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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!

Jason
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    A warm welcome to Quant.SE - there is a rich literature on option pricing in the face of regime-switching behaviour - did you do some digging? – vonjd Apr 10 '19 at 07:27
  • Yep! I mainly tried Duan's paper: https://faculty.weatherhead.case.edu/ritchken/documents/regime_switching.PDF. But I couldn't really understand much of it :( – Jason Apr 10 '19 at 08:49
  • I guess my question stems from my misunderstanding of risk neutral pricing. For example, how are options pricing models able to capture the drop in price of a call option when the market crashes? In the risk-neutral world, stocks should still return the risk free rate, but vol is up so the call would be priced higher? so confused haha – Jason Apr 10 '19 at 08:56
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    Does this help: https://quant.stackexchange.com/a/8252/12 and https://quant.stackexchange.com/a/107/12 ? – vonjd Apr 10 '19 at 10:18
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    Would be nice if you could upvote the answers then :-) ... just saying ;-) – vonjd Apr 10 '19 at 15:19
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    honest pay for honest work :p – Jason Apr 10 '19 at 15:55

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