Relevant bibliographies by topics / Trinomial Tree Model

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  1. Journal articles
  2. Dissertations / Theses
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  4. Conference papers

Academic literature on the topic 'Trinomial Tree Model'

Author: Grafiati
Published: 4 June 2021
Last updated: 14 February 2022

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Journal articles on the topic "Trinomial Tree Model"

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Gong, Wenxiu, and Zuoliang Xu. "Non-recombining trinomial tree pricing model and calibration for the volatility smile." Journal of Inverse and Ill-posed Problems 27, no. 3 (June 1, 2019): 353–66. http://dx.doi.org/10.1515/jiip-2018-0005.

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Abstract In this paper, we consider the non-recombining trinomial tree pricing model under the volatility, which is a function of time, establish the option pricing model and give the convergence rates of the non-recombining trinomial tree method. In addition, we research the calibration problem of volatility and adopt an exterior penalty method to transform this problem into a nonlinear unconstrained optimization problem. For the optimization problem, we use the quasi-Newton algorithm. Finally, we test our model by numerical examples and options data on the S&P 500 index. The results show the effectiveness of the non-recombining trinomial tree pricing model.
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Xiaoping, Hu, Guo Jiafeng, Du Tao, Cui Lihua, and Cao Jie. "Pricing Options Based on Trinomial Markov Tree." Discrete Dynamics in Nature and Society 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/624360.

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A trinomial Markov tree model is studied for pricing options in which the dynamics of the stock price are modeled by the first-order Markov process. Firstly, we construct a trinomial Markov tree with recombining nodes. Secondly, we give an algorithm for estimating the risk-neutral probability and provide the condition for the existence of a validation risk-neutral probability. Thirdly, we propose a method for estimating the volatilities. Lastly, we analyze the convergence and sensitivity of the pricing method implementing trinomial Markov tree. The result shows that, compared to binomial Markov tree, the proposed model is a natural combining tree and, while changing the probability of the node, it is still combining, so the computation is very fast and very easy to be implemented.
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ZHUO, XIAOYANG, and OLIVIER MENOUKEU-PAMEN. "EFFICIENT PIECEWISE TREES FOR THE GENERALIZED SKEW VASICEK MODEL WITH DISCONTINUOUS DRIFT." International Journal of Theoretical and Applied Finance 20, no. 04 (May 24, 2017): 1750028. http://dx.doi.org/10.1142/s0219024917500285.

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In this paper, we explore two new tree lattice methods, the piecewise binomial tree and the piecewise trinomial tree for both the bond prices and European/American bond option prices assuming that the short rate is given by a generalized skew Vasicek model with discontinuous drift coefficient. These methods build nonuniform jump size piecewise binomial/trinomial tree based on a tractable piecewise process, which is derived from the original process according to a transform. Numerical experiments of bonds and European/American bond options show that our approaches are efficient as well as reveal several price features of our model.
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Yuen, Fei Lung, and Hailiang Yang. "Option Pricing in a Jump-Diffusion Model with Regime Switching." ASTIN Bulletin 39, no. 2 (November 2009): 515–39. http://dx.doi.org/10.2143/ast.39.2.2044646.

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AbstractNowadays, the regime switching model has become a popular model in mathematical finance and actuarial science. The market is not complete when the model has regime switching. Thus, pricing the regime switching risk is an important issue. In Naik (1993), a jump diffusion model with two regimes is studied. In this paper, we extend the model of Naik (1993) to a multi-regime case. We present a trinomial tree method to price options in the extended model. Our results show that the trinomial tree method in this paper is an effective method; it is very fast and easy to implement. Compared with the existing methodologies, the proposed method has an obvious advantage when one needs to price exotic options and the number of regime states is large. Various numerical examples are presented to illustrate the ideas and methodologies.
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Dou, Changsheng, Li Wang, and Chenxi Zhu. "The Equation of Real Option Value under Trinomial Tree Model." Open Journal of Social Sciences 05, no. 03 (2017): 1–4. http://dx.doi.org/10.4236/jss.2017.53001.

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Zeng, Youzhi. "An Amended Trinomial Tree Model Based on China Convertible Bonds Market." Research Journal of Applied Sciences, Engineering and Technology 5, no. 12 (April 10, 2013): 3350–53. http://dx.doi.org/10.19026/rjaset.5.4578.

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Yan, Zhikai. "THE PRICING MODEL OF THE BARRIER OPTION UNDER THE TRINOMIAL TREE." Journal of Mathematical Sciences: Advances and Applications 52, no. 1 (July 10, 2018): 21–33. http://dx.doi.org/10.18642/jmsaa_7100121957.

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Han, Youngchul, and Geonwoo Kim. "Efficient Lattice Method for Valuing of Options with Barrier in a Regime Switching Model." Discrete Dynamics in Nature and Society 2016 (2016): 1–14. http://dx.doi.org/10.1155/2016/2474305.

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We propose an efficient lattice method for valuation of options with barrier in a regime switching model. Specifically, we extend the trinomial tree method of Yuen and Yang (2010) by calculating the local average of prices near a node of the lattice. The proposed method reduces oscillations of the lattice method for pricing barrier options and improves the convergence speed. Finally, computational results for the valuation of options with barrier show that the proposed method with interpolation is more efficient than the other tree methods.
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Dai, Tian-Shyr, and Yuh-Dauh Lyuu. "The Bino-Trinomial Tree: A Simple Model for Efficient and Accurate Option Pricing." Journal of Derivatives 17, no. 4 (May 31, 2010): 7–24. http://dx.doi.org/10.3905/jod.2010.17.4.007.

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Liu, Jianye, Zuxin Li, Dongkun Luo, and Ruolei Liu. "Study on the Valuation Method for Overseas Oil and Gas Extraction Based on the Modified Trinomial Tree Option Pricing Model." Mathematical Problems in Engineering 2020 (May 12, 2020): 1–15. http://dx.doi.org/10.1155/2020/4803909.

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Wandering of oil prices at lower values and the bitter reality have forced people to look for a more accurate valuation method for overseas oil and gas extraction of China. However, the currently available resource classification method, discount cash flow (DCF) method, and real option method all suffer from their own disadvantages. This paper identifies multiple uncertainty factors such as oil prices and reserves. It then investigates the transmission mechanism of how each uncertainty factor impacts the oil and gas extraction value and quantifies the transmission efficiency. The probability distribution patterns of each uncertainty factor have been determined; the trinomial tree option pricing model is modified, with consideration upon the nonstandardness of the probability distribution. Decision points and strategies space are designed in accordance with the practical oil and gas production; and the Bermuda option is adopted to replace the conventional decision-based tree model with the probability-based tree. Finally, a backward algorithm is developed to calculate the probability at each decision point, which avoids difficulties in determining the asset volatility ratio; and a case study is presented to demonstrate application of the proposed method. Results show that decision rights for overseas investment are valuable. The value of extraction does not yet necessarily grow with higher uncertainty, and instead, it is under joint effects of the cash flow and strategy space. So, valuation should incorporate the composite value of future cash flow and decision rights. Volatility of the value of extraction is not solely dependent on the oil price, but affected by multiple factors. Similar to the Bermuda option, the decision-making behavior for oil and gas extraction occurs only at finite decision points, to which the trinomial tree option pricing model is applicable. The adoption of probability distribution can to a great extent exploit the uncertain information. Replacement of the decision-based tree with the probability-based tree provides more accurate probability distribution of the calculated value of extraction, and moreover the disperse degree of the probability can reflect how high risks are, which is conducive to decision-making for investment.
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Dissertations / Theses on the topic "Trinomial Tree Model"

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Rehnman, Gustav, and Ted Tigerschiöld. "Analysis of Student Loan Asset-Backed Securities : Construction of a Valuation Model using a Trinomial Interest Rate Tree." Thesis, KTH, Matematisk statistik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-189021.

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Student debt in the U.S has grown rapidly over the last decades. A common practice among lenders is to pool the loans into securities that are sold off and traded between institutional investors. Since these securities have no market price this thesis aims to develop a valuation model. A time discrete approach is used, based on the Hull-White short-rate model to create a trinomial interest rate tree. This tree serves as a basis for the discounting of future cash flows generated from a specific student loan asset-backed security. In order to assess the credit risk, the student loan market and potential speculative bubbles are discussed. The model is applied on the ”Navient Student Loan Trust 2015-2” and each tranche’s intrinsic value and yield to maturity is calculated. Since the model lacks proper quantification of the credit risk, the result is a valuation model that is best used when valuing asset-backed securities that can be deemed risk- free.
Studentskulden i USA har växt kraftigt under de senaste decennierna. Ofta samlar de långivande bankerna ihop studentlånen och skapar värdepapper av lånen. Dessa säljs vidare och handlas sedan mellan institutionella investerare. Eftersom dessa värdepapper saknar marknadspris, ämnar den här uppsatsen att skapa en värderingsmodell. Detta görs i diskret tid, utifrån Hull-Whites korträntemodell skapas ett trinomialt träd. Detta träd tjänar sedan som bas för att diskontera framtida kassaflöden från ett specifikt studentlånsvärdepapper. För att uppskatta kreditrisken diskuteras studentlånemarknaden och potentiella spekulativa bubblor.   Modellen appliceras på ”Navient Student Loan Trust 2015-2” och det diskonterade värdet samt avkastning för varje specifik tranche beräknas. Då modellen saknar en kvantifiering av kreditrisken, är resultatet en modell som är mest applicerbar vid värdering av tillgångssäkrade värdepapper som kan bedömas som riskfria.
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Yuen, Fei-lung, and 袁飛龍. "Pricing options and equity-indexed annuities in regime-switching models by trinomial tree method." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B45595616.

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FILHO, PAULO ROBERTO LIMA DIAS. "OPTION PRICING USING THE IMPLIED TRINOMIAL TREES MODEL: APPLIED TO THE BRAZILLIAN STOCK MARKET." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2012. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=20294@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
Esta dissertação visa analisar como o modelo de apreçamento de opções, utilizando o conceito de árvore trinomial implícita, pode ser aplicado no mercado acionário brasileiro, com resultados mais consistentes, se comparado ao modelo de Black-Scholes. Esse modelo incorpora o conceito de volatilidade implícita, sendo consideradas as expectativas futuras em relação ao preço de um ativo. A volatilidade implícita apresenta diferentes valores para diferentes preços de exercício ao longo do tempo. A denominação sorriso de volatilidade deve-se ao formato da curva da volatilidade implícita em função do preço de exercício. O formato do sorriso varia de acordo com o ativo-objeto da opção. Assim, a volatilidade varia ao longo tempo no cálculo da árvore, pois leva em considerando as oscilações do mercado, o que, conseqüentemente, impacta no preço do ativo e sua opção.
This Paper aims to analyze how the option pricing model, using the concept of Implied Trinomial Trees can be applied to the Brazilian stock market, achieving more accurate results, if compared to the Black-Scholes model. This model includes the Implied Volatility concept, which means that future expectations are considered to price an asset. It presents different values for different Strike Prices through time. The volatility smile is named this way because of the shape of the Implied Volatility x Strike Price curve, which reminds a smile. Its shape changes according to the asset to be priced. Thus, as volatility varies with time, the option pricing using Implied Trinomial Trees is affected by the market’s oscillations, whose consequences can be observed in the asset’s price and its option price, consequently.
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Yolcu, Yeliz. "One Factor Interest Rate Models: Analytic Solutions And Approximations." Master's thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/2/12605863/index.pdf.

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The uncertainty attached to future movements of interest rates is an essential part of the Financial Decision Theory and requires an awareness of the stochastic movement of these rates. Several approaches have been proposed for modeling the one-factor short rate models where some lead to arbitrage-free term structures. However, no definite consensus has been reached with regard to the best approach for interest rate modeling. In this work, we briefly examine the existing one-factor interest rate models and calibrate Vasicek and Hull-White (Extended Vasicek) Models by using Turkey'
s term structure. Moreover, a trinomial interest rate tree is constructed to represent the evolution of Turkey&rsquo
s zero coupon rates.
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Lu, Cheng-tong, and 呂正東. "FUZZY TRINOMIAL TREE OPTION PRICING MODEL." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/46951117091270826047.

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碩士
大同大學
事業經營研究所碩士在職專班
91
ABSTRACT Option is one of the tools used by investors for arbitrage and hedging. currently, Black-Scholes and CRR models are commonly used for option pricing. However, they can only provide a theoretical reference. Though Yu (2002) has integrated the concept of fuzzy theory into CRR model to establish Fuzzy Binomial Tree Option Pricing Model (FBTOPM), which fuzzified the “Up” and “Down” jumping of stock prices, there is still a gap between the “triangular fuzzy number” derived from FBTOPM and the market real price. Like conventional pricing models, FBTOPM is also attributed to system bias. Based on Yu’s FBTOPM, this study intends to take into consideration the volatility of “Horizontal” jumping of stock prices and to fuzzify that volatility by establishing Fuzzy Trinomial Tree Option Pricing Model(FTTOPM) with a hope to see if the triangular fuzzy number derived from this model can be closer to the market real price. This study found that taking into consideration the volatility ”Horizontal” of stock prices in this model can substantially improve the problem of system bias and derive a triangular fuzzy number that is closer to the market real price. In addition, this FTTOPM provides more suitable option pricing for different risk preference as investment strategy references.
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Huang, Hsien-Chun, and 黃顯鈞. "A Trinomial Tree for the CIR model." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/6566c7.

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碩士
國立臺灣大學
資訊工程學研究所
107
The Cox–Ingersoll–Ross (CIR) model is a popular short rate model. Nawalkha and Beliaeva propose a trinomial tree for the CIR model to price zero-coupon bonds efficiently. This thesis proposes a different trinomial tree based on Dai and Lyuu. This results in smoother convergence.
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Chen, Cung-Ting, and 陳俊廷. "Pricing Warrants with Credit Risk─Trinomial Tree Model." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/95103389998131469336.

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碩士
世新大學
財務金融學研究所(含碩專班)
93
In the realistic investment environment, diversification of the financial goods and the complicating of economic system, often make the risk that investors face greatly increase, among them the most direct one is the credit risks of warrant issuer. There is no adequate margin settlement mechanism for prevailing covered warrant in Taiwan, and thus the credit risks of warrant issuer must be considered when investors evaluate the price of covered warrant. This thesis applies Klein’s (1996) vulnerable option valuation model and using the trinomial tree model to pricing vulnerable warrant. Besides, this thesis will also compare the difference of empirically result among the simulate value, Klein’s (1996) vulnerable option price, Black & Scholes option price and the market price of warrant by using the domestic American warrant data.
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HUANG, CHEN HUI, and 陳輝煌. "The Valuation of Taiwan Catastrophe Index Option With Hull and White''s Trinomial Tree Model." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/79754689202283629513.

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碩士
實踐大學
企業管理研究所
89
Due to the shortage of international reinsurance capacity, the high development of insurance risk exchange and catastrophe insurance derivatives has been treated a good resolution. These related products, as catastrophe futures, catastrophe index options and catastrophe bonds, have payoffs that depend on indices measured insured losses from catastrophe events in specific geographical regions. In principle, insures can use these securitized styles to transfer their regional exposure to numerous international investors. After adopting the concepts of catastrophe risk securitization, we also concern whether the framework is acceptable. Additionally, due the losses cap, mean-reverting and jump-diffusion characteristics, we make use of trinomial tree of Hull and White（1996）combined with jump-diffusion process of Merton（1976）to follow the related behaviors, then to estimate the suitable value and analyze their relative sensitivity of catastrophe index claims. As shown in the result, the mean-reverting behavior of Taiwan catastrophe losses series would lead to reduce the call value and sensitivity which was estimated by Black-Scholes option pricing model. The jump behavior would derive losses index to rise quickly, and the related sensitivity would be more stable and smaller in comparison with Hull and White Model.
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Huang, Wen-Jie, and 黃文潔. "Pricing of Convertible Bond with Correlation between Interest Rate and Stock Price under Recombining Trinomial Tree Model." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/60220616632253060100.

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碩士
國立臺灣大學
國際企業學研究所
98
Abstract This thesis discusses the pricing of convertible bonds, especially when the correlation of interest rate and stock price should be considered. In addition, I also take default risk into consideration. The interest rate model considered in the thesis follows the Hull-White tree model to fit initial term structure and limited upside or downside bound on interest rate tree, and the stock tree process is simulated by the trinomial tree model in Kamrad and Ritchken (1991). Two kinds of methods to determine the default intensity are discussed in this thesis: first is based on the credit spreads of risky corporate bonds, and the other is based on the credit migration probabilities for different credit levels. Furthermore, this thesis also ensures that the length of the time step is small enough such that the branching probabilities are valid in this model. Then I provide real numerical sensitivity analysis to see how our model behaves. At the end, I conclude and show what can be improved to our model when pricing CBs.
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Cheng, Wen-Chieh, and 鄭文杰. "Valuation of Callable Accreting Interest Rate Swaps: Comparison between the Least-Squares Monte-Carlo Method and Trinomial Tree under Hull-White Interest Rate Model." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/a42rtn.

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碩士
國立政治大學
金融學系
107
This paper discusses two problems based on Hull-White term structure model as follow: (i) How to conduct a valuation of callable accreting interest rate swap(CAIRS) ? (ii) CAIRS is a type of widely used risk management instruments for zero callable bonds (ZCB) . Is it suitable enough to hedge risks of zero callable bond? First, CAIRS can be decomposed into accreting payer interest rate swaps and Bermudan swaptions. Considering financial valuation of both components, the former can be directly valued by the pricing formula, while the latter has no close form due to its early exercise characteristics. In order to solve the problem, the approaches here include LSM method in Longstaff and Schwartz (2001) and trinomial tree in Hull and White (1994) . We find out that the two options embedded in ZCB and CAIRS have same exercise strategy since the terms of the swaps will consist with the bonds in practice. However, the cash flow of risk management in swaps and bonds can be different when considering the discount of time value. Hence, CAIRS are not the best financial instrument for managing risks of zero callable bonds under current design.
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Book chapters on the topic "Trinomial Tree Model"

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Deutsch, Hans-Peter. "Binomial and Trinomial Trees." In Derivatives and Internal Models, 147–66. London: Palgrave Macmillan UK, 2002. http://dx.doi.org/10.1057/9780230502109_11.

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Deutsch, Hans-Peter. "Binomial and Trinomial Trees." In Derivatives and Internal Models, 149–68. London: Palgrave Macmillan UK, 2004. http://dx.doi.org/10.1057/9781403946089_11.

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Deutsch, Hans-Peter. "Binomial and Trinomial Trees." In Derivatives and Internal Models, 161–83. London: Palgrave Macmillan UK, 2009. http://dx.doi.org/10.1057/9780230234758_10.

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Deutsch, Hans-Peter, and Mark W. Beinker. "Binomial and Trinomial Trees." In Derivatives and Internal Models, 139–63. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-22899-6_9.

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"Market incompleteness and one-period trinomial tree models." In Actuarial Finance, 291–324. Hoboken, NJ, USA: John Wiley & Sons, Inc., 2019. http://dx.doi.org/10.1002/9781119526438.ch13.

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Conference papers on the topic "Trinomial Tree Model"

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Ganikhodjaev, Nasir, and Kamola Bayram. "Random trinomial tree models and vanilla options." In INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND STATISTICS 2013 (ICMSS2013): Proceedings of the International Conference on Mathematical Sciences and Statistics 2013. AIP, 2013. http://dx.doi.org/10.1063/1.4823907.

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