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Regime-Switching Volatility and Risk-Neutral Option Prices

Article Quant Q&A · Author: Jason
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Summary

The document raises a modeling question about a two-regime option-pricing setup built around a risk-neutral GARCH process. The author fits crash and normal regimes and observes that options are more expensive in the higher-volatility crash regime. The question is how to reconcile this price difference with risk-neutral valuation and whether to add a relationship between returns and volatility.

The excerpt contains no answer or proposed calibration method, so it does not resolve how to specify regime transitions, risk premia, or return–volatility dependence. It does, however, identify an important distinction: risk-neutral valuation constrains discounted expected payoffs under the pricing measure, while regime-dependent volatility can still affect option values. Further conclusions about the model would require its exact dynamics and risk-neutral measure specification.

Key ideas

  • The author considers separate normal and crash regimes in a risk-neutral GARCH option model.
  • Higher volatility in the crash regime is associated with higher option prices in the stated setup.
  • Risk-neutral pricing constrains discounted expected payoffs but does not require equal option values across regimes.
  • The excerpt does not provide a solution or enough model detail to assess the proposed return–volatility relationship.

Tags

OptionsVolatilityDerivatives pricingRisk management
Full text
# Risk-Neutral Pricing with Regime Switching


# Risk-Neutral Pricing with Regime Switching












As the title suggests, I am currently trying to implement a dual regime-switching options pricing model. In its simplest form, I am fitting a risk-neutral GARCH(1,1) to a crash and normal regime. However, because the volatility in the crash regime is higher, I am finding that the options actually have higher prices in the crash regime. I am wondering how to reconcile this, or introduce a term that provides a negative relationship between returns and vol. But I don't know how to do this, as risk neutral pricing implies the discounted expected value of an option must be the risk-free rate. Thanks!

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.