South Korea KOSPI 200 SVIX

KRSVIX is the KOSPI 200 SVIX of Martin (2017), the annualized thirty-day risk-neutral volatility of the simple market return, reported in volatility points on the VKOSPI scale. Its estimand is model-free, namely 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), under Martin's equal-dollar strike weighting rather than any parametric option model. The measured object is the risk-neutral variance of the gross simple return, so KRSVIX summarizes the whole risk-neutral distribution of the market's one-month return through its second moment, in the model-free-implied-volatility tradition of Britten-Jones and Neuberger (2000), Jiang and Tian (2005), and Andersen and Bondarenko (2007).

KRSVIX is a distinct estimand from the official VKOSPI, and it is not a Korean re-labeling of that index. The published VKOSPI is the VIX-style fair variance built from the log contract, whose strip weights each strike by one over its squared price, whereas the SVIX strip of Martin (2017) weights every strike equally in dollars and prices the simple rather than the log return (Bakshi, Kapadia, and Madan 2003; Whaley 2009). The two therefore measure different functionals of the same option surface, so KRSVIX sits slightly below the official index, a difference of weighting and of traded-only coverage rather than an error of either gauge.

Two properties of the construction are disclosed rather than smoothed over. First, KRSVIX integrates only authentic traded option prices and never manufactures or extrapolates an unquoted strike, so on days when the listed strikes do not span the risk-neutral tail the series publishes an honest gap rather than filling the missing wing with a Black-Scholes price as the official index does. Coverage accordingly thins through the 2020 and 2021 crisis-and-de-grossing window and lapses entirely in the 2026 rally, whose blackout is a roughly 125-trading-day null run, and the series resumes only when traded strikes again span the tail (Kang 2022; Cho 2015). Second, the price basis is the daily last-trade price with a next-day base-price fallback in place of an intraday quote midpoint, a settlement-mark substitution disclosed in the domestic daily-price register (Cho 2015; Choi and Lee 2014; Han, Kutan, and Ryu 2015).

KRSVIX is a volatility index and carries no expected-return reading. The Martin (2017) lower bound on the expected market return is a separate estimand that KRED withholds, so nothing in this series is a forecast of returns, and the volatility level should be read as a risk-neutral variance gauge in the variance-risk-premium tradition rather than as a pure forecast of realized volatility (Carr and Wu 2009; Bekaert and Hoerova 2014).

KRSVIX is computed each day from that day's KOSPI 200 option settlement chain, with no filter and no cross-day smoothing, so the whole panel is recomputed on every run.

(1) Out-of-the-money selection and the spanning integral. At each listed expiry the risk-neutral variance of the simple return is the equal-dollar-weighted strip of out-of-the-money option prices of Martin (2017), split at the forward, in the state-price spanning of Breeden and Litzenberger (1978) and Carr and Madan (2001).

Each strike contributes its cheaper leg, the out-of-the-money side by put-call parity, so no forward is needed to classify a strike (Martin 2017).

(2) The forward and the discount factor from put-call parity. Over the strikes whose paired legs both pass the authenticity screen, the forward $F_{t,T}$ and the gross rate $R_{f,t}$ are recovered from the put-call-parity relation by the outlier-robust Theil-Sen estimator of van Binsbergen, Diamond, and Grotteria (2022).

(3) Discretization. The spanning integral is evaluated by the Martin and CBOE centered-width rectangle sum over the post-screen strike grid, with single-sided widths at the endpoints (Jiang and Tian 2005).

The per-expiry variance is then $\text{SVIX}^2_{t\to T}=2\,W_{t,T}\big/\big[(T-t)\,R_{f,t}\,S_t^{2}\big]$, with $\Omega$ the out-of-the-money leg at each strike (Andersen and Bondarenko 2007; Britten-Jones and Neuberger 2000).

(4) Constant-horizon interpolation to thirty days. The thirty-day variance is a linear-in-total-variance interpolation between the two monthly expiries that bracket the horizon, in the fair-variance convention that the model-free-implied-volatility literature shares (Jiang and Tian 2005; Bakshi, Kapadia, and Madan 2003).

When the nearest eligible expiry already exceeds thirty days its single-term variance is used without a blend, and extrapolation is never used, so an unspanned horizon is left null rather than filled (Cho 2015; Kang 2022).

(5) The near-term roll and annualization. The front expiry is dropped once its remaining life falls below fourteen days, past which the near leg is too coarse to resolve, and time is measured in seconds on the exchange year convention so the variance is already annualized. The published series is the annualized volatility in points at the thirty-day horizon.

with $h$ the thirty-day horizon. This is the market-index member of the SVIX family, and the same construction defines the single-stock version of Martin and Wagner (2019).

KRSVIX belongs to the model-free risk-neutral moment tradition, in which option prices across the strike range pin down the risk-neutral distribution of the underlying without a parametric model. Breeden and Litzenberger (1978) show that the second strike derivative of the call price is the risk-neutral density, Bakshi, Kapadia, and Madan (2003) turn that density into closed-form risk-neutral moments, and Jiang and Tian (2005) establish that the resulting model-free implied volatility is a valid and informative measure of expected volatility, so a thirty-day risk-neutral variance read off the KOSPI 200 surface is a well-defined object independent of any pricing model (Britten-Jones and Neuberger 2000; Andersen and Bondarenko 2007).

The economic content of that object is a risk-neutral, not a physical, variance. Because it is priced under the risk-neutral measure, KRSVIX embeds both the market's expectation of future variance and the premium investors pay to hedge it, the variance risk premium that Carr and Wu (2009) and Bekaert and Hoerova (2014) isolate by differencing option-implied from realized variance. That premium is itself economically informative, carrying return-predictive content at the quarterly frequency in Bollerslev, Tauchen, and Zhou (2009) and a structural interpretation in the long-run-risk account of Drechsler and Yaron (2011), which is why a risk-neutral volatility gauge is read as more than a forecast of realized volatility (Whaley 2009).

For the Korean market specifically, a model-free thirty-day risk-neutral volatility gauge is read as the price the option market places on near-term uncertainty about the KOSPI 200. Domestic work on the official volatility index documents its behavior against the domestic and United States return-and-volatility cycle, and KRSVIX supplies a companion built on the equal-dollar simple-return weighting of Martin (2017) rather than the log-contract convention (Han, Kutan, and Ryu 2015; Cho 2015). It describes the risk-neutral variance level and its movements, and no expected-return reading attaches to it, since the expected-return bound of Martin (2017) and Martin and Wagner (2019) is a separate quantity that this series does not carry.

On a markets desk KRSVIX is read as a thirty-day risk-neutral volatility gauge for the KOSPI 200, the option market's dollar-weighted price of near-term uncertainty, and it is used for monitoring and relative-value work rather than as a directional signal. Because it is the equal-dollar simple-return strip of Martin (2017), it is the natural volatility companion to a variance-swap or volatility-trading book, whose static-replication logic Carr and Madan (2001) and Carr and Wu (2009) set out, and it can be compared cleanly 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 when read against the official index and against realized volatility. KRSVIX and the log-contract VKOSPI weight the same option surface differently, so their spread is a weighting-and-coverage read rather than a mispricing, and the domestic volatility-index literature supplies the behavior of the official series against the return cycle for that comparison (Han, Kutan, and Ryu 2015; Cho 2015). The model-free-implied-volatility foundation makes the level comparable across days without a model, so a rise is an increase in the risk-neutral variance priced into the surface and not an artifact of a fitted parameter (Britten-Jones and Neuberger 2000; Jiang and Tian 2005; Bakshi, Kapadia, and Madan 2003).

Two operational limits govern its use. The series carries authentic traded prices only, so it goes null when listed strikes fail to span the tail rather than extrapolating a wing, and a desk must treat those gaps as missing data rather than as low volatility, a coverage limit the thin-wing critique of the domestic options market anticipates (Kang 2022; Andersen and Bondarenko 2007). And KRSVIX is a volatility index, so it is read for the level and dynamics of risk-neutral variance and not as a return forecast, the expected-return bound of Martin and Wagner (2019) being a separate quantity this series does not publish (Drechsler and Yaron 2011).

KRSVIX is the published thirty-day headline in annualized volatility points, and the object tested is its natural logarithm on the signed published span running from 2018-10-01 onward, 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. The series is a model-free deterministic transform of each day's option chain computed from that day alone, with no two-sided filter and no full-sample re-estimation, so 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 1508 published days from 2018-10-01 to 2025-12-29 the unit-root reading is ambiguous. The augmented Dickey-Fuller test rejects the unit root at p = 0.000399 and the Phillips-Perron test rejects it at p = 0.000, yet the KPSS test rejects level stationarity at p = 0.049, so the two null types point in opposite directions and no clean order of integration is assigned, the near-unit-root ambiguity of a highly persistent but mean-reverting volatility level (Dickey and Fuller 1979; Said and Dickey 1984; Phillips and Perron 1988; Kwiatkowski et al. 1992; Ng and Perron 2001). The generalized-least-squares refinement is reserved for such borderline readings and only confirms the augmented Dickey-Fuller leg (Elliott, Rothenberg, and Stock 1996). The first-order autocorrelation of the log level is 0.96196 with an implied half-life of about 17.87 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 1394 consecutive-trading-day steps that remain once differences spanning the coverage-driven null gaps are excluded by pre-registration. The Ljung and Box (1978) portmanteau, refining the Box and Pierce (1970) form, rejects white noise at lags 10 and 20 with Q = 24.8677 and Q = 35.9569 at p = 0.006 and p = 0.016, and the automatic portmanteau of Escanciano and Lobato (2009) rejects at 4.80048 with p = 0.028, the mandated companion because vol-of-vol clustering is the defining feature of a volatility index and the plain portmanteau over-rejects under the conditional heteroskedasticity it induces. The differenced-log dependence is that volatility clustering and not a mean dynamic, and 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). Because the series carries only authentic traded prices and publishes a null when listed strikes cannot span the tail, its persistence and stability readings are statements about the published, spanned days, and the finite 1508-day sample makes them weak rather than strong.