South Korea KOSPI 200 Volatility Index (V-KOSPI 200)

KRVKOSPI is the official V-KOSPI 200, the thirty-day model-free implied volatility of the KOSPI 200 reported in annualized volatility points. Its estimand is a risk-neutral variance recovered from a static portfolio of out-of-the-money option prices by the state-price spanning of Breeden and Litzenberger (1978) and the twice-differentiable-payoff replication of Carr and Madan (2001), in the fair-variance-swap tradition of Demeterfi, Derman, Kamal, and Zou (1999). It is specifically the VIX-style log-contract form, whose strip weights each strike by one over its squared price, so it summarizes the risk-neutral distribution of the market's one-month return through the log-contract second moment (Britten-Jones and Neuberger 2000; Jiang and Tian 2005; Bakshi, Kapadia, and Madan 2003). KRED republishes the official published close verbatim with no transformation, so KRVKOSPI is the official index and not a KRED estimate.

KRVKOSPI is a distinct estimand from the model-free KRSVIX, and neither is a re-labeling of the other. The official V-KOSPI 200 is the log-contract fair variance that weights each strike by one over its squared price, whereas KRSVIX is KRED's equal-dollar SVIX of Martin (2017), whose strip weights every strike equally in dollars and prices the simple rather than the log return. The two therefore measure different functionals of the same KOSPI 200 option surface, so under log-normality the equal-weight SVIX sits above the VIX-type index and the two carry genuinely different numbers, a weighting difference and not an error of either gauge (Whaley 2000; Whaley 2009; Carr and Wu 2006).

Because KRVKOSPI and KRSVIX interrogate the same-underlying KOSPI 200 risk-neutral variance and differ only in strike weighting, the two are strongly correlated and must not be read as independent or mutually corroborating gauges of that variance. The official index is also continuous where KRSVIX is honestly gapped, since the official construction supplements its own thin option wings by a Black-Scholes and put-call-parity calculation within the recipe, whereas KRSVIX carries authentic traded prices only and publishes a null when listed strikes cannot span the tail. That continuity is the very complement KRED offers alongside KRSVIX, namely an official gapless benchmark next to KRED's traded-only reconstruction with disclosed gaps, and the domestic literature documents the official index against the domestic and United States return-and-volatility cycle (Han, Kutan, and Ryu 2015; Cho 2015).

The V-KOSPI 200 is computed by the official index from listed KOSPI 200 option prices as a model-free fair-variance strip, and KRED applies no transformation and serves the official published value verbatim. The construction is described here so the republished object is read correctly, and it is the official index rather than a KRED estimator.

(1) Per-expiry fair variance. At each of the two nearest expiries the risk-neutral variance is the one-over-strike-squared strip of out-of-the-money option prices with the at-the-money correction, in the state-price spanning of Breeden and Litzenberger (1978) and Carr and Madan (2001) and the variance-swap replication of Demeterfi, Derman, Kamal, and Zou (1999).

The first term is the discretized model-free variance integral and the second corrects for the discrete reference strike $K_0$, the ceiling strike nearest at or above the forward, while $Q(K_i)$ is the out-of-the-money option price at strike $K_i$, a put below the reference strike and a call above it (Britten-Jones and Neuberger 2000; Bakshi, Kapadia, and Madan 2003).

(2) Forward and strike interval. The forward at each expiry follows from put-call parity at the strike that minimizes the call-put price gap (Jiang and Tian 2005).

Each strike carries the centered interval with single-sided widths at the endpoints (Andersen and Bondarenko 2007).

(3) Constant-thirty-day blend and annualization. The two per-expiry variances are blended to a constant thirty-day horizon and annualized, in the constant-horizon fair-variance convention the model-free-implied-volatility literature shares (Carr and Wu 2006; Fleming, Ostdiek, and Whaley 1995).

When the near expiry already exceeds thirty days the next term is dropped and the near term alone is used, so the index is $\text{V\text{-}KOSPI\,200}=100\sqrt{\sigma_1^2}$ without a blend (Whaley 1993).

(4) Thin-wing supplementation. When too few strikes are listed to span the tail, the official construction prices the missing strikes by Black-Scholes with put-call parity before the strip is formed, so the published index is continuous rather than gapped (Jiang and Tian 2007). This within-construction supplementation makes the published index a discrete-strike approximation of the model-free integral whose truncation and discretization error is bounded in the model-free-implied-volatility literature (Jiang and Tian 2005; Martin 2017). KRED performs none of these steps, and it selects the published close and serves it, so KRVKOSPI is a passthrough of the official V-KOSPI 200 and not a KRED computation.

The V-KOSPI 200 belongs to the investor-fear-gauge tradition of the volatility index, in which the option market's price of near-term uncertainty rises with expected market volatility, so a high level marks heightened fear and a low level complacency (Whaley 1993; Whaley 2000; Fleming, Ostdiek, and Whaley 1995). A continuous official thirty-day risk-neutral volatility level is therefore read as the market-consensus gauge of near-term uncertainty about the KOSPI 200 (Whaley 2009).

The object is a model-free risk-neutral variance, well-defined without a parametric option model, since option prices across the strike range pin down the risk-neutral density and its closed-form moments (Breeden and Litzenberger 1978; Bakshi, Kapadia, and Madan 2003; Jiang and Tian 2005; Britten-Jones and Neuberger 2000; Andersen and Bondarenko 2007). Because it is priced under the risk-neutral measure, the level embeds both the market's expectation of future variance and the premium investors pay to hedge it, the variance risk premium isolated by differencing option-implied from realized variance (Carr and Wu 2009; Bekaert and Hoerova 2014). That premium is itself informative, carrying return-predictive content at the quarterly frequency and a long-run-risk interpretation, which is why a risk-neutral volatility gauge is read as more than a pure forecast of realized volatility (Bollerslev, Tauchen, and Zhou 2009; Drechsler and Yaron 2011).

For the Korean market a continuous official thirty-day risk-neutral volatility gauge is read as the price the option market places on near-term KOSPI 200 uncertainty, and the domestic literature documents its behavior against the domestic and United States return-and-volatility cycle and its statistical properties on daily closes (Han, Kutan, and Ryu 2015; Cho 2015; Choi and Lee 2014). The gauge describes the risk-neutral variance level and its movements, and no expected-return reading attaches to it, since the option-implied expected-return bound of Martin (2017) is a separate quantity that this volatility index does not carry, while the thin next-month wings of the domestic options market are the standing caveat on any such gauge (Kang 2022).

On a markets desk the V-KOSPI 200 is read as a thirty-day risk-neutral volatility gauge for the KOSPI 200, the option market's price of near-term uncertainty, and it is used for hedging, monitoring, and relative-value work rather than as a directional signal (Whaley 2000; Whaley 2009). As the log-contract fair-variance index it is the natural benchmark for a variance-swap or volatility book whose static-replication logic Carr and Madan (2001) and Carr and Wu (2009) set out, and it is compared against realized volatility to read the variance risk premium a hedger pays (Bekaert and Hoerova 2014; Bollerslev, Tauchen, and Zhou 2009).

The gauge is most informative read against KRED's own KRSVIX and against realized volatility. Because the official construction supplements its own thin wings within the recipe, the V-KOSPI 200 is continuous and supplies a gapless official benchmark, the complement to KRED's traded-only KRSVIX, which gaps honestly when listed strikes cannot span the tail. The two weight the same option surface differently, the log-contract one-over-squared-price index against the equal-dollar SVIX, so their spread is a weighting-and-coverage read rather than a mispricing, and the two are strongly correlated same-underlying gauges that must not be treated as independent reads of the risk-neutral variance (Martin 2017; Han, Kutan, and Ryu 2015; Cho 2015).

Two limits govern its use. It is a risk-neutral variance index, so it carries a variance risk premium and is not a pure forecast of realized volatility, and no expected-return reading attaches to it (Drechsler and Yaron 2011; Carr and Wu 2009). And the domestic options market's thin next-month wings are a known limitation of any KOSPI 200 volatility gauge, so the level is read as a risk-neutral variance summary rather than as a precise tail reading on illiquid days (Kang 2022; Choi and Lee 2014; Fleming, Ostdiek, and Whaley 1995).

KRVKOSPI is the official V-KOSPI 200 published in annualized volatility points and served verbatim, and the object tested is its natural logarithm on the full continuous span from 2010-01-04 to 2026-07-06, a strictly positive, right-skewed volatility level whose innovations scale multiplicatively with the level, so the log is the natural scale and the deterministic term is pinned to a constant. A deterministic trend in log-volatility would imply the level diverging to zero or infinity, so trend-stationarity is excluded a priori as uninformative rather than tested, and the level is treated as a mean-reverting volatility index whose order of integration is a genuine empirical question. Because the published index is the official model-free construction that tracks each day's option prices rather than a two-sided-filtered or full-sample-re-estimated latent state, its measured persistence is a property of the option-price dynamics and not a smoother gain (Stock and Watson 1998; Hamilton 2018), and the log removes the zero lower bound so the regulated-process distortion of unit-root inference under a bound and under nonstationary volatility does not apply (Cavaliere 2005; Cavaliere and Taylor 2009; Cavaliere and Xu 2014).

Over 4063 daily observations the unit-root reading is ambiguous with the Phillips-Perron test the sole dissenter. The augmented Dickey-Fuller test fails to reject the unit root at −2.75047 with p = 0.066 and the KPSS test rejects level stationarity at 1.82262 with p < 0.01, the two concurring on a highly persistent non-stationary reading, while the Phillips-Perron test rejects the unit root at −3.48418 with p = 0.008, a lone rejection consistent with the known Phillips-Perron over-rejection under negative moving-average errors and conditional heteroskedasticity (Dickey and Fuller 1979; Said and Dickey 1984; Phillips and Perron 1988; Kwiatkowski et al. 1992; Ng and Perron 2001). No clean order of integration is assigned, the near-unit-root ambiguity of a highly persistent but mean-reverting volatility level, and the generalized-least-squares refinement reserved for such borderline readings only confirms the augmented Dickey-Fuller leg (Elliott, Rothenberg, and Stock 1996). The first-order autocorrelation of the log level is 0.98764 with an implied half-life of about 55.7 trading days, a descriptive persistence summary and not an integration claim, read against the near-unity small-sample downward bias of the autoregressive estimate (Andrews 1993).

Serial-dependence and break diagnostics are read on the first difference of the log level over the 4062 consecutive-trading-day steps, whose only excluded gaps are ordinary exchange non-trading days rather than any quality-gate null run. The Ljung and Box (1978) portmanteau, refining the Box and Pierce (1970) form, rejects white noise at lags 10 and 20 with Q = 47.6891 and Q = 66.6636, both at p = 0.000, yet the conditional-heteroskedasticity-robust automatic portmanteau of Escanciano and Lobato (2009) fails to reject at 0.75712 with p = 0.384. The divergence is diagnostic, since the plain portmanteau over-rejects under the vol-of-vol clustering that is the defining feature of a volatility index while its robust companion corrects for that conditional heteroskedasticity, so the dependence in the differenced log is volatility clustering in the conditional variance rather than a mean dynamic. The Bai and Perron (1998) procedure by the Bai and Perron (2003) algorithm finds no break in the mean of the differenced log series (Perron 1989).

The series is daily and carries no low-integer seasonal period, and the constant-thirty-day interpolation removes any expiry-cycle periodicity, so the seasonal-unit-root and seasonal-stationarity batteries are inapplicable and are not run (Hylleberg et al. 1990; Canova and Hansen 1995; Beaulieu and Miron 1992; Ghysels and Osborn 2001). These readings are a descriptive characterization of the official index over a sixteen-year gapless sample and carry no publish gate and no predictive claim, and because KRVKOSPI and the model-free KRSVIX interrogate the same-underlying KOSPI 200 risk-neutral variance differing only in strike weighting, their persistence readings are strongly dependent and are not independent corroboration of one another.