Abstract: In this paper, we examined the risk character of the NSEASI index across 10 years (January 1, 2013 - August 31, 2023), consisting of around 2,590 valid trading days following intensive cleaning and outliers adjustment of the data. A daily log return was calculated and shown as a high-risk, low-reward market, with average log returns of 0.0018 and an 11.73% daily volatility. It had extremely high kurtosis (328.199) and almost zero skewness (0.009), implying that the distribution of returns was very skewed to extremes and was not skewed. The characteristic function-based Value at Risk (VaR) model was applied in a stochastic volatility system to rectify the flaw of traditional risk models in the face of this heavy-tailed behaviour. Realistic stochastic dynamics of volatility of returns were obtained using parameter estimation using the method of moments. Comparative analysis using Delta, Delta-Gamma, and Monte-Carlo simulation techniques revealed that the fat-tailed behaviour of the return distribution was better captured when using the CF-based and Monte-Carlo-based approaches. The estimates of VaR at the 5% and 1% confidence levels based on CF (2.80 and 5.10) were significantly higher than those of the Delta and the Delta-Gamma method, which underestimated tail risk. It provides formal backtesting via the Kupiec and Christoffersen tests. It performs a sensitivity analysis and discusses policy implications in the context of financial regulation and corresponding portfolio risk management. We would conclude that CF-based VaR is a more practical and theoretically-grounded alternative to more common methods, in non-Gaussian settings that characterize emerging markets; nevertheless, our findings demonstrate the shortcomings of standard Gaussian-based models in turbulent emerging markets like Kenya. This article recommends the use of advanced stochastic methods in the field of financial risk management and regulation. Future research opportunities include introducing the dynamics of jump-diffusion processes, modeling interdependencies at the constituent level, and improving the dynamic portfolio risk estimation.

Keywords: Value at Risk (VaR), Stochastic Volatility, Characteristic Function, Emerging Markets, NSEASI Index.

| DOI: 10.17148/IARJSET.2025.12650