Browsing by Author "Dai, Tian-Shyr"

Now showing 1 - 20 of 25

A flexible tree for evaluating guaranteed minimum withdrawal benefits under deferred life annuity contracts with various provisions
(2013-03-01)
Yang, Sharon S.
;
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
Valuing guaranteed minimum withdrawal benefit (GMWB) has attracted significant attention from both the academic field and real world financial markets. However, some popular provisions of GMWB contracts, like the deferred life annuity structure, rollup interest rate guarantees, and surrender options are hard to be evaluated analytically and are rarely addressed in the academic literature. This paper proposes a flexible tree model that can accurately evaluate the values and the fair insurance fees of GMWBs. The flexibility of our tree allows us to faithfully implement the aforementioned provisions without introducing significant numerical pricing errors. The mortality risk can also be easily incorporated into our pricing model. Our numerical results verify the robustness of our tree and demonstrate how the aforementioned provisions and the mortality risk significantly influence the values and the fair insurance fees of GMWBs. (c) 2012 Elsevier B.V. All rights reserved.
A Modified Reduced-Form Model with Time-Varying Default and Recovery Rates and Its Applications in Pricing Convertible Bonds
(2017-06-01)
Wang, Jr-Yan
;
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
Due to the lack of proper credit derivatives and opaque financial status of a reference entity, it is difficult to accurately estimate recovery rates in reducedform models. In addition, most reduced-form models adopt a constant recovery rate assumption that fails to capture the time-varying dynamics and inverse relationships between recovery and default rates found in empirical studies. Most revisions that incorporate this inverse relationship require strict calibration procedures or limit the wide applicability of reducedform models due to introducing complexity models involving stochastic processes. The authors propose a notion of the expected recovery rate conditional on the default rate by combining a regression relationship between these two rates and a transformation between default rates under the physical and riskneutral measures. This notion can be simply incorporated into any reduced-form model to simultaneously produce reliable time-varying recovery and default rates. To demonstrate their idea, they revise Jarrow and Turnbull's [1995] reduced-form model used in Chambers and Lu [2007] for pricing convertible bonds. The resulting tree structure is also adjusted to alleviate the infeasible branching probability problem.
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.
A Reliable Fingerprint Orientation Estimation Algorithm
(2011-01-01)
Liu, Limin
;
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
Correctly estimating fingerprint ridge orientation is an important task in fingerprint image processing. A successful orientation estimation algorithm can drastically improve the performance of tasks such as fingerprint enhancement, classification, and singular points extraction. Gradient-based orientation estimation algorithms are widely adopted in academic literature, but they cannot guarantee the correctness of ridge orientations. Even worse, they assign orientations to blocks with singular points. A novel and reliable orientation estimation algorithm is proposed in this paper. This algorithm runs in two phases. The first phase assigns reliable orientations to blocks with parallel structures and marks other blocks with noise, singular points, and minutiae as uncertain. Since most uncertain blocks marked in the first phase do have unique ridge orientations, the second phase of our algorithm restores the orientations of these uncertain blocks from their neighbor blocks orientations. Different from other orientation estimation algorithms, our algorithm leaves the blocks containing singular points and assigns reliable orientations to the other blocks. Detailed examples are given in this paper to show how our algorithm works. We use NIST-4 fingerprint database in our experiment to verify the superiority of our algorithm.
Accurate and efficient lattice algorithms for American-style Asian options with range bounds
(2009-03-15)
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
Asian options are popular path-dependent options and it has been a long-standing problem to price them efficiently and accurately. Since there is no known exact pricing formula for Asian options, numerical pricing formulas like lattice models must be employed. A lattice divides a certain time interval into n time steps and the pricing results generated by the lattice (called desired option values for convenience) converge to the theoretical option value as n -> infinity. Since a brute-force lattice pricing algorithm runs in subexponential time in n, some heuristics, like interpolation method, are used to strike the balance between the efficiency and the accuracy. But the pricing results might not converge due to the accumulation of interpolation errors. For pricing European-style Asian options, the evaluation on the major part of the lattice can be done by a simple formula, and the interpolation method is only required on the minor part of the lattice. Thus polynomial time algorithms with convergence guarantee for European-style Asian options can be derived. However, such a simple formula does not exist for American-style Asian options. This paper suggests an efficient range-bound algorithm that bracket the desired option value. By taking advantages of the early exercise property of American-style options, we show that part of the lattice can be evaluated by a simple formula. The interpolation method is required on the remaining part of the lattice and the upper and the lower bounds option values produced by the proposed algorithm are essentially numerically identical. Thus the theoretical option value is said to be obtained practically when the range bound algorithm runs on a lattice with large number of time steps. (C) 2008 Elsevier Inc. All rights reserved.
Accurate approximation formulas for stock options with discrete dividends
(2009)
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
Pricing options on a stock that pays discrete dividends has not been satisfactorily settled in the literature. Frishling (2002) shows that there are three different models to model stock price with discrete dividends, but only one of these models is close to reality and generates consistent option prices. We follow Frishling (2002) by calling this model Model 3. Unfortunately, there is no analytical option pricing formula for Model 3, and many popular numerical methods such as trees are inefficient when used to implement Model 3. A new stock price model is proposed in this article. To guarantee that the option prices generated by this new model are close to those generated by Model 3, the distributions of the new model at exdividend dates and maturity approximate the distributions of Model 3at those dates. To achieve this, a discrete dividend in Model 3 is replaced by a continuous dividend yield that can be represented as a function of discrete dividends and stock returns in the new model. Thus, the new model follows a lognormal diffusion process and the analytical option pricing formulas can be easily derived. Numerical experiments show that our analytical pricing formulas provide accurate pricing results.
Adaptive placement method on pricing arithmetic average options
(2008-03-01)
Dai, Tian-Shyr
;
Wang, Jr-Yan
;
Wei, Hui-Shan
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Since there is no analytic solution for arithmetic average options until present, developing an efficient numerical algorithm becomes a promising alternative. One of the most famous numerical algorithms is introduced by Hull and White (J Deriv 1:21-31, 1993). Motivated by the common idea of reducing the nonlinearity error in the adaptive mesh model in Figlewski and Gao (J Financ Econ 53:313-351, 1999) and the adaptive quadrature method, we propose an adaptive placement method to replace the logarithmically equally-spaced placement rule in the Hull and White's model by placing more representative average prices in the highly nonlinear area of the option value as the function of the arithmetic average stock price. The basic idea of this method is to design a recursive algorithm to limit the error of the linear interpolation between each pair of adjacent representative average prices. Numerical experiments verify the superior performance of this method for reducing the interpolation error and hence improving the convergence rate. To show that the adaptive placement method can improve any numerical algorithm with the techniques of augmented state variables and the piece-wise linear interpolation approximation, we also demonstrate how to integrate the adaptive placement method into the GARCH option pricing algorithm in Ritchken and Trevor (J Finance 54:377-402, 1999). Similarly great improvement of the convergence rate suggests the potential applications of this novel method to a broad class of numerical pricing algorithms for exotic options and complex underlying processes.
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 Economic Model for Utilizing Cloud Computing Resources via Pricing Elasticity of Demand and Supply
(2015)
Qanbari, Soheil
;
Li, Fei
;
Dustdar, Schahram
;
Dai, Tian-Shyr
;
資訊管理與財務金融系註：原資管所+財金所
In this study, we elaborate two economic variables which have direct impact on prospective aspects of trading like Cloud resource allocation over future demands. These variables are Pricing Elasticity of Demand (PEoD) and Pricing Elasticity of Provisioning (PEoP). To leverage the pricing elasticity of upcoming demand and supply, we employ financial option theory as a method to alleviate the risk in resource provisioning over future demands. Our approach finds the optimal option price of the federated resource in the Cloud to come to an equilibrium between PEoD and PEoP. The asset equilibrium price occurs when the supply resource pool matches the aggregate demand indicating an optimal resource utilization. This study proposes a novel Cloud Asset Pricing Tree (CAPT) model that finds the optimal premium price of the Cloud federation options efficiently. The CAPT enables cloud service providers to make proper decisions when to trade options in advance and when to exercise them to achieve more economies of scale. Our empirical evidences suggest that utilizing the CAPT model, exploits the Cloud federation market as an opportunity for more resource utilization and future capacity planning.
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.
An efficient, and fast convergent algorithm for barrier options
(2007)
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
A barrier option is an option whose payoff depends on whether the price path of the underlying asset ever reaches certain predetermined price levels called the barriers. A single- (double-) barrier option is a barrier option with one (two, respectively) barrier(s). No simple and exact closed-form pricing formula for double-barrier options has been reported in the literature. This paper proposes a novel tree model that can price both single- and double-barrier options efficiently and accurately. This tree model achieves the high efficiency by combinatorial techniques and numerical accuracy by hitting the barriers exactly. Numerical experiments are given to verify the superiority of our method.
An exact subexponential-time lattice algorithm for Asian options
(2007-04-01)
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
Asian options are popular financial derivative securities. Unfortunately, no exact pricing formulas exist for their price under continuous-time models. Asian options can also be priced on the lattice, which is a discretized version of the continuous- time model. But only exponential-time algorithms exist if the options are priced on the lattice without approximations. Although efficient approximation methods are available, they lack accuracy guarantees in general. This paper proposes a novel lattice structure for pricing Asian options. The resulting pricing algorithm is exact (i.e., without approximations), converges to the value under the continuous-time model, and runs in subexponential time. This is the first exact, convergent lattice algorithm to break the long-standing exponential-time barrier.
An ingenious, piecewise linear interpolation algorithm for pricing arithmetic average options
(2007)
Dai, Tian-Shyr
;
Wang, Jr-Yan
;
Wei, Hui-Shan
;
資訊管理與財務金融系註：原資管所+財金所
;
Department of Information Management and Finance
Pricing arithmetic average options continues to intrigue researchers in the field of financial engineering. Since there is no analytical solution for this problem until present, developing an efficient numerical algorithm becomes a promising alternative. One of the most famous numerical algorithms for pricing arithmetic average options is introduced by Hull and White [10]. In this paper, motivated by the common idea of reducing the nonlinearity error in the adaptive mesh model [7] and the adaptive quadrature numerical integration method [6], the logarithmically equally-spaced placement rule in the Hull and White's model is replaced by an adaptive placement method, in which the number of representative average prices is proportional to the degree of curvature of the option value as a function of the arithmetic average price. Numerical experiments verify the superior performance of our method in terms of reducing the interpolation error. In fact, it is straightforward to apply this method to any pricing algorithm with the techniques of augmented state variables and the piece-wise linear interpolation approximation.
Efficient option pricing on stocks paying discrete or path-dependent dividends with the stair tree
(2009)
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
Pricing options on a stock that pays discrete dividends has not been satisfactorily settled because of the conflicting demands of computational tractability and realistic modelling of the stock price process. Many papers assume that the stock price minus the present value of future dividends or the stock price plus the forward value of future dividends follows a lognormal diffusion process; however, these assumptions might produce unreasonable prices for some exotic options and American options. It is more realistic to assume that the stock price decreases by the amount of the dividend payout at the ex-dividend date and follows a lognormal diffusion process between adjacent ex-dividend dates, but analytical pricing formulas and efficient numerical methods are hard to develop. This paper introduces a new tree, the stair tree, that faithfully implements the aforementioned dividend model without approximations. The stair tree uses extra nodes only when it needs to simulate the price jumps due to dividend payouts and return to a more economical, simple structure at all other times. Thus it is simple to construct, easy to understand, and efficient. Numerous numerical calculations confirm the stair tree's superior performance to existing methods in terms of accuracy, speed, and/or generality. Besides, the stair tree can be extended to more general cases when future dividends are completely determined by past stock prices and dividends, making the stair tree able to model sophisticated dividend processes.
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.
Linear-time option pricing algorithms by combinatorics
(2008-05-01)
Dai, Tian-Shyr
;
Liu, Li-Min
;
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
Options are popular financial derivatives that play essential roles in financial markets. How to price them efficiently and accurately is very important both in theory and practice. Options are often priced by the lattice model. Although the prices computed by the lattice converge to the theoretical option value under the continuous-time model, they may converge slowly. Worse, for some options like barrier options, the prices can even oscillate wildly. For Such options, huge amounts of computational time are required to achieve acceptable accuracy. Combinatorial techniques have been used to improve the performance in pricing a wide variety of options. This paper uses vanilla options, power options, single-barrier options, double-barrier options, and lookback options as examples to show how combinatorics can help us to derive linear-time pricing algorithms. These algorithms compare favorably against popular lattice methods, which take at least quadratic time. (C) 2007 Elsevier Ltd. All rights reserved.
Pricing Asian option by the FFT with higher-order error convergence rate under Levy processes
(2015-02-01)
Chiu, Chun-Yuan
;
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
Pricing Asian options is a long-standing hard problem; there is no analytical formula for the probability density of its payoff even when the process of the underlying asset follows the simple lognormal diffusion process. It is known that the density function of a discretely-sampled Asian option\'s payoff can be efficiently approximated by the Fast Fourier Transform (FFT). As a result, we can accurately price the option under more general Levy processes. This paper shows that the pricing error of this approach, called the FFT approach, can be decomposed into the truncation error, the integration error, and the interpolation error. We prove that previous algorithms that follow the FFT approach converge quadratically. To improve the error convergence rate, our proposed algorithms reduce the integration error by the higher-order Newton-Cotes formulas and new integration rules derived from the Lagrange interpolating polynomial. The interpolation error is reduced by the higher-order Newton divided-difference interpolation formula. Consequently, our algorithms can be sped up by the FFT to achieve the same time complexity as previous algorithms, but with a faster error convergence rate. Numerical results are given to verify the efficiency and the fast convergence of our algorithms. (c) 2014 Elsevier Inc. All rights reserved.