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A volatility smile-based uncertainty index

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Abstract

We propose a new uncertainty index based on the discrepancy of the smile of FX options. We show that our index spikes near turbulent periods, forecasts economic activity and its innovations hold a significant and negative equity premium. Unlike other uncertainty indexes, our index is supported by equilibrium models, which relate the difference of options prices across moneyness to uncertainty. Moreover, our index is based on investment decisions, can be easily and continuously updated and is comparable across countries.

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Notes

  1. Bakshi et al. (2003) show that the risk-neutral expected value of the square return of the underlying is the integral of the volatility surface.

  2. Other papers have pointed out the lack of uncertainty sources in the Black–Scholes model. For example, Kelly et al. (2016) assert when there is no political uncertainty, the price of options is governed by the Black–Scholes formula. However, when uncertainty is present, implied volatility does not equal expected volatility.

  3. For example, Brazil has at least five major newspapers, but EPU only analyzes Folha de São Paulo.

  4. See Ahir et al. (2018)

  5. Bakshi et al. (2003) derive a method to compute the model-free volatility from a cross-section of calls and puts prices. They show that the variance of squared returns is given by the integral of calls and puts prices over the strike price. This integral can be computed by numerical procedures.

  6. On August 8, 2011 US and global stock markets crashed following the credit rating downgrade of the United States sovereign debt. The S&P Index dropped 6.66% and Dow Jones plummeted 7.05%.

  7. For Chile, the policy uncertainty website hosts two EPU indexes, both based on Cerda et al. (2017). Although these authors follow the same index construction methodology of Baker et al. (2016), they stress that, as Chile is heavily exposed to the world economy, Chilean newspapers carry many articles about economic matters that are not necessarily domestically related. Thus Cerda et al. (2017) construct two indexes: one that considers articles pertaining to economic policy uncertainty, and another that considers the subset of articles pertaining to domestic Chilean sources of economic policy uncertainty. The first one, labeled EPU index, is a measure of total economic policy uncertainty in Chilean newspapers, and the second one, EPUC index, is a measure of domestic policy uncertainty in Chilean newspapers only. In this work, we analyze the EPUC. Since the correlation between the two indexes is 96%, the results are very similar and it does not matter which index we use.

  8. As an alternative to FX options, we may use stock index options. However, the liquidity of the latter is lower.

  9. The Hausman (1978) test considers random effects uncorrelated with the explanatory variables as the null hypothesis (random effects are preferred) and difference between random and fixed effects estimates of the coefficients as test statistic. Applied to our data base, the test do not reject the null hypothesis.

  10. In order to allow for heteroscedasticity and correlation in the error term, we also compute cluster-robust standard errors as proposed by Cameron and Miller (2015). The results is very similar to the ones obtained using OLS. Thus we do not report them here.

  11. See, for instance, Epstein and Wang (1994) and Chen and Epstein (2003).

  12. We use the following stock indexes: Ibovespa for Brazil, NIFTY 50 for India, S&P/BMV IPC for Mexico, MOEX for Russia and S&P/CLX IPSA for Chile.

  13. To remove serial correlation in the market return, we also run regressions with autoregressive terms. Qualitatively, the results are unchanged.

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Correspondence to José Valentim Machado Vicente.

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Vicente, J.V.M., Marins, J.T.M. A volatility smile-based uncertainty index. Ann Finance 17, 231–246 (2021). https://doi.org/10.1007/s10436-021-00384-6

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