Information Content in Sneer Asymmetry: An Application to Out-of-Sample Implied Volatility Forecasting

ABSTRACT

The ad hoc Black-Scholes (AHBS) is one of the most widely used option valuation models among practitioners. The main contribution of this study is that we improve the out-of-sample forecast accuracy of the AHBS model. First, we make the empirical observation that the call and put sneers are discontinuous and have different slopes when moneyness is equal to one. Next, we propose a new data usage methodology that incorporates the information contained in the asymmetric response of the call and put sneers. Our new method provides more accurate out-of-sample forecasts for several intraday time horizons. Our results are robust across several dimensions, including time period, forecast horizon, moneyness, and model specification.

KEY WORDS:

• ad hoc Black-Scholes (AHBS)
• asymmetric volatility sneer
• data usage
• implied volatility

Acknowledgments

The authors thank Elisabeth Bui, Gideon Saar, and Haluk Ünal for comments on an earlier draft of this article. The authors thank seminar participants at the following conferences: FDIC 23rd Annual Derivatives Securities and Risk Management Conference in Arlington, VA; First International Conference on Derivative Securities and Markets in Beijing, China; and 8th Conference of the Asia-Pacific Association of Derivatives in Busan, Korea.

Notes

1. This is referred to as the “overfitting problem.”

2. http://www.pbs.org/newshour/bb/business/jan-june12/highhfrequency_03-15.html.

3. See Cremers and Weinbaum (2010) for a summary of this literature.

4. For example, see Brandt and Wu (2002), Christoffersen and Jacobs (2004a), Dumas et al. (1998), and Jackwerth and Rubenstein (2001).

5. Our filtering condition is as follows: (1) Option price is greater than 0.02; (2) OTM or ATM option prices are used; (3) arbitrage condition used is: Option price $\ge$ value of forward contracts; that is, (a) for a call option, $C\ge S-K{e}^{-r_f\tau }$ and (b) for a put option, $P\ge K{e}^{-r_f\tau }-S$

6. The stock and option market trade periods in Korea are as follows: (1) Stock market: synchronized bidding starts at 2:50 PM and closes at 3:00 PM, and (2) Option market: synchronized bidding starts at 3:05 PM and closes at 3:15 PM.

7. We refer to the ${\mathrm{A}\mathrm{H}\mathrm{B}\mathrm{S}}_{A3}$ model of Choi et al. (2012) as ${\mathrm{A}\mathrm{H}\mathrm{B}\mathrm{S}}_{Aq}$.

8. We extend our study to include a cubic model as we focus on short-horizon forecasts. Thus, the overfitting problem is not severe, implying there may be gains to increasing the order of the estimated polynomial.

9. The details of this method are explained in Choi et al. (2012).

10. When using the underlying stock, one needs to buy exp(−q(T−t)) units of the underlying stock at time t to have one unit of the underlying asset at time T, where q is the actual dividend yield of stock. However, if one uses the underlying forward, then one needs to buy exp(−r(T−t)) units of the underlying forward at time t to have one unit of the underlying asset at time T.

11. Results for each year individually are available in the working paper version on SSRN at http://ssrn.com/abstract=2180379.

12. The calculation use Equation 6; for example $0.367=\left(0.0581-0.0368\right)/0.0581=\left(MA{E}_{CON,q}-MA{E}_{CON,c}\right)/MA{E}_{CON{,}_q}$, while $0.102=\left(0.0325-0.0292\right)/0.0325=\left(MA{E}_{SEP,q}-MA{E}_{SEP,c}\right)/MA{E}_{SEP{,}_q}$.

13. Brzeszczynski and Welfi (2007) demonstrate that trading strategies based on cross-market transmission can be profitable.

Additional information

Funding

Youngsoo Choi is grateful to the Hankuk University of Foreign Studies for research support.