Fast Monte Carlo Simulation for Pricing Equity-Linked Securities
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Fast Monte Carlo Simulation for Pricing Equity-Linked Securities Hanbyeol Jang1 · Sangkwon Kim2 · Junhee Han1 · Seongjin Lee1 · Jungyup Ban1 · Hyunsoo Han1 · Chaeyoung Lee2 · Darae Jeong3 · Junseok Kim2 Accepted: 1 November 2019 © Springer Science+Business Media, LLC, part of Springer Nature 2019
Abstract 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. Keywords Monte Carlo simulation · Equity-linked securities · Option pricing · Brownian bridge
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Junseok Kim [email protected]
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Department of Financial Engineering, Korea University, Seoul 02841, Republic of Korea
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Department of Mathematics, Korea University, Seoul 02841, Republic of Korea
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Department of Mathematics, Kangwon National University, Chuncheon-si, Gangwon-do 24341, Republic of Korea
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H. Jang et al.
1 Introduction The equity-linked security (ELS) is the financial derivative whose return on investment is dependent on the performance of the linked underlying equity. It has been one of the most popular financial derivatives since it was introduced to South Korea in 2003. The value of annual issuance for this derivative is over half-trillion US dollars (Jo and Kim 2013). In 2015, ELS was issued with about 0.65 trillion US dollars. However, the collapse of China’s stock market took place in June 2015. The global stock market was influenced by the black swan incident occurred two months later on August 24th. On that day, the Dow Jones Industrial Average of the US plummeted by more than 1000 points as the two major composite indices of China plunged 8%. Furthermore, Japanese and European stock indices dropped more than 4% (Tsai 2017). For this reason, ELS has faced critical crisis during the second half of that year. Therefore, there is a need for more detailed studies about the structure of ELS to manage risk related to ELS. In this paper, we consider a step-down ELS with a knock-in barrier and describe the one-, two-, and three-asset step-down ELS. Figure 1 il
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