Browsing by Author "Wang, Chuan-Ju"

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A Multi-Phase, Flexible, and Accurate Lattice for Pricing Complex Derivatives with Multiple Market Variables
(2012)
Wang, Chuan-Ju
;
Dai, Tian-Shyr
;
Lyuu, Yuh-Dauh
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
With the rapid growth of financial markets, many complex derivatives have been structured to meet specific financial goals. But most complex derivatives have no analytical formulas for their prices, e. g., when more than one market variable is factored. As a result, they must be priced by numerical methods such as lattice. A derivative is called multivariate if its value depends on more than one market variable. A lattice for a multivariate derivative is called a multivariate lattice. This paper proposes a flexible multi-phase method to build a multivariate lattice for pricing derivatives accurately. First, the original, correlated processes are transformed into uncorrelated ones by the orthogonalization method. A multivariate lattice is then constructed for the transformed, uncorrelated processes. To sharply reduce the nonlinearity error of many numerical pricing methods, our lattice has the flexibility to match the so-called "critical locations" - the locations where nonlinearity of the derivative\'s value function occurs. Numerical results for vulnerable options, insurance contracts guaranteed minimum withdrawal benefit, and defaultable bonds show that our methodology can be applied to the pricing of a wide range of complex financial contracts.
A Multiphase, Flexible, and Accurate Lattice for Pricing Complex Derivatives with Multiple Market Variables
(2013-09-01)
Dai, Tian-Shyr
;
Wang, Chuan-Ju
;
Lyuu, Yuh-Dauh
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
With the rapid growth and the deregulation of financial markets, many complex derivatives have been structured to meet specific financial goals. Unfortunately, most complex derivatives have no analytical formulas for their prices, particularly when there is more than one market variable. As a result, these derivatives must be priced by numerical methods such as lattice. However, the nonlinearity error of lattices due to the nonlinearity of the derivative's value function could lead to oscillating prices. To construct an accurate, multivariate lattice, this study proposes a multiphase method that alleviates the oscillating problem by making the lattice match the "critical locations," locations where nonlinearity of the derivative's value function occurs. Moreover, our lattice has the ability to model the jumps in the market variables such as regular withdraws from an investment account, which is hard to deal with analytically. Numerical results for vulnerable options, insurance contracts guaranteed minimum withdrawal benefit (GMWB), and defaultable bonds show that our methodology can be applied to the pricing of a wide range of complex financial contracts.
An Accurate Lattice Mode for Pricing Catastrophe Equity Put Under the lump-Diffusion Process
(2018-11-01)
Wang, Chuan-Ju
;
Dai, Tian-Shyr
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
A catastrophe equity put (CatEPut) is constructed to recapitalize an insurance company that suffers huge compensation payouts due to catastrophic events (CEs). The company can exercise its CatEPut to sell its stock to the counterparty at a predetermined price when its accumulated loss due to CEs exceeds a predetermined threshold and its own stock price falls below the strike price. Much literature considers the evaluations of a CatEPut that can only be exercised at maturity; however, most CatEPuts can be exercised early so the company can receive timely funding. This paper adopts lattice approaches to evaluate CatEPuts with early exercise features. To solve the combinatorial exposition problem due to the trigger of CatEPuts' accumulated loss, our method reduces the possible number of accumulated losses by taking advantage of the closeness of integral additions. We also identify and alleviate a new type of nonlincarity error that yields unstable numerical pricing results by adjusting the lattice structure. We provide a rigorous mathematical proof to show how the proposed lattice can be constructed under a mild condition. Comprehensive numerical experiments are also given to demonstrate the robustness and efficiency of our lattice.
An efficient and accurate lattice for pricing derivatives under a jump-diffusion process
(2010-12-01)
Dai, Tian-Shyr
;
Wang, Chuan-Ju
;
Lyuu, Yuh-Dauh
;
Liu, Yen-Chun
;
資訊管理與財務金融系註：原資管所+財金所
Derivatives are popular financial instruments whose values depend on other more fundamental financial assets (called the underlying assets). As they play essential roles in financial markets, evaluating them efficiently and accurately is critical. Most derivatives have no simple valuation formulas; as a result, they must be priced by numerical methods such as lattice methods. In a lattice, the prices of the derivatives converge to theoretical values when the number of time steps increases. Unfortunately, the nonlinearity error introduced by the nonlinearity of the option value function may cause the pricing results to converge slowly or even oscillate significantly. The lognormal diffusion process, which has been widely used to model the underlying asset's price dynamics, does not capture the empirical findings satisfactorily. Therefore, many alternative processes have been proposed, and a very popular one is the jump-diffusion process. This paper proposes an accurate and efficient lattice for the jump-diffusion process. Our lattice is accurate because its structure can suit the derivatives' specifications so that the pricing results converge smoothly. To our knowledge, no other lattices for the jump-diffusion process have successfully solved the oscillation problem. In addition, the time complexity of our lattice is lower than those of existing lattice methods by at least half an order. Numerous numerical calculations confirm the superior performance of our lattice to existing methods in terms of accuracy, speed, and generality. (C) 2010 Elsevier Inc. All rights reserved.
An efficient and accurate lattice for pricing derivatives under a jump-diffusion process
(2010-12-01)
Dai, Tian-Shyr
;
Wang, Chuan-Ju
;
Lyuu, Yuh-Dauh
;
Liu, Yen-Chun
;
資訊管理與財務金融系註：原資管所+財金所
Derivatives are popular financial instruments whose values depend on other more fundamental financial assets (called the underlying assets). As they play essential roles in financial markets, evaluating them efficiently and accurately is critical. Most derivatives have no simple valuation formulas; as a result, they must be priced by numerical methods such as lattice methods. In a lattice, the prices of the derivatives converge to theoretical values when the number of time steps increases. Unfortunately, the nonlinearity error introduced by the nonlinearity of the option value function may cause the pricing results to converge slowly or even oscillate significantly. The lognormal diffusion process, which has been widely used to model the underlying asset's price dynamics, does not capture the empirical findings satisfactorily. Therefore, many alternative processes have been proposed, and a very popular one is the jump-diffusion process. This paper proposes an accurate and efficient lattice for the jump-diffusion process. Our lattice is accurate because its structure can suit the derivatives' specifications so that the pricing results converge smoothly. To our knowledge, no other lattices for the jump-diffusion process have successfully solved the oscillation problem. In addition, the time complexity of our lattice is lower than those of existing lattice methods by at least half an order. Numerous numerical calculations confirm the superior performance of our lattice to existing methods in terms of accuracy, speed, and generality. (C) 2010 Elsevier Inc. All rights reserved.
Evaluating corporate bonds and analyzing claim holders\' decisions with complex debt structure
(2016-11)
Liu, Liang-Chih
;
Dai, Tian-Shyr
;
Wang, Chuan-Ju
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Although many different aspects of debt structures such as bond covenants and repayment schedules are empirically found to significantly influence values of bonds and equity, many theoretical structural models still oversimplify debt structures and fail to capture phenomena found in financial markets. This paper proposes a carefully designed structural model that faithfully models typical complex debt structures containing multiple bonds with various covenants. For example, the ability for an issuing firm to meet an obligation is modeled to rely on its ability to meet previous repayments, and the default trigger is shaped according to the characteristics of its debt structure such as the amount and schedule of bond repayments. Thus our framework reliably provides theoretical insight and concrete quantitative measurements consistent with extant empirical research such as the shapes of yield spread curves under various firm\'s financial statuses, and the impact of payment blockage covenants on newly-issued and other outstanding bonds. We also develop the forest, a novel quantitative method to handle contingent changes in the debt structure due to premature bond redemptions. A forest consists of several trees that capture different debt structures, for instance those before or after a bond redemption. This method can be used to analyze how poison put covenants in the target firm\'s bonds influence the bidder\'s costs of debt financing for a leveraged buyout, or investigate how the presence of wealth transfer among the remaining claim holders due to a bond redemption influences the firm\'s call policy, or further reconcile conflicts among previous empirical studies on call delay phenomena. (C) 2016 Elsevier B.V. All rights reserved.
Evaluating corporate bonds with complicated liability structures and bond provisions
(2014-09-01)
Wang, Chuan-Ju
;
Dai, Tian-Shyr
;
Lyuu, Yuh-Dauh
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
This paper presents a general and numerically accurate lattice methodology to price risky corporate bonds. It can handle complex default boundaries, discrete payments, various asset sales assumptions, and early redemption provisions for which closed-form solutions are unavailable. Furthermore, it can price a portfolio of bonds that accounts for their complex interaction, whereas traditional approaches can only price each bond individually or a small portfolio of highly simplistic bonds. Because of the generality and accuracy of our method, it is used to investigate how credit spreads are influenced by the bond provisions and the change in a firm\'s liability structure due to bond repayments. (C) 2014 Elsevier B.V. All rights reserved.
FIN10K: A Web-based Information System for Financial Report Analysis and Visualization
(2016)
Liu, Yu-Wen
;
Liu, Liang-Chih
;
Wang, Chuan-Ju
;
Tsai, Ming-Feng
;
資訊管理與財務金融系註：原資管所+財金所
In this demonstration, we present FIN10K, a web-based information system that facilitates the analysis of textual information in financial reports. The proposed system has three main components: (1) a 10-K Corpus, including an inverted index of financial reports on Form 10-K, several numerical finance measures, and pre-trained word embeddings; (2) an information retrieval system; and (3) two data visualizations of the analyzed results. The system can be of great help in revealing valuable insights within large amounts of textual information. The system is now online available at http: //clip.csie.org/10K/.