The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well

By Peter F. Christoffersen, Steven Heston, Kris Jacobs. Management Sciences, 2009

596 citations recorded by the source corpus.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/997fa2863146a1296ddfb95d623da690479b12c7

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Citations in the corpus

Lifting the Heston model (2018, methodology): “‡ The double Heston model is defined in Christoffersen et al. (2009) as follows: dSt = St (√ U1 t dB 1 t + √ U2 t dB 2 t ) , (11)”
Volatility dynamics for the S&P 500: Further evidence from non-affine, multi-factor jump diffusions (2012, methodology): “Christoffersen et al., 2010) by using Wednesday option price data only. Then calculating implied volatility root mean square error (RMSE) over all options and over the entire out-of-sample period yields the results displayed in Table 5. The RMSE measures the dispersion of the model prices about the ”
The Risk Premia Embedded in Index Options (2015, methodology): “These features are precluded in the typical (14)Instead, our specification shares critical features with the discrete-time GARCH type model of Christoffersen et al. (2012).”
Resolution of Policy Uncertainty and Sudden Declines in Volatility (2017, unknown): “To ensure the tractability of this general non-affine class of models, we assume that the underlying N-dimensional factor Xt follows a multivariate affine process, similar to the affine term structure model discussed in Dai and Singleton (2000), but allowing for jumps, e.g., as in Duffie et al. (200”
Heston stochastic vol-of-vol model for joint calibration of VIX and S&P 500 options (2017, background): “Generalization 4 It should be straight forward to adapt the machinery developed here to deal with the two-factor model of Christoffersen et al. (2014): ⎧⎪⎨⎪⎪⎪⎩ dSt = (r − q)St dt + √ V (1) t St dW S1 t + √ V (2) t St dW S2 t , dV (1) t = κ1(m1 − V (1) t )dt + η1(Y ε t , Z δ t ) √ V (1) t dW V 1 t , ”
Stochastic Volatility of Volatility and Variance Risk Premia (2013, unknown): “They form a very natural generalisation of the classical one factor SV models and are very successful in the context ofoption pricing, see e.g. Christoffersen et al. (2009, 2008).”
Tail risk premia and return predictability (2014, background): “…while one-factor models, as in, e.g., Pan (2002), Broadie, Chernov, and Johannes (2007), and SantaClara and Yan (2010), are quite common, the empirical evidence in Bates (2000) and Christoffersen, Heston, and Jacobs (2009), among others, clearly suggests that multiple volatility factors are needed.”
Riding on the smiles (2011, unknown): “In fact, Christoffersen et al. (2009) describe the leverage by a stochastic process involving both factors.”
Forecasting with Option-Implied Information (2012, unknown): “Bates (2000) and Christoffersen, Heston, and Jacobs (2009) keep the structural parameters fixed over time.”