Pricing Options When Underlying Data Are Sparse and Volatile

Summary

The document considers pricing American and European options on an unusual underlying with sparse, interpolated observations, very high volatility, and unusually strong recent returns. With no comparable traded options or clearly correlated assets, the questioner has tried Heston stochastic volatility but found parameter calibration from underlying prices unstable. The central challenge is producing a reasonable estimate without market option quotes to anchor the model.

The response recommends first analyzing the underlying itself and decomposing it into components that have more liquid substitutes. Those substitutes can provide a better-supported baseline for the pricing model. It also suggests accounting for illiquidity through a premium and monitoring the model as liquidity and underlying characteristics change. This is a qualitative workflow rather than a specified valuation technique: it gives no decomposition, premium calculation, calibration procedure, or validation results. The reliability of any estimate remains dependent on finding meaningful proxies and monitoring how well they continue to represent the underlying.

Key ideas

• Sparse underlying data and unstable volatility calibration make option valuation uncertain.
• The response recommends analyzing the underlying and identifying components with liquid substitutes.
• Liquid proxies can provide a more data-supported baseline for pricing.
• An illiquidity premium and ongoing model monitoring are suggested.
• The document gives no formula or evidence for selecting proxies or sizing the premium.

Tags

# Pricing an option with sparse data, high underlying volatility and returns


# Pricing an option with sparse data, high underlying volatility and returns












I'm currently pricing American and European options on an underlying with sparse data (interpolated), high annual volatility and returns over the last year around 300%. The product isn't similar to anything quoted in the market at the moment, nor does the underlying have anything particularly correlated to it. Does anyone have any suggestions on how to go about this please? I've started with Heston's stochastic volatility model but as there's no option data available and calibrating it on price data doesn't seem to work due to the high sensitivity of the parameters probably so won't give such an accurate price. I realise this will be hard to get a good price on but need a decent idea of what it should be. Thanks!

## Answer by chjortlund (score 1)

https://quant.stackexchange.com/a/40339

I would take one step back and focus on the underlying.

Dissecting the underlying to identify components that you can find replacements with liquidity, that can be used in your pricing model. This will give you a baseline, with more data points. Since this sounds like some really exotic stuff, add a nice liquidity premium (as also suggested by Antoine Conze, in the comments of the question). Doing it this way obviously require good monitoring of your model over time, as the model fit might slide as the liquidity and 'characteristics' change over time.

Once you have a good / better pricing source, your options opens up and it's time to start the option modeling (pardon the pun).

In general dealing with modeling, there's the saying: Garbage in, garbage out.

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