Page 48 - CCFA Journal - Sixth Issue

Quant Corner 数量分析 加中金融

Table 1: The log-moneyness

log-moneyness: log(S(t)/K), S(t)=1550
-0.91629 -0.69315 -0.28768 -0.16252 -0.10536 -0.05129 -0.02532
0.157184 0.024693 0.04879 0.09531 0.182322 0.262364 0.405465

Table 2: SPX market implied volatilities

T market Implied volatilities
0.587221 0.513714 0.32232 0.254947 0.222083 0.18944 0.173213
0.136986
0.157184 0.127565 0.109529 0.115812 0.135668 0.174655 0.249074
0.338887 0.304301 0.240475 0.220919 0.212158 0.204045 0.200229
3.002739
0.196574 0.193079 0.189748 0.173241 0.165596 0.157567 0.160559
0.315779 0.29452 0.253342 0.240236 0.234281 0.228707 0.22606
6.002739
0.223507 0.221046 0.218676 0.214211 0.206364 0.199922 0.190868

Table 3: the calibrated parameters at the different slices

T a b  m 

0.136986 -0.003856 0.035390 -0.504754 0.03269058 0.1818372
3.002739726 -0.01780142 0.19989018 -0.5153762 0.19212407 0.5347478

6.002739726 0.0081896 0.30771102 -0.25647679 0.49910294 0.65109202

Figure 1: S&P implied volatility surface Figure 2: SVI model vols vs. market implied vols.

0.32
SVI Model
Market Implied Vol
0.3

0.28
0.26
Implied Volatility
0.24
0.22

0.2

0.18
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
Log-moneyness

Figure 3: SVI model vols vs. market implied vols. Figure 4: SVI model vols vs. market implied vols.

0.6 SVI Model
0.55 Market Implied Vol

0.5
0.45
Implied Volatility 0.35
0.4
0.3

0.25

0.2
0.15

0.1
-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8
Log-moneyness

CCFA JOURNAL OF FINANCE February 2022
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