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JTDerp


Total Posts: 38
Joined: Nov 2013
 
Posted: 2017-01-03 20:23
"Abstract: In this article, we consider a model of time-varying volatility which generalizes the classical Black-Scholes model to include regime-switching properties. Specifically, the unobservable state variables for stock fluctuations are modeled by a Markov process, and the drift and volatility parameters take different values depending on the state of this hidden Markov process. We provide a closed-form formula for the arbitrage-free price of the European call option, when the hidden Markov process has a finite number of states. Two simulation methods, the discrete diffusion method and the Markovian tree method, for computing the European call option price are presented for comparison." ( link )

Topically-speaking, there's a similar paper titled "Option Pricing In a Jump-Diffusion Model With Regime Switching." ( link )

If you've happened to test an option pricing model with 'regime switching' for the volatility estimate, did you see much improvement in capturing small-scale changes versus a stochastic volatility model?


Side note: An old(ish) thread in Pricing & Modeling subforum, 'Markov Chains for Price Modeling' discussed HMMs and Kalman filters used to forecast equity prices, and I found the several comments (plus some code) by jslade useful at the high-level conceptuals.

The clouded mind seeks; the emptied mind finds.

jslade


Total Posts: 1060
Joined: Feb 2007
 
Posted: 2017-01-06 07:32
These are interesting papers JTDerp, but please don't cite me as someone dispensing any great secrets.

I am a humble code merchant who provides software to traders and whoever else will pay me. That said, people do use these ideas all over the place. Most people just use Kalman filters, but HMMs have their place.

"Learning, n. The kind of ignorance distinguishing the studious."

pj


Total Posts: 3307
Joined: Jun 2004
 
Posted: 2017-01-06 10:52
> I am a humble code merchant
Nice humblebrag

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

sigma


Total Posts: 105
Joined: Mar 2009
 
Posted: 2017-01-06 22:56
>> If you've happened to test an option pricing model with 'regime switching' for the volatility estimate, did you see much improvement in capturing small-scale changes versus a stochastic volatility model?

I am not sure if there any use in "an option pricing model" using a regime-switching model. For me it is mostly about the option value or its relative value to market price. An n-state regime switching model has n volatilities conditional on the regimes. It's a good model for the real-world modeling, but it is not a model for "small-scale changes"
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