Equity-linked Securities Research Articles

Valuing rebate options and equity-linked products

In this article, we propose rebate options with multi-step barriers, which are an extension of rebate options with a constant barrier. Despite the applicability and marketability of rebate options, there have been only a few research on obtaining analytical formulas. Accordingly, in this paper, we derive closed-form pricing formulas for these options under the Black–Scholes framework. The rebate options with multi-step barriers allow a flexible barrier structure, and thus we propose complex equity-linked products embedded with rebate options with barriers and derive pricing formulas for them. We conduct numerical studies on the pricing of rebate options with multi-step barriers, equity-linked securities, and equity-indexed annuities. The numerical studies validate the prices obtained from the pricing formulas.

A Practical Monte Carlo Method for Pricing Equity-Linked Securities with Time-Dependent Volatility and Interest Rate

A Practical Monte Carlo Method for Pricing Equity-Linked Securities with Time-Dependent Volatility and Interest Rate

Numerical Investigation of Fractional Step-Down ELS Option

In this paper, we use the finite difference methods to explore step-down Equity Linked Securities (ELS) options under the fractional Black-Scholes model. We establish Crank-Nicolson scheme under one asset and study the impact of Hurst exponent (H) on return of repayment under fixed stock price. We also explore the impact of stock price on return of repayment under different H. Through numerical experiments, it is found that the return of repayment of options is related to H, and the result of difference scheme will increase with the increase of H. In the case of two assets, we establish implicit scheme, and in the case of three assets, we use operator splitting method (OSM) method to establish semi-implicit scheme. We get the result that the H also influences the return of repayment in two and three assets. We also conduct Greeks analysis. Through Greeks analysis, we find that the long-term correlation of stocks has a huge impact on investment gains or losses. Therefore, we take historical volatility (fractal exponents) into account which can significantly reduce risk and increase revenue for investors.

Valuation of step-down knock-in in one stock linked security using numerical and Monte Carlo integration

This paper shows a new methodology for evaluating the value and sensitivity of autocall knock-in type equity-linked securities. While the existing evaluation methods, Monte Carlo simulation and finite difference method, have limitations in underestimating the knock-in effect, which is one of the important characteristics of this type, this paper presents a precise joint probability formula for multiple autocall chances and knock-in events. Based on this, the calculation results obtained by utilizing numerical and Monte Carlo integration are presented and compared with those of existing models. The results of the proposed model show notable improvements in terms of accuracy and calculation time.

Equity-linked securities option pricing by fractional Brownian motion

Abstract In this paper, we use the Monte Carlo simulation (MCS) method to price the Equity-Linked Securities (ELS) option by fractional Brownian motion (fBm). We use the fBm that satisfy the Ito process instead of the geometric Brownian motion, and we call the proposed model ELS-fBm model. We first do the convergence test with the number of MCS. Then, we price the one-, two-, and three-asset ELS by employing the classical ELS model and the ELS-fBm model, respectively. We see that the price of ELS varies with different Hurst exponent, which indicates that the ELS pricing model considering the long-range dependence is necessary and more suitable for the financial market under uncertain environment. In addition, we prove the superiority of our proposed model with an actual three-assets ELS product which is issued by Future Asset company. We find the ELS price calculated by the proposed ELS-fBm model almost the same as the ELS price in the ELS product contract issued by Future Asset company, while the classical ELS model produces a great deviation.

Modeling and Risk Analysis Using Parametric Distributions with an Application in Equity-Linked Securities

In this study, we model the returns of a stock index using various parametric distribution models. There are four indices used in this study: HSCEI, KOSPI 200, S&P 500, and EURO STOXX 50. We applied 12 distributions to the data of these stock indices—Cauchy, Laplace, normal, Student’s t, skew normal, skew Cauchy, skew Laplace, skew Student’s t, hyperbolic, normal inverse Gaussian, variance gamma, and general hyperbolic—for the parametric distribution model. In order to choose the best-fit distribution for describing the stock index, we used the information criteria, goodness-of-fit test, and graphical tail test for each stock index. We estimated the value-at-risk (VaR), one of the most popular management concepts in the area of risk management, for the return of stock indices. Furthermore, we applied the parametric distributions to the risk analysis of equity-linked securities (ELS) as they are a very popular financial product on the Korean financial market. Relevant risk measures, such as VaR and conditional tail expectation, are calculated using various distributions. For calculating the risk measures, we used Monte Carlo simulations under the best-fit distribution. According to the empirical results, investing in ELS is more risky than investing in securities, and the risk measure of the ELS heavily depends on the type of security.

Super-Fast Computation for the Three-Asset Equity-Linked Securities Using the Finite Difference Method

In this article, we propose a super-fast computational algorithm for three-asset equity-linked securities (ELS) using the finite difference method (FDM). ELS is a very popular investment product in South Korea. There are one-, two-, and three-asset ELS. The three-asset ELS is the most popular financial product among them. FDM has been used for pricing the one- and two-asset ELS because it is accurate. However, the three-asset ELS is still priced using the Monte Carlo simulation (MCS) due to the curse of dimensionality for FDM. To overcome the limitation of dimension for FDM, we propose a systematic non-uniform grid with an explicit Euler scheme and an optimal implementation of the algorithm. The computational time is less than 6 s. We perform standard ELS option pricing and compare the results from the fast FDM with the ones from MCS. The computational results confirm the superiority and practicality of the proposed algorithm.

A risk analysis of step-down equity-linked securities based on regime-switching copula

The globalization of financial markets has broadened investment opportunities. International investors’ investment portfolios consist of financial instruments from various countries; consequently, the risks associated with economic dependence among countries should be carefully considered. Step-down equity-linked securities (ELS) are a structured financial product that have recently become popular among Korean investors. Payoffs are based on two or three stock indices from different regions; therefore, dependence between the indices should be reflected in the risk analysis. In this study, we consider a regime-switching copula model to describe the joint behavior of two stock indices- the Eurostoxx50 and the Hang Seng China Enterprises Index (HSCEI). These indices are commonly used as underlying assets of step-down ELS. Using historical data, we analyze the risk associated with step-down ELS through the probabilities of early redemption. A regime-switching copula model can accommodate complicated dependence. Thus, it should be considered in the risk analysis of step-down ELS.

The Evolution of Complexity of the ELS and the Financial Consumer Protection in Korea

금융상품의 복잡성에 대해, 단지 금융혁신의 부산물이라는 견해(incidental complexity view)와, 고의적으로 금융상품의 불투명성을 증대시키는 수단이라는 견해(obfuscation or shrouding view)가 대비된다. 최근 연구들에 의하면, 복잡한 구조를 지닌 소매구조화금융상품들이 금융혁신에 기인한다는 증거가 분명하지 않고, 오히려 정보우위의 판매자(금융회사)가 정보열위의 구매자(금융소비자)를 착취하는 수단이 되는 것으로 보인다. 복잡한 소매금융상품일수록 사전적으로 기본적인 가치에 비해 비싼 가격에 판매되며, 사후적으로도 수익 성과가 열등함이 발견되었다. 그리고 이론적으로 금융상품의 이러한 복잡성 효과는 시장경쟁에 의해서도 소멸되지 않고 지속될 수 있다. 본 논문은 금융상품 복잡성 관점에서, 국내 ELS 금융상품의 경제적 제도적 특성을 설명하고, 금융소비자보호에 관한 주요 이슈를 분석하며, 관련된 감독당국의 견해의 변화를 분석함으로써, 결론적으로 금융소비자보호에 관한 정책적 시사점을 제시한다.Concerning the complexity of the financial products, there are two contrasting view points. The incidental complexity view argues that the complexity is the incidental by-product following the efficiency-increasing financial innovation. The obfuscation or shrouding view explains that the complexity obfuscates or shrouds the information asymmetry between the sellers and the buyers. Recent studies seems to support the shrouding view by showing that the complex financial products are expensive ex-ante and have bad performance ex-post. This paper takes into account the complexity concept and explains the economic and the institutional characteristics of the ELS(equity linked securities) in Korea. We analyze the related financial consumer protection issues, the evolutionary process of the ELS products, and the changes in the perception of the ELS characteristics or the stance by the supervisory authorities. Lastly we provide the policy implications about the complex financial products and the financial consumer protection.

Fast Monte Carlo Simulation for Pricing Equity-Linked Securities

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.

Equity-linked security pricing and Greeks at arbitrary intermediate times using Brownian bridge

Abstract We develop a numerical algorithm for predicting prices and Greeks of equity-linked securities (ELS) with a knock-in barrier at any time over the total time period from issue date to maturity by using Monte Carlo simulation (MCS). The ELS is one of the most important financial derivatives in Korea. In the proposed algorithm, first we calculate the probability ( 0 ≤ p ≤ 1 {0\leq p\leq 1} ) that underlying asset price never hits the knock-in barrier up to the intermediate evaluation date. Second, we compute two option prices V n ⁢ k {V_{nk}} and V k {V_{k}} , where V n ⁢ k {V_{nk}} is the option value which knock-in event does not occur and V k {V_{k}} is the option value which knock-in event occurs. Finally, we predict the option value with a weighted average. We apply the proposed algorithm to two- and three-asset ELS. We provide the pseudo-numerical algorithm and computational results to demonstrate the usefulness of the proposed method.

Economic Benefits of Derivatives for Long Term Investments-Equity Linked Securities

In this paper, we examined the economic benefits of derivatives in the aspect of investment assets. Our study differs from previous studies in that it analyzed the differences in the economic benefits of derivatives between for short term investors and for long term investors, and focused on the equity linked securities (ELS) rather than plain vanilla derivatives. We found the following results from the analysis over 1 to 20 years of investment horizons for four different types of equity linked securities, including ‘Auto-callable ELS’, ‘Knock-out ELS’, ‘Digital ELS’ and ‘Reverse Convertible ELS.’ First, equity linked securities contribute to improving the performance of the optimal portfolio for most investors, except for some investors who have extremely low degrees of risk aversion. Second, these economic benefits of equity linked securities are consistently observed regardless of investment horizon. Third, investment demand for equity linked securities is higher for investors with a medium-level of risk aversion rather than for aggressive or conservative investors. In addition, equity linked securities are mainly used as substitutes for risk-free bonds rather than risky assets (i.e., stocks). Finally, most of our results are still valid even when different market environments are assumed or alternative decision rules are used to derive investors’ optimal portfolio.

The Effect of Equity Linked Securities on Financial Stability in Korea

Since the introduction of ELS (Equity-linked securities) in 2003, the structured products have become one of the most important investment vehicles to Korean retail investors. However, the rapid growth of those structured products has induced the imbalance of Korean financial markets and may have eventually damaged the financial stability of Korean economy. In this paper, we investigate how Korean securities companies issuing the structured products hedge their positions and how their activities affect the financial stability. In addition, we conduct a simple empirical analysis to examine the relationship between the issue of ELS and the financial stability using FSI (financial stability index) provided by Bank of Korea. According to the results, the balance of ELS affects the financial stability negatively and this is significant even after adjusting for the control variables such as the KOSPI index, VKOSPI, the risk-free interest rate, and CPI. More specifically, the balance rather than the amount of monthly issuance is significant to financial stability. In addition, the decrease in underlying indices reduces the early redemption, thereby damaging the financial stability. Lastly, we suggest several solutions to alleviate the negative effects.

Empirical Analysis of Credit Risk in Autocallable Structured Product Market: Evidence from Korean Equity-Linked Securities (ELS) Market

In this research, we analyze the role of credit risk in the structured product markets, represented by Korean Equity Linked Securities (ELS). We find empirical evidences that the credit risk of the issuer is incorporated in the returns of the ELS. ELS that is issued by higher credit risk issuer provides higher ELS coupon rates to compensate the investors for extra credit riskiness. Especially, our research exploits the new method to capture the returns of the ELS without using any price dynamic model assumption that causes potential mispricing or bias results.

ELS Hedging Method based on CVaR Using Stocks Portfolio and Futures

In this paper, we analyze the hedging risk intrinsic in the auto call step down equity linked securities (ELS) based on two underlying indices including HSCEI, which are major products of the ELS market. And we also propose new hedging strategies based on Conditional Value at Risk (CVaR) using stocks portfolio and futures. Due to the non-symmetric bimodal distribution for return of ELS, which comes from the Knock-In (KI) property inherent in step down ELS structure, and inherent shortfall risk in the ELS structure, a local delta hedging strategy has a limit. In addition, hedging using futures are difficult because of 1) frequent roll-over related with HSCEI futures, 2) price difference between underlying index and futures and 3) lack of futures liquidity caused by excessive ELS issue based on HSCEI. As a way to manage these problems, this paper proposes new hedging strategies : First, construct stocks portfolio tracking index using method suggested by Rockafellar and Uryasev (2002), Alexander, Coleman and Li (2006). Second, do hedging by using this stocks portfolio and futures. This paper shows that 1) index-tracking stocks portfolio based on CVaR has a better performance and lower shortfall risk than index by comparing market ratio, information ratio and Sharpe Ratio, and 2) hedging using stocks portfolio is better than futures. As the policy proposals, if ETF, which tracks the underlying indices of ELS based on CVaR, is to be listed on the exchange (KRX), various kinds of product structures for mid-risk-mid-return structured products will be able to develop further, as well as offer more convenience with hedging.

A Study on Retail Structured Product Market and Financial Regulation in Korea

This study looks at the characteristics and current status of retail structured product market of Korea and tries to explain, in particular, issues related to issue price, cost of hedging, and overpricing. We also analyzed the perspective of the government and the related regulatory policies. We examined various performance measures for portfolios composed of the KOSPI200 Covered Call Index and other assets in order to change the viewpoint of the authorities that the trading of structured products, such as ELS (equity-linked securities) and DLS (debt-linked securities), is in fact not a zero-sum game between the issuers and investors. The empirical results show that the KOSPI200 Covered Call Index has a superior performance compared to the KOSPI200 Index and the others. In addition, from the perspective of certainty equivalent excess returns, the KOSPI200 Covered Call Index also displays the possibility of improving the utility level of risk-averse retail investors. However, it is difficult in reality for individual investors to construct efficient portfolios that employ covered call strategies using options. Hence, individual investors can form optimal portfolios that benefit indirectly from such covered call strategies via investment in financial derivative products issued by securities firms that are able to more easily utilize investment strategies that incorporate options to form optimum portfolios. This means that both the issuer and investor can profit from these financial derivative products and, therefore, it is not a zero-sum game.

Analysis of Disputes Concerning Delta Hedging Trades of ELS(Equity-Linked Securities)

Analysis of Disputes Concerning Delta Hedging Trades of ELS(Equity-Linked Securities)

A practical finite difference method for the three-dimensional Black–Scholes equation

In this paper, we develop a fast and accurate numerical method for pricing of the three-asset equity-linked securities options. The option pricing model is based on the Black–Scholes partial differential equation. The model is discretized by using a non-uniform finite difference method and the resulting discrete equations are solved by using an operator splitting method. For fast and accurate calculation, we put more grid points near the singularity of the nonsmooth payoff function. To demonstrate the accuracy and efficiency of the proposed numerical method, we compare the results of the method with those from Monte Carlo simulation in terms of computational cost and accuracy. The numerical results show that the cost of the proposed method is comparable to that of the Monte Carlo simulation and it provides more stable hedging parameters such as the Greeks.

Knock-In and Stocks Market Effect Due to ELS Issuance and Hedging

In this paper we analyze the shortfall risk implied in the auto call step down equity linked securities (ELS) based on two underlying assets, which is a major product of the rapidly growing ELS market as the low interest rate environment continues. And we also present the hedging strategies for managing shortfall risk. In the position of auto call step down ELS issuer, 1) until the underlying asset price reaches at knock-in (KI) level, the delta of the underlying is continually and significantly increased in order to hedge the short position of the Down and Out (DO) option and the long position of the put option inherent in ELS, 2) however, the hedger must reduce this delta as soon as the underperformed underlying price touches KI level, which triggers the vanishing of the DO option. As a way to manage these shortfall risks, this paper proposes two new hedging strategies of minimizing these shortfall risks and depending on the KI probability. Also this paper shows that these hedging strategies provide better performance than traditional BS hedging strategy when these hedging strategies are applied to a sample product with real market data. As the policy proposals, first, in order to prevent the concentration of the KI prices, ELS issue amount based on the same underlying is needed to be determined in consideration of both the average market trading volume and maximum leverage delta. Second, in the realm of pin risk such as Knock-In or Knock-Out, where the leverage increases, it is recommended to mitigate the risk management delta limit based on the BS model which is made under the assumption of continuous hedging infinitesimally.

The pricing of convertible bonds in the presence of structured conversion clauses: the case of Cashes

The aim of this paper is to analyse the pricing of highly structured convertible bonds by taking a real world case. To this end we examine the Cashes (Convertible And Subordinated Hybrid Equity-linked Securities), which are characterised by both voluntary and mandatory conversion that depend on different triggering events, as well as floating coupons whose payment hinges on dividends and earning of the issuer. Our results highlight that prices are very sensitive to the modelling of the sources of uncertainty, both market and credit risk, and underscore the relevance of the time horizon chosen for the estimation.