MaxVaR for non-normal and heteroskedastic returns¶

Bhattacharyya, Malay; Misra, Nityanand; Kodase, Bharat

doi:10.1080/14697680802595684

“…2 Notable exceptions are Kritzman and Rich (2002), Boudoukh et al (2004), Rossello (2008), Bhattacharyya et al (2009) and Bakshi and Panayotov (2010). The intra-horizon risk was originally studied in Stulz (1996), in the context of cash flow risk in corporate risk management.…”

Section: Introductionmentioning

confidence: 99%

“…Kritzman and Rich (2002) and Boudoukh et al (2004) considered the Black-Scholes model and derived a closed-form expression for the probability of an interim loss of a given magnitude. Rossello (2008) and Bhattacharyya et al (2009) studied the first-passage distribution in the doubleexponential jump-diffusion setting and a GARCH model with non-normal innovations, respectively, using Monte Carlo methods. 4 We thereby generalize the disentanglement result obtained by Leippold and Vasiljević (2017).…”

Section: Introductionmentioning

confidence: 99%

Option-Implied Intrahorizon Value at Risk

Leippold

¹

,

Vasiljević

²

2020

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In this paper, we theoretically and empirically study the intra-horizon value at risk (iVaR) in a general jump-diffusion setting. We propose a new class of models of asset returns, the displaced mixed-exponential model (D-MEM), which can arbitrarily closely approximate finite-and infiniteactivity Lévy processes. We then derive analytical results for the iVaR and disentangle, in a theoretically consistent way, the jump and diffusion contributions to the intra-horizon risk. We estimate historical and option-implied VaR and iVaR for several popular jump models using the S&P 100 index and American options. Empirically disentangling the contribution of the jumps from the contribution of the diffusion, we conclude that jumps account for about 90 percent of the iVaR on average. Our backtesting results indicate that the option-implied estimates are much more responsive to market changes than their historical counterparts, which perform poorly.Keywords: value at risk, intra-horizon risk, displaced mixed-exponential model, first-passage disentanglement, option-implied estimates.JEL classification: G01, G11, G13, C51, C52.3 Finally, we expand on the empirical analysis of Bakshi and Panayotov (2010) by providing a backtesting study for historical and option-implied VaR and iVaR figures across different models.While we do find differences of iVaR and VaR violations across different models, these differences are small compared to those between historical and option-implied VaR and iVaR figures. Our backtesting procedure shows that, irrespectively of the model used, the option-implied VaR and iVaR estimates are considerably more perceptive and responsive to asset price fluctuations, and they produce more accurate results than do the historical estimates. For this reason, we conclude that whenever options data is available, the option-implied estimates of risk measures provide additional information that should not be neglected.The paper is structured as follows. In Section 2, we introduce the D-MEM class of exponential Lévy models and connect the VaR and iVaR to the payoffs of European and one-touch digital puts. In Section 3, we describe the data treatment and summarize the calibration and the models' performance results. Our empirical findings for the VaR and iVaR are discussed in Section 4. We conclude in Section 5.

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“…2 Notable exceptions are Kritzman and Rich (2002), Boudoukh et al (2004), Rossello (2008), Bhattacharyya et al (2009) and Bakshi and Panayotov (2010). The intra-horizon risk was originally studied in Stulz (1996), in the context of cash flow risk in corporate risk management.…”

Section: Introductionmentioning

confidence: 99%

“…Kritzman and Rich (2002) and Boudoukh et al (2004) considered the Black-Scholes model and derived a closed-form expression for the probability of an interim loss of a given magnitude. Rossello (2008) and Bhattacharyya et al (2009) studied the first-passage distribution in the doubleexponential jump-diffusion setting and a GARCH model with non-normal innovations, respectively, using Monte Carlo methods. 4 We thereby generalize the disentanglement result obtained by Leippold and Vasiljević (2017).…”

Section: Introductionmentioning

confidence: 99%

Option-Implied Intra-Horizon Value-at-Risk

Leippold

¹

,

Vasiljević

²

2017

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In this paper, we theoretically and empirically study the intra-horizon value at risk (iVaR) in a general jump-diffusion setting. We propose a new class of models of asset returns, the displaced mixed-exponential model (D-MEM), which can arbitrarily closely approximate finite-and infiniteactivity Lévy processes. We then derive analytical results for the iVaR and disentangle, in a theoretically consistent way, the jump and diffusion contributions to the intra-horizon risk. We estimate historical and option-implied VaR and iVaR for several popular jump models using the S&P 100 index and American options. Empirically disentangling the contribution of the jumps from the contribution of the diffusion, we conclude that jumps account for about 90 percent of the iVaR on average. Our backtesting results indicate that the option-implied estimates are much more responsive to market changes than their historical counterparts, which perform poorly.

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“…Another contribution of this study included two different estimation methods for the skewed t model in a GARCH setting as Bhattacharyya et al (2008Bhattacharyya et al ( , 2009 implemented for the Pearson type IV (PIV) distribution using developed country stock index data. In this study, I extend their approach to the skewed t distributed errors.…”

mentioning

confidence: 99%