Abstract
Empirical studies have concluded that stochastic volatility is an important component of option prices. We introduce a regime-switching mechanism into a continuous-time Capital Asset Pricing Model which naturally induces stochastic volatility in the asset price. Under this Stressed-Beta model, the mechanism is relatively simple: the slope coefficient—which measures asset returns relative to market returns—switches between two values, depending on the market being above or below a given level. After specifying the model, we use it to price European options on the asset. Interestingly, these option prices are given explicitly as integrals with respect to known densities. We find that the model is able to produce a volatility skew, which is a prominent feature in option markets. This opens the possibility of forward-looking calibration of the slope coefficients, using option data, as illustrated in the paper.
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Work of J.-P. Fouque was partially supported by NSF grant DMS-0806461.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Fouque, JP., Tashman, A.P. Option pricing under a stressed-beta model. Ann Finance 8, 183–203 (2012). https://doi.org/10.1007/s10436-009-0141-y
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DOI: https://doi.org/10.1007/s10436-009-0141-y
Keywords
- Stressed-beta model
- CAPM
- Stochastic volatility
- Regime-switching
- Option pricing
- Implied volatility skews
- Calibration