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Journal articles on the topic 'The Cox-Ross-Rubinstein model'

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Published: 24 April 2022

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1

Motoczyński, Michał, and Łukasz Stettner. "On option pricing in the multidimensional Cox-Ross-Rubinstein model." Applicationes Mathematicae 25, no. 1 (1998): 55–72. http://dx.doi.org/10.4064/am-25-1-55-72.

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2

Wrede, Marcus, and Norbert Schmitz. "Variations of the Cox-Ross-Rubinstein model - conservative pricing strategies." Mathematical Methods of Operations Research (ZOR) 53, no. 3 (2001): 505–15. http://dx.doi.org/10.1007/s001860100126.

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3

Carassus, Laurence, and Tiziano Vargiolu. "Super-replication price: it can be ok." ESAIM: Proceedings and Surveys 64 (2018): 54–64. http://dx.doi.org/10.1051/proc/201864054.

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We consider a discrete time financial model where the support of the conditional law of the risky asset is bounded. For convex options we show that the super-replication problem reduces to the replication one in a Cox-Ross-Rubinstein model whose parameters are the law support boundaries. Thus the super-replication price can be of practical use if this support is not to large. We also make the link with the recent literature on multiple-priors models.
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4

Hunzinger, Chadd B., and Coenraad C. A. Labuschagne. "The Cox, Ross and Rubinstein tree model which includes counterparty credit risk and funding costs." North American Journal of Economics and Finance 29 (July 2014): 200–217. http://dx.doi.org/10.1016/j.najef.2014.06.002.

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5

Wolczyńska, Grażyna. "An Explicit Formula for Option Pricing in Discrete Incomplete Markets." International Journal of Theoretical and Applied Finance 01, no. 02 (1998): 283–88. http://dx.doi.org/10.1142/s0219024998000151.

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Some aspects of the pricing of European call option are disscussed. We consider the simplest case of an incomplete market in the situation when the model of the market is discrete and increments of shares prices have a multinomial distribution. We look for similarities between this model and the model of Cox, Ross and Rubinstein. In particular we consider the possibility of using induction backwards and we look for an optimal price and strategy using the method of risk-minimization step by step from the date of realization T to 0.
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6

LINARAS, CHARILAOS E., and GEORGE SKIADOPOULOS. "IMPLIED VOLATILITY TREES AND PRICING PERFORMANCE: EVIDENCE FROM THE S&P 100 OPTIONS." International Journal of Theoretical and Applied Finance 08, no. 08 (2005): 1085–106. http://dx.doi.org/10.1142/s0219024905003359.

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This paper examines the pricing performance of various discrete-time option models that accept the variation of implied volatilities with respect to the strike price and the time-to-maturity of the option (implied volatility tree models). To this end, data from the S&P 100 options are employed for the first time. The complex implied volatility trees are compared to the standard Cox–Ross–Rubinstein model and the ad-hoc traders model. Various criteria and interpolation methods are used to evaluate the performance of the models. The results have important implications for the pricing accuracy
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7

Castro, Isabel, and Carlos G. Pacheco. "Modeling and pricing with a random walk in random environment." International Journal of Financial Engineering 07, no. 04 (2020): 2050053. http://dx.doi.org/10.1142/s242478632050053x.

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We propose a parsimonious model for financial pricing that incorporates the existence of a random environment; such construction can be though as an extension of the Cox–Ross–Rubinstein (CRR) model. Our model is motivated from the Sinai random walk, but we mention the difficulty of applying such model if we try to use it with the CRR procedure. As it was done with Sinai’s walk, we provide a method to connect the most visited sites of the model with the minimum points of a function of the environment. We present some simulations and a numerical experiment to bring a new perspective.
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8

Llemit, Dennis G. "On a recursive algorithm for pricing discrete barrier options." International Journal of Financial Engineering 02, no. 04 (2015): 1550047. http://dx.doi.org/10.1142/s2424786315500474.

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An alternative and simple algorithm for valuating the price of discrete barrier options is presented. This algorithm computes the price just exactly the same as the Cox–Ross–Rubinstein (CRR) model. As opposed to other pricing methodologies, this recursive algorithm utilizes only the terminal nodes of the binomial tree and it captures the intrinsic property, the knock-in or knock-out feature, of barrier options. In this paper, we apply the algorithm to compute the price of an Up and Out Put (UOP) barrier option and compare the results obtained from the CRR model. We then determine the time comp
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9

HEUWELYCKX, FABIEN. "CONVERGENCE OF EUROPEAN LOOKBACK OPTIONS WITH FLOATING STRIKE IN THE BINOMIAL MODEL." International Journal of Theoretical and Applied Finance 17, no. 04 (2014): 1450025. http://dx.doi.org/10.1142/s0219024914500253.

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In this paper, we study the convergence of a European lookback option with floating strike evaluated with the binomial model of Cox–Ross–Rubinstein to its evaluation with the Black–Scholes model. We do the same for its delta. We confirm that these convergences are of order [Formula: see text]. For this, we use the binomial model of Cheuk–Vorst which allows us to write the price of the option using a double sum. Based on an improvement of a lemma of Lin–Palmer, we are able to give the precise value of the term in [Formula: see text] in the expansion of the error; we also obtain the value of the
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10

Tehranchi, Michael R. "On the Uniqueness of Martingales with Certain Prescribed Marginals." Journal of Applied Probability 50, no. 2 (2013): 557–75. http://dx.doi.org/10.1239/jap/1371648961.

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This note contains two main results. (i) (Discrete time) Suppose that S is a martingale whose marginal laws agree with a geometric simple random walk. (In financial terms, let S be a risk-neutral asset price and suppose that the initial option prices agree with the Cox-Ross-Rubinstein binomial tree model.) Then S is a geometric simple random walk. (ii) (Continuous time) Suppose that S=S0eσ X-σ2〈 X〉/2 is a continuous martingale whose marginal laws agree with a geometric Brownian motion. (In financial terms, let S be a risk-neutral asset price and suppose that the initial option prices agree wit
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11

Tehranchi, Michael R. "On the Uniqueness of Martingales with Certain Prescribed Marginals." Journal of Applied Probability 50, no. 02 (2013): 557–75. http://dx.doi.org/10.1017/s0021900200013565.

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This note contains two main results. (i) (Discrete time) Suppose that S is a martingale whose marginal laws agree with a geometric simple random walk. (In financial terms, let S be a risk-neutral asset price and suppose that the initial option prices agree with the Cox-Ross-Rubinstein binomial tree model.) Then S is a geometric simple random walk. (ii) (Continuous time) Suppose that S=S 0eσ X-σ2〈 X〉/2 is a continuous martingale whose marginal laws agree with a geometric Brownian motion. (In financial terms, let S be a risk-neutral asset price and suppose that the initial option prices agree wi
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12

LEDUC, GUILLAUME, and KENNETH PALMER. "WHAT A DIFFERENCE ONE PROBABILITY MAKES IN THE CONVERGENCE OF BINOMIAL TREES." International Journal of Theoretical and Applied Finance 23, no. 06 (2020): 2050040. http://dx.doi.org/10.1142/s0219024920500405.

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In the [Formula: see text]-period Cox, Ross, and Rubinstein (CRR) model, we achieve smooth convergence of European vanilla options to their Black–Scholes limits simply by altering the probability at one node, in fact, at the preterminal node between the closest neighbors of the strike in the terminal layer. For barrier options, we do even better, obtaining order [Formula: see text] convergence by altering the probability just at the node nearest the barrier, but only the first time it is hit. First-order smooth convergence for vanilla options was already achieved in Tian’s flexible model but h
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13

Nika, Zsolt, and Tamás Szabados. "Strong approximation of Black-Scholes theory based on simple random walks." Studia Scientiarum Mathematicarum Hungarica 53, no. 1 (2016): 93–129. http://dx.doi.org/10.1556/012.2016.53.1.1331.

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A basic model in financial mathematics was introduced by Black, Scholes and Merton in 1973. A classical discrete approximation in distribution is the binomial model given by Cox, Ross and Rubinstein in 1979. In this work we give a strong (almost sure, pathwise) discrete approximation of the BSM model using a suitable nested sequence of simple, symmetric random walks. The approximation extends to the stock price process, the value process, the replicating portfolio, and the greeks. An important tool in the approximation is a discrete version of the Feynman-Kac formula as well. Our aim is to sho
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14

Prabowo, Agung, Zulfatul Mukarromah, Lisnawati Lisnawati, and Pramono Sidi. "PENENTUAN HARGA OPSI BELI ATAS SAHAM PT. ANTAM (PERSERO) MENGGUNAKAN MODEL BINOMIAL FUZZY." Jurnal Matematika Sains dan Teknologi 19, no. 1 (2018): 8–24. http://dx.doi.org/10.33830/jmst.v19i1.124.2018.

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Option is a financial instrument where price depends on the underlying stock price. The pricing of options, both selling options and purchase options, may use the CRR (Cox-Ross-Rubinstein) binomial model. Only two possible parameters were used that is u if the stock price rises and d when the stock price down. One of the elements that determine option prices is volatility. In the binomial model CRR volatility is constant. In fact, the financial market price of stocks fluctuates so that volatility also fluctuates. This article discusses volatility of fluctuating stock price movements by modelin
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15

NAYMAN, NIV. "SHORTFALL RISK MINIMIZATION UNDER FIXED TRANSACTION COSTS." International Journal of Theoretical and Applied Finance 21, no. 05 (2018): 1850034. http://dx.doi.org/10.1142/s0219024918500346.

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In this work, we deal with market frictions which are given by fixed transaction costs independent of the volume of the trade. The main question that we study is the minimization of shortfall risk in the Black–Scholes (BS) model under constraints on the initial capital. This problem does not have an analytical solution and so numerical schemes come into the picture. The Cox–Ross–Rubinstein (CRR) binomial models are an efficient tool for approximating the BS model. In this paper, we study in detail the CRR models with fixed transaction costs. In particular, we construct an augmented state-actio
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16

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 (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
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17

KHALIQ, A. Q. M., and R. H. LIU. "NEW NUMERICAL SCHEME FOR PRICING AMERICAN OPTION WITH REGIME-SWITCHING." International Journal of Theoretical and Applied Finance 12, no. 03 (2009): 319–40. http://dx.doi.org/10.1142/s0219024909005245.

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This paper is concerned with regime-switching American option pricing. We develop new numerical schemes by extending the penalty method approach and by employing the θ-method. With regime-switching, American option prices satisfy a system of m free boundary value problems, where m is the number of regimes considered for the market. An (optimal) early exercise boundary is associated with each regime. Straightforward implementation of the θ-method would result in a system of nonlinear equations requiring a time-consuming iterative procedure at each time step. To avoid such complications, we impl
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18

Yam, S. C. P., S. P. Yung, and W. Zhou. "Two Rationales Behind the ‘Buy-And-Hold or Sell-At-Once’ Strategy." Journal of Applied Probability 46, no. 03 (2009): 651–68. http://dx.doi.org/10.1017/s0021900200005805.

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The trading strategy of ‘buy-and-hold for superior stock and sell-at-once for inferior stock’, as suggested by conventional wisdom, has long been prevalent in Wall Street. In this paper, two rationales are provided to support this trading strategy from a purely mathematical standpoint. Adopting the standard binomial tree model (or CRR model for short, as first introduced in Cox, Ross and Rubinstein (1979)) to model the stock price dynamics, we look for the optimal stock selling rule(s) so as to maximize (i) the chance that an investor can sell a stock precisely at its ultimate highest price ov
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19

Yam, S. C. P., S. P. Yung, and W. Zhou. "Two Rationales Behind the ‘Buy-And-Hold or Sell-At-Once’ Strategy." Journal of Applied Probability 46, no. 3 (2009): 651–68. http://dx.doi.org/10.1239/jap/1253279844.

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The trading strategy of ‘buy-and-hold for superior stock and sell-at-once for inferior stock’, as suggested by conventional wisdom, has long been prevalent in Wall Street. In this paper, two rationales are provided to support this trading strategy from a purely mathematical standpoint. Adopting the standard binomial tree model (or CRR model for short, as first introduced in Cox, Ross and Rubinstein (1979)) to model the stock price dynamics, we look for the optimal stock selling rule(s) so as to maximize (i) the chance that an investor can sell a stock precisely at its ultimate highest price ov
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20

Chung, San-Lin, and Pai-Ta Shih. "Generalized Cox-Ross-Rubinstein Binomial Models." Management Science 53, no. 3 (2007): 508–20. http://dx.doi.org/10.1287/mnsc.1060.0652.

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21

Baidya, Tara Keshar Nanda, and Alessandro de Lima Castro. "CONVERGÊNCIA DOS MODELOS DE ÁRVORES BINOMIAIS PARA AVALIAÇÃO DE OPÇÕES." Pesquisa Operacional 21, no. 1 (2001): 17–30. http://dx.doi.org/10.1590/s0101-74382001000100002.

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Black & Scholes (1973) desenvolveram um modelo para a avaliação de opções de compra e venda do tipo Europeu. Merton (1973) estendeu o modelo para ações que pagam dividendos. Muitos outros desenvolvimentos foram feitos acerca dos dois trabalhos citados, mas talvez um dos mais importantes foi proposto por Cox, Ross & Rubinstein (1979), onde o processo estocástico (para o preço da ação objeto) em tempo e estado contínuo (Movimento Geométrico Browniano) proposto por Black & Scholes foi aproximado por um processo de tempo e estado discreto (Random Walk). O modelo de Cox, Ross & Rubi
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22

Mendoza Jaimes, Sergio Andrés. "Consideraciones sobre los efectos de incorporar costos de transacción fijos y proporcionales en la valoración de opciones financieras por el modelo Cox, Ross, Rubinstein." ODEON, no. 15 (May 13, 2019): 7–52. http://dx.doi.org/10.18601/17941113.n15.02.

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Este documento desarrolla una extensión del modelo presentado por Cox, Ross y Rubinstein en 1979 para la valoración de opciones financieras, incorporando costos de transacción. Se consideran costos de transacción proporcionales y fijos modelados como un spread bid/ask simétrico fijado por un creador de mercado. El trabajo extiende los resultados de Phelim Boyle y Ton Vorst (1995), y de Tomás Tichý (2005). Se analizan los resultados obtenidos en términos de valoración y toma de decisiones.
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23

Castellanos Orejuela, José Mauricio. "Implicaciones de asumir constante la tasa libre de riesgo y la volatilidad en el modelo binomial para valoración de opciones." ODEON, no. 11 (May 18, 2017): 67. http://dx.doi.org/10.18601/17941113.n11.04.

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El método utilizado por la ciencia financiera se ha centrado en la valoración (dar/establecer un precio) bajo el principio de no arbitraje, lo cual lleva al resultado conocido como Ley de Único Precio; siendo así como se establecen los resultados de modelos como el de Black-Scholes y el de Cox-Ross-Rubinstein, el cual es una excelente aproximación al modelo continuo, en donde se pueden analizar de forma simplificada los complejos conceptos inmersos en el modelo Black-Scholes. Sin embargo, la aplicación de algunos de los supuestos que hacen parte de este, que a través del modelo CRR se pueden a
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24

Jabbour, George M., Marat V. Kramin, and Stephen D. Young. "A Generalization Of Lattice Specifications For Currency Options." Journal of Business & Economics Research (JBER) 1, no. 5 (2011). http://dx.doi.org/10.19030/jber.v1i5.3013.

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<p class="MsoNormal" style="text-align: justify; margin: 0in 0.5in 0pt; mso-pagination: none;"><span style="font-family: Times New Roman; font-size: x-small;">This article revisits the topic of two-state pricing of currency options.<span style="mso-spacerun: yes;">  </span>It examines the models developed by Cox, Ross, and Rubinstein, Rendleman and Bartter, and Trigeorgis, and presents two alternative binomial models based on the continuous and discrete time Geometric Brownian Motion processes respectively.<span style="mso-spacerun: yes;">  </
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25

"Computing Risk Measures of Life Insurance Policies through the Cox–Ross–Rubinstein Model." Journal of Derivatives, December 1, 2018. http://dx.doi.org/10.3905/jod.2018.26.2.086.

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The problem of computing risk measures of life insurance policies is complicated by the fact that two different probability measures, the real-world probability measure along the risk horizon and the risk-neutral one along the remaining time interval, have to be used. This implies that a straightforward application of the Monte Carlo method is not available and the need arises to resort to time consuming nested simulations or to the least squares Monte Carlo approach. We propose to compute common risk measures by using the celebrated binomial model of Cox, Ross, and Rubinstein (1979) (CRR). Th
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26

Talponen, Jarno, and Minna Turunen. "Option pricing: a yet simpler approach." Decisions in Economics and Finance, June 16, 2021. http://dx.doi.org/10.1007/s10203-021-00338-7.

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AbstractWe provide a lean, non-technical exposition on the pricing of path-dependent and European-style derivatives in the Cox–Ross–Rubinstein (CRR) pricing model. The main tool used in this paper for simplifying the reasoning is applying static hedging arguments. In applying the static hedging principle, we consider Arrow–Debreu securities and digital options, or backward random processes. In the last case, the CRR model is extended to an infinite state space which leads to an interesting new phenomenon not present in the classical CRR model. At the end, we discuss the paradox involving the d
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27

Attalienti, Antonio, and Michele Bufalo. "Expected vs. real transaction costs in European option pricing." Discrete & Continuous Dynamical Systems - S, 2022, 0. http://dx.doi.org/10.3934/dcdss.2022063.

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<p style='text-indent:20px;'>As an application and extension of some previous results contained in [<xref ref-type="bibr" rid="b1">1</xref>], we face up the problem of the option pricing in presence of transaction costs and hence in the framework of incomplete markets. The model proposed herein passes through defining properly the expected transaction costs, opposite to the real transaction costs in trading. The analysis is carried out both in the discrete and the continuous case and leads to suitable modifications of Cox-Ross-Rubinstein and Black-Scholes formulas. An applica
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28

Marques, Naielly Lopes, Carlos de Lamare Bastian-Pinto, and Luiz Eduardo Teixeira Brandão. "A Tutorial for Modeling Real Options Lattices from Project Cash Flows." Revista de Administração Contemporânea 25, no. 1 (2021). http://dx.doi.org/10.1590/1982-7849rac2021200093.

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ABSTRACT Context: several methods for evaluating real options have been extensively studied and published. But recombining binomial trees, known as lattices, are perhaps one of the most practical and intuitive approaches to model uncertainty and price project managerial flexibilities for real options applications. Although the Cox, Ross, and Rubinstein (1979) lattice model is simple to implement for financial options, modeling real options lattices requires a different approach such as the one proposed by Copeland and Antikarov (2001), which considers project cash flows as dividends in the lat
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