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Journal articles on the topic 'Trinomial Tree Model'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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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11

NG, LESLIE. "NUMERICAL PROCEDURES FOR A WRONG WAY RISK MODEL WITH LOGNORMAL HAZARD RATES AND GAUSSIAN INTEREST RATES." International Journal of Theoretical and Applied Finance 16, no. 08 (December 2013): 1350049. http://dx.doi.org/10.1142/s0219024913500490.

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In this work, we present some numerical procedures for a wrong way risk model that can be used for credit value adjustment (CVA) calculations. We look at a model that uses a multi-factor Hull–White model for interest rates and a single-factor lognormal Black–Karasinski default intensity model for counterparty credit, where the default intensity driver is correlated with all interest rate drivers. We describe how a trinomial tree-based approach for implementing single factor short rate models by Hull and White (1994) can be modified and used to calibrate the intensity model to credit default swaps (CDSs) in the presence of correlation. We also provide approximate pricing methods for CDS options and single swap contingent CDS contracts. The latter methods could also be used for model calibration purposes subject to data availability.

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12

Gu, Qing-Hua, Qiong Wu, and Cai-Wu Lu. "Trinomial tree model of the real options approach used in mining investment price forecast and analysis." Journal of Coal Science and Engineering (China) 19, no. 4 (December 2013): 573–77. http://dx.doi.org/10.1007/s12404-013-0421-z.

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13

Zhang, Wei-Guo, and Ping-Kang Liao. "Pricing Convertible Bonds with Credit Risk under Regime Switching and Numerical Solutions." Mathematical Problems in Engineering 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/381943.

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This paper discusses the convertible bonds pricing problem with regime switching and credit risk in the convertible bond market. We derive a Black-Scholes-type partial differential equation of convertible bonds and propose a convertible bond pricing model with boundary conditions. We explore the impact of dilution effect and debt leverage on the value of the convertible bond and also give an adjustment method. Furthermore, we present two numerical solutions for the convertible bond pricing model and prove their consistency. Finally, the pricing results by comparing the finite difference method with the trinomial tree show that the strength of the effect of regime switching on the convertible bond depends on the generator matrix or the regime switching strength.

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14

Chang, Carolyn W., and Jack S. K. Chang. "Doubly-Binomial Option Pricing with Application to Insurance Derivatives." Review of Pacific Basin Financial Markets and Policies 08, no. 03 (September 2005): 501–23. http://dx.doi.org/10.1142/s0219091505000439.

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We generalize the standard lattice approach of Cox, Ross, and Rubinstein (1976) from a fixed sum to a random sum in a subordinated process framework to accommodate pricing of derivatives with random-sum characteristics. The asset price change now is determined by two independent Bernoulli trials on information arrival/non-arrival and price up/down, respectively. The subordination leads to a nonstationary trinomial tree in calendar-time, while a time change to information-time restores the simpler binomial tree that now grows with the intensity of information arrival irrespective of the passage of calendar-time. We apply the model to price the CBOT catastrophe futures call spreads as a binomial sum of binomial prices, which illuminates the information conveyed by the randomness of catastrophe arrival. Numerical results demonstrate that the standard binomial formula that ignores random claim arrival produces largest undervaluation error for out-of-money short-maturity options when a small number of significant catastrophes may strike during the option's maturity.

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15

Luo, Xiankang, and Jie Xing. "Optimal Surrender Policy of Guaranteed Minimum Maturity Benefits in Variable Annuities with Regime-Switching Volatility." Mathematical Problems in Engineering 2021 (July 13, 2021): 1–20. http://dx.doi.org/10.1155/2021/9969937.

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This study investigates valuation of guaranteed minimum maturity benefits (GMMB) in variable annuity contract in the case where the guarantees can be surrendered at any time prior to the maturity. In the event of the option being exercised early, early surrender charges will be applied. We model the underlying mutual fund dynamics under regime-switching volatility. The valuation problem can be reduced to an American option pricing problem, which is essentially an optimal stopping problem. Then, we obtain the pricing partial differential equation by a standard Markovian argument. A detailed discussion shows that the solution of the problem involves an optimal surrender boundary. The properties of the optimal surrender boundary are given. The regime-switching Volterra-type integral equation of the optimal surrender boundary is derived by probabilistic methods. Furthermore, a sensitivity analysis is performed for the optimal surrender decision. In the end, we adopt the trinomial tree method to determine the optimal strategy.

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16

Ma, Jingtang, and Tengfei Zhu. "Convergence rates of trinomial tree methods for option pricing under regime-switching models." Applied Mathematics Letters 39 (January 2015): 13–18. http://dx.doi.org/10.1016/j.aml.2014.07.020.

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17

Leippold, Markus, and Zvi Wiener. "Efficient Calibration of Trinomial Trees for One-Factor Short Rate Models." Review of Derivatives Research 7, no. 3 (December 2004): 213–39. http://dx.doi.org/10.1007/s11147-004-4810-8.

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18

Fabbri, Mattia, and Pier Giuseppe Giribone. "Design, implementation and validation of advanced lattice techniques for pricing EAKO — European American Knock-Out option." International Journal of Financial Engineering 06, no. 04 (December 2019): 1950032. http://dx.doi.org/10.1142/s2424786319500324.

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The paper presents a series of advanced lattice methods aimed at evaluating an EAKO European-American Knock-Out contract. The first part of the paper deals with the numerical methods implemented for pricing: Binomial and Trinomial Stochastic trees, Adaptive Mesh Model, Pentanomial and Heptanomial lattice. In the second part, specific tests are designed to validate the code written in Matlab language. The study concludes by applying the most performing model to a real market case.

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19

Lok, U. Hou, and Yuh‐Dauh Lyuu. "Efficient trinomial trees for local‐volatility models in pricing double‐barrier options." Journal of Futures Markets 40, no. 4 (December 3, 2019): 556–74. http://dx.doi.org/10.1002/fut.22080.

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20

O’Sullivan, Conall, and Stephen O’Sullivan. "Accelerated trinomial trees applied to American basket options and American options under the Bates model." Journal of Computational Finance 19, no. 4 (June 2016): 29–72. http://dx.doi.org/10.21314/jcf.2016.212.

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21

HAUG, ESPEN GAARDER. "CLOSED FORM VALUATION OF AMERICAN BARRIER OPTIONS." International Journal of Theoretical and Applied Finance 04, no. 02 (April 2001): 355–59. http://dx.doi.org/10.1142/s0219024901001012.

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Closed form formulae for European barrier options are well known from the literature. This is not the case for American barrier options, for which no closed form formulae have been published. One has therefore had to resort to numerical methods. Lattice models like a binomial or a trinomial tree, for valuation of barrier options are known to converge extremely slowly, compared to plain vanilla options. Methods for improving the algorithms have been described by several authors. However, these are still numerical methods that are quite computer intensive. In this paper we show how some American barrier options can be valued analytically in a very simple way. This speeds up the valuation dramatically as well as give new insight into barrier option valuation.

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22

Clayton, Michael A. "Time-Series Heston Model Calibration Using a Trinomial Tree." SSRN Electronic Journal, 2020. http://dx.doi.org/10.2139/ssrn.3718697.

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23

Palivonaitė, Rita, and Eimutis Valakevičius. "Investigation of the barrier options pricing models." Lietuvos matematikos rinkinys 50 (December 20, 2009). http://dx.doi.org/10.15388/lmr.2009.57.

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In the article three methods of barrier option pricing are analysed and compared: Black–Scholes, trinomial ant adaptive mesh algorithm. Investigation with Lithuanian firm’s stock showed, that to get better results it is offered to adapt higer resolution mesh on critical regions of trinomial tree.

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24

Lok, U. Hou, and Yuh-Dauh Lyuu. "A Valid and Efficient Trinomial Tree for General Local-Volatility Models." Computational Economics, August 6, 2021. http://dx.doi.org/10.1007/s10614-021-10166-x.

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25

Leippold, Markus, and Zvi Wiener. "Efficient Calibration of Trinomial Trees for One-Factor Short Rate Models." SSRN Electronic Journal, 2003. http://dx.doi.org/10.2139/ssrn.398261.

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26

Leippold, Markus, and Zvi Wiener. "Algorithms behind Term Structure Models of Interest Rates II: The Hull-White Trinomial Tree of Interest Rates." SSRN Electronic Journal, 2001. http://dx.doi.org/10.2139/ssrn.292223.

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