Binomial Tree Model Research Articles

Quantum walk option pricing model based on binary tree

In this paper, we present a novel quantum model for financial markets constructed within the risk-neutral framework. We innovatively integrate the theory of quantum walks into the binomial tree model for option pricing, thereby achieving a more precise simulation of asset price dynamics. Furthermore, we explore the multi-step quantum binomial tree model and enhance the traditional approach by incorporating the concept of quantum superposition. This advancement enables our model to simultaneously consider multiple states of asset prices at various nodes, effectively reducing computational complexity as time steps increase while significantly improving option pricing accuracy. The superior performance of our quantum model is demonstrated through simulation experiments.

A Binomial Tree-Based Empirical Study on the Biases of American Call Option

The application of financial derivatives, particularly options, has become pervasive in modern finance, offering effective tools for risk management. Among these, American options, allowing flexibility in exercising rights prior to expiration, dominate the derivatives market. Accurate pricing of American options is crucial for informed investment decisions and risk assessments. While various pricing models exist, the binomial tree model is welcomed for its simplicity and accessibility. However, inherent biases in pricing models raise questions about their efficacy across different sectors of the market. Based on the binomial tree model, this study empirically examines the pricing accuracy of American call options in both the technology sector and the industrial sector, by collecting data from top five largest companies in each sector. For the technology sector, samples are mainly from semiconductor manufacturers, software companies, etc., which are all situated in thriving fields; while those five companies from the industrial sector mainly belong to traditional industries, such as energy and engine suppliers. By analyzing prediction biases between two sectors, this research tries to give out reasons behind it and grasps a deeper understanding of option pricing nuances between sectors, and also the limitations of the binomial tree model.

Convertible Bond Pricing in Chinese Transportation Industry : A Comparison Methods Between Binomial Tree model and Black-Scholes Model

Convertible Bond Pricing in Chinese Transportation Industry : A Comparison Methods Between Binomial Tree model and Black-Scholes Model

Evaluation of Data Assets for Internet Enterprises: A Case Study on K Company

The "Digital China" agenda has made data assets crucial for enterprises’ competitiveness, especially on the Internet sector. However, the current method of evaluating their worth needs improvement. Taking K Company as an example, this study, based on analytic hierarchy process, uses the binomial tree model to evaluate the value of data assets by determining their potential worth. It aims to promote the growth of the data economy and digital transformation in manufacturing organizations by focusing on revenue.

Numerical Methods for Option Pricing

Nowadays, financial markets have become more complex and have given rise to more research opportunities, one of which focuses on research related to the pricing of various financial instruments used in options trading. In this essay, a gradual process of reflection is used to deepen the option pricing theory. Firstly, an effective mathematical method for pricing option contracts is using the binomial tree model, a relatively straightforward way of calculating the value of an option. However, it has only two upward and downward trends and has limitations that are the most different from the actual market conditions. That is why the study will have to continue in-depth to get as close as possible to the real situation in the market. The next step is to make the model more in line with market reality by adding a possible rate of change, resulting in the Trinomial Tree Model. The model incorporates the possibility of future price increases, decreases, or stabilization (the third change). The Trinomial Tree Model follows the no-arbitrage principle and removes the assumption of a risk-free market opportunity. This paper derives a method for constraining market prices under risk-neutral conditions. This is crucial for investors seeking profitable outcomes in options trading. The main objective of this research-based paper is to develop a complete theory of option pricing in a one-step trinomial tree model.

Research on Real Estate Investment Project Valuation Based on the Binomial Tree Model

Research on Real Estate Investment Project Valuation Based on the Binomial Tree Model

Calculation Option Price on Shares PT. Nippon Indosari Corpindo Tbk. with Fuzzy Binomial Tree Model

The Cox-Ross-Rubinstein binomial tree model is widely used in stock and derivative securities calculations, such as options calculations. The binomial CRR model assumes that the parameter increases in option prices and decreases in option prices so this model produces stock price movements up and down stock price movement. However, stock price movements show price fluctuations and cause the volatility of the value to be unsuitable. In this study, modeling stock and option price movements using a fuzzy binomial tree model. The data used was data on the movement of the stock price of Nippon Indosari Corpindo Ltd Plc from February 2021 to January 2022. The results showed that for February 2022, with a risk size of 90%, the selling price options with the greatest volatility of 51.6484081, medium volatility of 33.33154354, and the smallest volatility of 28.17155892.

A Review of the Option Pricing Model and Further Development

The Black Scholes model and binomial tree model have been the main research objects of scholars in the past fifty years. This article summarizes the optimization process of these two classic option pricing models to understand the different directions of optimizing the models and to provide ideas for future model improvement. Improvements from scholars to the Black-Scholes model mainly focus on the basic model and the relevant variables involved in option pricing, while the optimization of the binomial tree model focuses on the reduction of pricing errors as well as the improvement of model fitting speed. Empirical studies of option pricing models have shown that improved models while enhancing the accuracy of pricing in various financial markets, unavoidably increase computational complexity and reduce efficiency. This article also demonstrates the future integration of financial derivatives pricing models in multiple fields by describing the application of real options in the agriculture, technology, and biology industries.

Research on option pricing of Tesla based on Black-Scholes-Merton, Binomial Tree, and Cox-Ingersoll-Ross Models

This study examines the predictive accuracy of three option pricing models—Black-Scholes-Merton (BSM), Binomial Tree, and Cox-Ingersoll-Ross (CIR)—using Tesla Inc's real data. The research surveys the evolution of option pricing models and their significance in risk management and speculation. By applying these models to Tesla's volatile stock, the paper compares their predictions against actual prices. Results indicate that while outcome yielded from all three models resembles the real price to a reasonable extent, the Binomial Tree model's superior performance offers closer mean values and correlations with real prices. This research advances the practical understanding of option pricing, contributing valuable insights for traders and investors facing dynamic market conditions.

Option Pricing and Risk Hedging in the Current Financial Market: A Case for Google

In the past few decades, financial derivative securities have been developing rapidly around the world, and the issue of options and investment consumption has attracted more and more attention from mathematicians and financiers at home and abroad. In this paper, option pricing models are constructed and calibrated based on the Black Scholes Merton model, binomial tree model, historical data model and Monte Carlo diffusion model. The differences between different option pricing models for options and stock hedging of the same company in a short period of time are discussed and analyzed. In this article, the Monte Carlo model outperforms the traditional Black Scholes Merton model, while the binomial tree model and the historical data model do not perform well. The results of this paper are beneficial for investors to use the optimal model to predict option prices, weaken the aggregate risk, and improve the aggregate return level.

Predictable forward performance processes: Infrequent evaluation and applications to human‐machine interactions

AbstractWe study discrete‐time predictable forward processes when trading times do not coincide with performance evaluation times in a binomial tree model for the financial market. The key step in the construction of these processes is to solve a linear functional equation of higher order associated with the inverse problem driving the evolution of the predictable forward process. We provide sufficient conditions for the existence and uniqueness and an explicit construction of the predictable forward process under these conditions. Furthermore, we find that these processes are inherently myopic in the sense that optimal strategies do not make use of future model parameters even if these are known. Finally, we argue that predictable forward preferences are a viable framework to model human‐machine interactions occurring in automated trading or robo‐advising. For both applications, we determine an optimal interaction schedule of a human agent interacting infrequently with a machine that is in charge of trading.

Pricing Technique for European Option and Application

In financial mathematics, the pricing technique for derivatives is constantly debated. In this paper, the pricing technique of the European Option is mainly discussed, and the binomial tree (BN) model is first applied to the pricing process of European options. The previous results show that carbon credit index can be traded as an option, and BN model can correctly simulate the future price of call option constructed by consuming the carbon credit index. Secondly, the Black-Scholes (BN) model is also a crucial technique for pricing European options, and it is successfully applied to predicting the future three months' CSI 300 index option price. Finally, BN model is compared with BS model, and the result reflects that BN model can perform as well as BS model for pricing European Option When the step reaches 2000. However, the efficiency of the BN model is stable under low volatility. Under higher volatility, such as 1.5 sigmas, the required steps will increase to achieve the same accuracy level. For American options, the BN simulator of a put option is close to the actual value, but the call option simulator will fluctuate. For the stock-pricing process, both models estimate far above Monte-Carlo method. The result of this paper is to provide some clues for pricing European options with different methods.

Inclusion of “managing flexibility” valuations in the pricing of PPP projects: a multi-objective decision-making method

PurposeThe Public–Private Partnership (PPP) modality plays an important role in the procurement of global infrastructure projects. Regarding PPP's complex transaction structure, pricing of a PPP project is critical to both parties where the government pursues a high value for money (VFM) and the investor strives to maximize its financial gains. Despite the straightforward win–win principle, a formidable compromise is often the case to end up with a fairly acceptable price, subject to many determinants such as the risk profile, expected return, technological innovation and capacities of both parties. Among them, this study chooses to examine the “managing flexibility” (MF) capacity of investors in pricing of a PPP project, in light of the widely recognized importance of a real-option perspective toward the long term, complex and uncertain PPP arrangement. This study addresses two major questions: (1) how is MF in PPP projects to be valued and (2) how are PPP projects to be priced when considering a project's MF value.Design/methodology/approachA binomial tree model is used to evaluate the MF value in PPP projects. Based on the developed MF pricing model, net present value (NPV) and adjusted VFM value are then calculated. Finally, a multi-objective decision-making method (MODM) was adopted to determine the optimal level of returns based on invested capital (ROIC), return on operation maintenance (ROOM) and concession period.FindingsThe applicability and functionality of the proposed model is investigated using a real project case. For a given return, extended NPV and adjusted VFM value were calculated and analyzed using sensitivity analysis. Factor influence is shown by the model to be dependent on factor impact on cash flow. Subsequently, a multi-objective decision-making (MODM) model was adopted to determine the optimal level of returns, where the solution approximates the real-world bidding price. Results confirm that the pricing model provides a reliable and practical PPP proposal pricing tool.Originality/valueThis study proposes an integrated framework for valuing MF in PPP projects and thus more accurately determine optimal pricing of PPP projects than revealed in extant research. The model offers a practical tool to aid in the valuation of PPP projects.

Options Pricing Comparison between the Black-Scholes Model and the Binomial Tree Model: A Case Study of American Equity Option and European-style Index Option

In recent years, quantitative researchers used a wide range of models to price options, from the Black-Scholes model to more complex models such as the Heston model. This paper aims to analyze the effectiveness of the Black-Scholes model and the Binomial Tree model by using them to price Berkshire Hathaway’s equity options and European-style S&P 100 index options. The method used in this paper is gathering the market data of the options first. Second, using the data gathered to price the options by applying the Black-Scholes and Binomial Tree models. Third, comparing the derived theoretical price with the market price by getting the Sum of Square Errors. Lastly, determining the best model for each type of option. Through this research, the author found that comparing the two models, the Binomial Tree model derives a smaller Sum of Square Errors when pricing European-style index options, and the Black-Scholes model derives a smaller Sum of Square Errors when pricing American equity options. Thus, the Binomial Tree model is a better model to price European-style index options, and the Black-Scholes model is more effective when pricing American equity options.

Asset Allocation Strategy and Convergence with Epstein-Zin Utility function

In this paper, we study the optimal consumption and investment problems for an individual with the Epstein-Zin type utility. We employ the binomial tree model for dynamics of the risky asset and derive optimal policies. We show that the optimal policies converge to those in the continuous-time model of Schroder and Skiadas. The convergence rate of optimal policies is of the order of equal to the time interval between consecutive time points, and there is little difference in convergence rates between CRRA and Epstein-Zin utilities. We also show that the optimal consumption decreases as the elasticity of intertemporal substitution increases.

Tax-loss harvesting under uncertainty

We provide market-based evidence that a capital loss that is realized in the beginning of the year is less valuable than a loss that is taken at the end of the year. A simple binomial tree model that captures the resolution of tax rate uncertainty closely mimics observed market prices. Tax rate uncertainty arises from not knowing until the end of the calendar year whether the investor will have realized sufficient capital gains to fully benefit from losses harvested early in the year. We conclude that tax rate uncertainty influences investor behavior.

A parallel and pipelined implementation of a pascal-simplex based multi-asset option pricer on FPGA using OpenCL

Multi-asset option pricing is a financial tool that offers a competitive advantage in the global financial markets. To achieve the commercial advantage, performance and accuracy are two key desiderata of such tools. Techniques for financial option pricing have been actively researched for some time. Combined with recent advances in heterogeneous computing, new computing methods of lower latency option pricing have become available. Field-Programmable Gate Array technology offers a powerful framework for building architectures for highly parallel option pricing. This paper presents a versatile, high performance implementation of an accurate multi-asset option pricer on an Intel Stratix 10 GX device. The implementation is highly flexible for the number of assets supported, the maximum tree depth, and the pipelining parameters. The theory that this architecture is based on is that of a recombining multinomial tree approach, which is a generalization of the binomial tree model. This novel architecture was implemented on Field-Programmable Gate Array technology. The implementation presented in this paper enables the computation of an option price on up to 7 assets and can compute up to 43 times faster than a software implementation in a general-purpose processor.

Binomial tree method for option pricing: Discrete cosine transform approach

This paper discusses a new pricing method of European options through the binomial tree model using a discrete cosine transform. The discrete cosine transform has been used as a fundamental tool for image compression, including the creation of JPEG files. A discrete cosine transform was also recently used to derive the price of financial options. This method also enables us to derive the option prices using a binomial tree model. Using this approach, we derive the option prices on the classical Black and Scholes, exponential jump–diffusion, and exponential CGMY models. Because we compute the characteristic function numerically, we can derive option prices in various models without knowing the specific form of the characteristic functions. This study can unfold new research areas such as option pricing on various models, including the non-parametric jump and Lévy diffusion models.

Real Options Analysis for Land and Water Solar Deployment in Idle Areas of Agricultural Dam: A Case Study of South Korea

This study presents a real options-based framework for investment in land and water solar power projects in the idle areas of agricultural dams. The following four-step framework was verified through a case study conducted in South Korea: (1) select the location and size of the project; (2) define uncertainties in the project data (construction cost, O&M cost, sunshine hours, and mechanical efficiency) and market data (inflation, discount rate, risk-free interest rate, and electricity selling price); (3) estimate cash flow and project volatility to calculate the option value using a binomial tree model; and (4) make decisions regarding project investment. A case study was conducted for the Naju Agricultural Dam (NAD) project, which has a net present value of −6.67 million USD, but will have a profit of 38.17 million USD after an abandonment option is applied using the proposed framework. Our contributions provide a framework for evaluating the economic feasibility of installing solar projects in idle areas of agricultural dams and for improving the profitability of solar projects using the abandonment option. The proposed framework can assist investors in planning solar projects in idle areas of agricultural dams.

Pricing exotic options in the incomplete market: An imprecise probability method

AbstractThis article considers a novel exotic option pricing method for incomplete markets. Nonparametric predictive inference (NPI) is applied to the option pricing procedure based on the binomial tree model allowing the method to evaluate exotic options with limited information and few assumptions. As the implementation of the NPI method is greatly simplified by the monotonicity of the option payoff in the tree, we categorize exotic options by their payoff monotonicity and study a typical type of exotic option in each category, the barrier option and the look‐back option. By comparison with the classic binomial tree model, we investigate the performance of our method either with different moneyness or varying maturity. All outcomes show that our model offers a feasible approach to price the exotic options with limited information, which makes it can be utilized for both complete and incomplete markets.