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Autocallable Pricing with Stochastic Volatility Models

Article Quant Q&A · Author: Van Tom
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Summary

The document asks whether a Black-Scholes equation with an issuer credit spread is suitable for pricing an autocallable structured product, and how to examine its Delta, Vega, and hedge. The response advises against using Black-Scholes as the pricing model for autocallables and says they are typically valued with Monte Carlo under a chosen market model. It identifies local volatility, stochastic volatility, and stochastic-local-volatility as possible model families, with SLV described as a standard choice.

The response also flags complications for basket autocallables, including decorrelation and bilocality. For risk sensitivities, it suggests bump-and-reprice when suitable pricing tools are available, while noting that Greeks and hedging can be challenging. The answer is brief: it gives no product payoff specification, model calibration procedure, numerical examples, or detailed hedge construction, so it serves as orientation rather than a complete pricing guide.

Key ideas

  • Monte Carlo is a valuation implementation and must be paired with an underlying dynamics model.
  • The response lists local volatility, stochastic volatility, and stochastic-local-volatility models for autocallables.
  • Basket autocallables introduce additional modeling issues related to dependence and decorrelation.
  • Bump-and-reprice is suggested for estimating Greeks when an appropriate pricing tool is available.
  • The discussion provides no detailed calibration or hedging recipe.

Tags

Derivatives pricingOptionsVolatilityRisk management
Full text
# Pricing of autocallable structured product


# Pricing of autocallable structured product












I'm looking at this paper: https://doi.org/10.1057/jdhf.2011.25, which is on pricing autocallable structured product. The author uses the Black-Scholes equation to describe the product's dynamic value, that is $$\frac{\partial V}{\partial t}+\frac{1}{2}\sigma^2S^2\frac{\partial^2V}{\partial S^2}+(r-q)S\frac{\partial V}{\partial S}-(r+CDS)V=0, $$ where $CDS$ is the credit default swap spread of the issuer and $V$ is the product value. My question is why it is valid to use BS model to price this kind of structured product?

And, if possible, could anyone tell me what should I do if I want to find out what the Delta and Vega profile of this product looks like? Furthermore, how am I supposed to hedge this product?

I am quite new to quant finance and if there is any mistake in my description, please point it out. Thank you!

## Answer by AKdemy (score 4)

https://quant.stackexchange.com/a/63778

Short answer: Do not use BS for AC

Long answer: There are plenty of question here about this already. Typically it is priced via Monte Carlo but that is not a model, just an implementation of some model (LV, SV, SLV).

Standard would be to use SLV but even there are issues with decorrelation and bilocality if you look at basket AC (which are very common).

There is also an interesting (fun) tweet about AC hedging.

Edit: for Greeks, without a sophisticated tool from a bank or vendor, you will not find anything better than this in my opinion.

With a proper tool, it will be bump and reprice. The tweet I included above explains some of the problems you will face with regards to Greeks (or hedging).

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.