A computation of implied volatility leveraging model-free option-implied information

Figures & data

Figure 1. Comparison of the implied volatility obtained from the three approaches for SPX call and put options that mature on 21 November 2003.

Figure 2. Comparison of the IV smirk for out-of-the-money options obtained from the three approaches that mature on 21 November 2003.

Table 1. Parameter estimation results on the market data of SPX options (standard) maturing on 17 February 2023, 17 March 2023, 21 April 2023, 19 May 2023, 21 July 2023, and 19 January 2024. DF_zx represents the discount factor obtained via the approach in (Zhang & Xiang, 2008) and is calculated using the one-month, two-months, three-months, four-months, six-months and one-year treasury yield curve rates given respectively by 4.69%, 4.64%, 4.72%, 4.75%, 4.8% and 4.68%. DF_zx and DF_km are the implied discount factors obtained using the approach in the Cboe paper and our proposed approach, respectively

Time to maturity	$F_0^{zx}$	DFzx	$F_0^{cp}$	DFcp	$F_0^{km}$	DFkm
28	3977.31	0.9964087	3977.20	0.9961106	3977.16	0.9964120
56	3985.96	0.9929064	3986.09	0.9923645	3986.02	0.9925000
91	4000.15	0.9883013	4000.33	0.9879649	3999.92	0.9880973
119	4009.70	0.9846330	4010.01	0.9845612	4009.79	0.9844826
182	4034.47	0.9763499	4035.35	0.9755800	4035.35	0.9763463
364	4106.03	0.9544006	4105.81	0.9520073	4105.95	0.9529330

Figure 3. Comparison of the IV smirk for out-of-the-money options obtained from the three approaches for SPX call and put options that mature on 17 February 2023.

Figure 4. Comparison of the IV smirk for out-of-the-money options obtained from the three approaches for SPX call and put options that mature on 17 March 2023.

Figure 5. Comparison of the IV smirk for out-of-the-money options obtained from the three approaches for SPX call and put options that mature on 21 April 2023.

Figure 6. Comparison of the IV smirk for out-of-the-money options obtained from the three approaches for SPX call and put options that mature on 19 May 2023.

Figure 7. Comparison of the IV smirk for out-of-the-money options obtained from the three approaches for SPX call and put options that mature on 21 July 2023.

Figure 8. Comparison of the IV smirk for out-of-the-money options obtained from the three approaches for SPX call and put options that mature on 19 January 2024.

Zhang, J. E., & Xiang, Y. (2008). The implied volatility smirk. Quantitative Finance, 8(3), 263–284. https://doi.org/10.1080/14697680601173444

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