Time-Weighted Average Price Within a Price Band

Summary

The document defines a path-dependent put payoff based on the underlying asset’s average price during periods when its price remains between a lower and upper boundary. The averaging interval is therefore conditional: time spent outside the band does not contribute to either the accumulated price or the time used to normalize the average. The payoff is the positive part of the strike minus that conditional average.

This resembles an Asian put, but the price band makes the observation period depend on the asset’s path. The document asks what the option is called and provides no proposed name, valuation method, example, or market convention. It also does not specify how to handle paths that spend no time inside the band, an edge case that would need a payoff convention before implementation or pricing.

Key ideas

• The payoff depends on the asset’s average price while it lies inside a specified band.
• Time outside the band is excluded from both the price accumulation and the averaging duration.
• The payoff is put-like, taking the positive part of the strike less the conditional average.
• A zero duration inside the band requires an additional convention not given in the definition.

Tags

# Who knows what the name of this put option is? It's like a conditional Asian option, but with an upper boundary


# Who knows what the name of this put option is? It's like a conditional Asian option, but with an upper boundary












Let $a < K < b$, then this option formula is:

$$\left(K - \frac{1}{\int_0^T\mathbb{1}_{\{a<S_t<b\}}dt}\int_0^TS_t\mathbb{1}_{\{a<S_t<b\}}dt\right)^{\large+}$$

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.