In this paper, we present a fast Monte Carlo simulation (MCS) algorithm for pricing equity-linked securities (ELS). The ELS is one of the most popular and complex financial derivatives in South Korea. We consider a step-down ELS with a knock-in barrier. This derivative has several intermediate and final automatic redemptions when the underlying asset satisfies certain conditions. If these conditions are not satisfied until the expiry date, then it will be checked whether the stock path hits the knock-in barrier. The payoff is given depending on whether the path hits the knock-in barrier. In the proposed algorithm, we first generate a stock path for redemption dates only. If the generated stock path does not satisfy the early redemption conditions and is not below the knock-in barrier at the redemption dates, then we regenerate a daily path using Brownian bridge. We present numerical algorithms for one-, two-, and three-asset step-down ELS. The computational results demonstrate the efficiency and accuracy of the proposed fast MCS algorithm. The proposed fast MCS approach is more than 20 times faster than the conventional standard MCS.
Monte Carlo simulation Equity-linked securities Option pricing Brownian bridge
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The authors are grateful to the reviewers for their constructive and helpful comments on the revision of this article. The author (D. Jeong) was supported by 2018 Research Grant (PoINT) from Kangwon National University. The corresponding author (J.S. Kim) was supported by the Brain Korea 21 Plus (BK 21) from the Ministry of Education of Korea.
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