Using a realized-volatility model and risk-neutral correction for derivative valuation in an illiquid market

Dandamaev S.A., Dandamaev G.A.
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Derivatives offer broad opportunities for investment and hedging in financial markets. However, most stochastic pricing models rely on a liquid options market for calibration. In illiquid markets, including the current Russian financial market, this becomes a critical limitation.

This paper studies the use of realized-volatility models and an empirical risk-neutral correction for pricing derivatives written on a single underlying asset. The framework combines the HARGL model, estimated on historical high-frequency data, with the Empirical Martingale Simulation (EMS) technique used to adjust the simulated price paths. The choice of realized volatility is motivated by the fact that the model simulates both integrated variance and asset returns without requiring an implied-volatility surface. The choice of a risk-neutral measure is needed to satisfy the first fundamental theorem of asset pricing. In an incomplete market, infinitely many such measures exist, so EMS is used as an operational rule: it alters the historical dynamics as little as possible while enforcing strict martingality of the price process.

The validation procedure includes volatility-forecast testing, no-arbitrage checks, convergence analysis, and comparison with exchange-traded option quotes. The HARGL model describes the variance distribution accurately, with a mean PIT value of 0.46 versus the benchmark value of 0.5, while showing a moderately conservative bias: 96% of the observations fall inside the 90% confidence interval. In an illiquid market, such conservatism is a meaningful advantage. A comparison with observed vanilla option quotes shows that, even without using option data in calibration, the model gives a mean absolute pricing error of only 0.5 rubles. For 26% of the instruments, the model price falls inside the bid–ask spread, while the remaining prices lie slightly above the ask quote. This moderate upward bias supports the adequacy of the framework. The algorithm reaches numerical convergence already at 10 000 simulations. The sensitivity analysis shows that EMS is critically important: pricing under the physical measure without this correction distorts the option value by 37%. The expected sensitivity to the initial asset price (4.7%) and to forecast variance (6%) is also documented.

The results show that the HARGL – EMS combination provides a reliable computational tool for pricing and hedging. Since the algorithm produces full simulated paths, it can be extended naturally to exotic derivatives. In this sense, the framework gives a numerical implementation of the core ideas behind the fundamental theorems of asset pricing and provides a stable no-arbitrage valuation procedure under severe illiquidity.

Keywords: realized volatility, HARGL, empirical martingale simulation, illiquid market, Monte Carlo, option pricing
Citation in English: Dandamaev S.A., Dandamaev G.A. Using a realized-volatility model and risk-neutral correction for derivative valuation in an illiquid market // Computer Research and Modeling, 2026, vol. 18, no. 5, pp. 1417-1434
Citation in English: Dandamaev S.A., Dandamaev G.A. Using a realized-volatility model and risk-neutral correction for derivative valuation in an illiquid market // Computer Research and Modeling, 2026, vol. 18, no. 5, pp. 1417-1434
DOI: 10.20537/2076-7633-2026-18-5-1417-1434
URL: http://crm-en.ics.org.ru/journal/article/3788/
Creative Commons License This work is licensed under a Creative Commons Attribution-NoDerivs 3.0 Unported License.

Copyright © 2026 Dandamaev S.A., Dandamaev G.A.

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