AN ALGORITHM FOR ESTIMATING IMPLIED VOLATILITY IN EQUITY-LINKED SECURITIES

초록

This paper proposes a robust numerical framework for estimating the implied volatility of equity-linked securities (ELS), which are characterized by complex path-dependent features such as early redemption and knock-in barriers. By extending the classical Black-Scholes model and applying finite difference methods, we solve the pricing problem for ELS products with non-linear and discontinuous payoff structures. The proposed algorithm calibrates a constant implied volatility over the life of the product by minimizing the error between market-observed fair prices and model-generated prices using a least-squares optimization approach. Numerical experiments were conducted on real ELS contracts linked to the KOSPI 200 index, Samsung Electronics stock, and Tesla, Inc. stock. The results show that the method is applicable across different underlying assets and captures distinct volatility characteristics for each asset. For each underlying asset, implied volatilities estimated from ELS issued on different dates remain within a consistent range, demonstrating the method’s practical effectiveness in estimating ELS implied volatility.

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