Binomial Tree Method Research Articles

Research on the Option Pricing of Tesla’s Stock Based on B-S Model and Binomial Tree Method

With the announcement of price drop of Tesla’s multiple vehicles during 2022 and 2023, its stock also entered a very unstable age which cause many investors meet significant loss, so did its option prices. In this article, B-S model, Binomial Tree, and Monte Carlo Simulation are implemented to do research on Tesla’s stock price and its call options. The results shows that B-S model has a much lower value of option prices when Binomial Tree does not have multiple division of time period. On the other hand, Monte Carlo Simulation indicates that it would be hard to predict the actual price trend since actual price went to a very low percentile among all simulations. The meaning of this research is to prove Binomial Tree is complementary to B-S model with introduce the concept of time whereas B-S model only uses actual stock prices and calculate the average. Monte Carlo Simulation also warns the investors to continue to pay attention to the news and incidents happened around the companies they invested to.

Valuation of barrier and lookback options under hybrid CEV and stochastic volatility

In this paper, we evaluate down-and-out put option and floating strike lookback option prices when the underlying asset is driven by a hybrid model with constant elasticity of variance and stochastic volatility (SVCEV). Usually, it is difficult to get closed-form solutions for those exotic options under stochastic volatility models. Here, we use an asymptotic expansion approach and the Mellin transform method to obtain explicit closed-form formulae for the zero-order and first-order correction terms. In addition, we perform a sensitivity analysis numerically on the asymptotic terms and compare the option prices corresponding to the Black–Scholes, CEV and SVCEV models with those calculated by Monte-Carlo simulations and the binomial tree method to illustrate the accuracy of our pricing formulae.

Evaluation of mining projects subjected to economic uncertainties using the Monte Carlo simulation and the binomial tree method: Case study in a phosphate mine in Egypt

Mining project evaluation is a very complex process and time-consuming task. Any mining project passes through several study stages, like conceptual, preliminary feasibility, and feasibility studies, using a systematic and standardized approach. These studies allow investors to evaluate the exploitations alternatives according to economic and technical criteria to make a better decision. This research aims to study a model for investment risk analysis developed for the case study of “Abu Tartur mining project, Egypt.” Abu Tartur plateau is rich in phosphate rock, turned into phosphoric acid and fertilizers. This study used site-specific data that has been taken from the literature to build evaluation models using the Monte Carlo Simulation (MCS) and the Binomial Decision Tree (BDT) methods. The Discounted Cash Flow (DCF) is considered a benchmark method for all other evaluation methods. The MCS method uses a set of parameters that, in some cases, will give a higher NPV of the project and some others with lower values, but this depends on the probability of the input parameters. The developed evaluation models allowed a specific range of values, with confidence intervals as the MCS model. The advantage of using a probabilistic approach helps in the decisional phase, allowing for a more precise overview of the variability of the final economic value of the mine. Deterministic methods, like the DCF method, offer a solution that is limited to uncertainty analysis.

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.

Embedding a net present value analysis into a binomial tree with a real option analysis

A net present value (NPV) analysis with associated financial statements is embedded into a binomial tree that allows the analysis to evolve through time and, at any given moment in time, to vary with different states of the world. The modeling of the cash flows within the binomial tree requires a variable component based on relationships with a specifically defined random variable and a component that is fixed at a given moment in time. Although after‐tax operating cash flows are used in this treatment with a real options example, the binomial tree method can be applied to other definitions of project cash flows.

Binomial tree method for option pricing: Discrete Carr and Madan formula approach

This paper suggests a new Fourier analysis approach to evaluate the option prices and its sensitivities (Greeks) using the binomial tree model. In the last half of this paper, we show that option prices are efficiently and effectively evaluated using a semi-closed form formula for European option prices. We can compute option prices in a broad class of jump-diffusion models because we calculate the characteristic function for an underlying asset price numerically. Furthermore, we also compute the price of European options in the exp-Levy model. This numerical experiment gives new insights into option pricing in the nonparametric Levy model. The option prices and sensitivities can be computed very accurately and efficiently, even in binomial tree models with jumps.

Determination of optimal production rate under price uncertainty—Sari Gunay gold mine, Iran

Due to the long life, most mining projects face the risk of the parameters such as mineral price, grade, and cost. Uncertainty can lead to unfavorable results of the decisions made by managers and mining investors. Therefore, this paper aims to determine the Sari Gunay gold mine’s production planning, considering the certainty and uncertainty over the mineral price. Finally, the proposed planning will lead to the allocation of fixed or variable production rates throughout the mine life. These findings were assessed by Taylor and Zwiagin methods with 22 different scenarios in all conditions, including (a) price certainty and uncertainty such as daily price, 3- and 5-year average, Monte Carlo simulation, and binomial tree; (b) decreasing, increasing, and fixed production rates; and (c) mine life conditions. The scenarios evaluated under the price certainty conditions (scenarios 1 to 12) have lower NPV values than those under the price uncertainty conditions. This is because the price is fixed throughout the mine life. Due to historical price data and high fluctuations of estimated prices, this method’s NPV values fluctuate more than other scenarios evaluated by the Monte Carlo simulation. The binomial tree method scenarios have the lowest NPV value’s fluctuation because the fluctuation of the estimated prices is controlled, and the highest NPV values are related to this method. Out of the 22 scenarios, scenario 17 has the highest NPV value ($512,642,774). According to this scenario, the mine plan is determined, and the annual production rate is reduced to 3,241,977 tons in the first year and 270,165 tons in the last year with the Taylor life of 12 years.

Entropy binomial tree method and calibration for the volatility smile

In this paper, we combine the maximum entropy principle with binomial tree to construct a non-recombining entropy binomial tree pricing model under the volatility that is a function of time, and give the rate of convergence. The model may yield an unbiased and objective probability. In addition, we research the calibration problem of volatility with the entropy binomial tree, 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 confirm the effectiveness of the entropy binomial tree pricing model.

Convergence of binomial tree methods to Black Scholes model on determining stock option prices

There are many alternative investment tools that can be used to be the choice of investors. One of them is a derivative product. Derivative products that are more widely known and traded on financial markets are options. Option is a contract or agreement between two parties to buy or sell an instrument. To minimize risk, it is necessary to determine the option price by determining the fair price of the option. This option pricing can be done by using the Binomial Tree method and the Black Scholes method. Some factors that influence options are stock prices, strike prices, maturity, volatility, and interest rates. This paper discusses the European option pricing call on the shares of Bank Central Asia (BCA) with the Binomial Tree method and the Black Scholes Method. From the results of the research, it is found that the Binomial Tree method will converge to the Black Scholes method if the time partition increases.

Determining the Sustainability of a Community Micro Hydro Power System using Real Options Analysis

Micro hydro power is a clean source of renewable energy that has been utilized for remote communities for electricity generation. The technology is mature and operates the same principle as large hydroelectric power plant but with much lower power capacity. Sustainability relies on the financial and other benefits brought about the micro hydro power plant during its operation. Traditional valuation method is often used to valuate micro hydro projects however it does not incorporate uncertainty factors, specifically unpredictable changes in weather. Real Options Analysis, on the other hand, uses both the Black-Scholes Model and Binomial Tree Method which incorporates uncertainty. The valuation obtained through real option analysis represents the net present value of the project with decision flexibility option for the investor. In this study, real options analysis is applied to a micro hydro power plant to identify its financial sustainability. Head and flow rate are obtained to calculate the capital investment, electrical sales, maintenance, and cost of operating nearby agricultural facilities. Traditional financial valuation method revealed a positive outcome making the project financially viable. However, real options analysis provided a contradicting result indicating the implementation of the project should be delayed.

Pricing S&P500 barrier put option of American type under Heston–CIR model with regime-switching

In this paper, we consider the regime-switching Heston–CIR model, where the parameters of the volatility process are modulated by a Hidden Markov chain and the unobserved regimes. Then, we calibrate the parameters of the volatility and interest rate processes by the expectation maximization (EM) and maximum likelihood estimation (MLE) algorithms, respectively. Next, we use the least square Monte-Carlo (LSM) algorithm to determine the S&P500 American barrier put option under the Heston–CIR model. Finally, by the binomial tree method as a benchmark, we provide some numerical experiments to illustrate the accuracy of the achieved results.

Comparison of Numerical Methods on Pricing of European Put Options

Put option is a contract to sell some underlying assets in the future with a certain price. On European put options, selling only can be exercised at maturity date. Behavior of European put options price can be modeled by using the Black-Scholes model which provide an analytical solution. Numerical approximation such as binomial tree, explicit and implicit finite difference methods also can be used to solve Black-Scholes model. Some numerical methods are applied and compared with the analytical solution to determine the best numerical method. The results show that numerical approximations using the binomial tree is more accurate than explicit and implicit finite difference method in pricing European put options. Moreover when the value of T is higher then the error obtained is also higher, while the error obtained is lower when the value of N is higher. The value of T and N cause the increase of the computation time. When the value of T is higher the computation time is lower, while computation time is higher if the value of N is higher. Overall, the lowest computation time is obtained by using an explicit finite difference method with an exceptional as the value of T is big and the value of N is small. The lowest computation time is obtained by using a binomial tree method.

A New Binomial Tree Method for European Options under the Jump Diffusion Model

In this paper, the binomial tree method is introduced to price the European option under a class of jump-diffusion model. The purpose of the addressed problem is to find the parameters of the binomial tree and design the pricing formula for European option. Compared with the continuous situation, the proposed value equation of option under the new binomial tree model converges to Merton’s accurate analytical solution, and the established binomial tree method can be proved to work better than the traditional binomial tree. Finally, a numerical example is presented to illustrate the effectiveness of the proposed pricing methods.

PRICING BERMUDAN-TYPE CALL OPTION THROUGH BINOMIAL TREE METHOD

<p class="Default"><em>Bermudan option is a type of option that has characteristics between American option and European option whose its value never exceeds the value of the American option and is never less than the European option. The objective of this research is to calculate Bermudan call option of John Keels Stock through the binomial tree method using statistics software of Matlab R2010a. </em><em>Assessment of Bermudan type option relates to discrete issues, in which the Bermudan type option has a certain number of times of early exercise specified in the option contract, where such times can only be made at some time prior to the option due date. Precise pricing for Bermudan type option can be obtained by discrete models such as the binomial tree method, a numerical method that is one of the most popular approaches for calculating option prices. This research uses time series data obtained from BNI Financial Update Corner, FEB UGM. The Bermudan call option price calculation will be compared with the calculation of European option pricing and American option price with underlying asset without dividend. The results show that the price of John Keels's Bermudan type call option using the binomial tree method yields the same value as American type call option and European type call option.</em><em></em></p><strong><em>Keywords:</em></strong><em> Bermudan Type Option, Binomial Tree Method, Matlab R2010a, Spss 20</em>

Scheduling non-critical activities using multicriteria approach

In many projects the problem of selecting the start time of a non-critical activity arises. Usually it is possible to use the “as soon as possible” or “as late as possible” rules. In some situations, however, the result of such a decision depends on external factors such as exchange rate. This leads to an approach in which the problem of scheduling non-critical activities is solved using an expanded Cox–Ross–Rubinstein (CRR) binomial tree method. In the paper a bi-criteria problem of determining the start time of a non-critical activity is considered. We assume that the early start and the late start of the activity have been identified using Critical Path Method, but the project manager is free to select the time when the activity will actually be started. This decision cannot, however, be changed later, as it is associated with the allocation of key resources. Two main criteria are considered: cost and risk. While cost depends on exchange rate, risk increases with the delay of the start of the activity. The problem can be described as a dynamic process. We propose a new interactive technique for solving such a bi-criteria decision making problem under risk. The procedure uses trade-offs to identify a candidate solution. The CRR binomial method is applied to evaluate the cost of the activity.

Applying Greek letters to robust option price modeling by binomial-tree

In this paper, a new model is proposed for pricing a European option using the binomial tree method in conjunction with the Greek letters. In the proposed method, the covariance matrix of high and low stock prices was calculated in an uncertainty region. Applying robust option pricing model, an ‘interval’ of prices (instead of ‘spot’ prices) for an option was obtained. Greek letters were incorporated into a robust option model to ameliorate the accuracy of the interval price. It was found out that the interval prices obtained by the present model were flexible with increased accuracy compared with those obtained by the robust option using the binomial tree model. It is also indicated that the advantage of the present model over existing models is more tangible in the event of ‘out of the money’ call option. Furthermore, the accuracy improvement was found to be less noticeable when the maximum costs were equal to each other.

Binomial tree method for pricing a regime-switching volatility stock loans

Binomial model with regime switching may represents the price of stock loan which follows the stochastic process. Stock loan is one of alternative that appeal investors to get the liquidity without selling the stock. The stock loan mechanism resembles that of American call option when someone can exercise any time during the contract period. From the resembles both of mechanism, determination price of stock loan can be interpreted from the model of American call option. The simulation result shows the behavior of the price of stock loan under a regime-switching with respect to various interest rate and maturity.

PENENTUAN HARGA KONTRAK OPSI KOMODITAS EMAS MENGGUNAKAN METODE POHON BINOMIAL

Holding option contracts are considered as a new way to invest. In pricing the option contracts, an investor can apply the binomial tree method. The aim of this paper is to present how the European option contracts are calculated using binomial tree method with some different choices of strike prices. Then, the results are compared with the Black-Scholes method. The results obtained show the prices of call options contracts of European type calculated by the binomial tree method tends to be cheaper compared with the price of that calculated by the Black-Scholes method. In contrast to the put option prices, the prices calculated by the binomial tree method are slightly more expensive.

The Asian Option Pricing when Discrete Dividends Follow a Markov-Modulated Model

This paper is concerned with the pricing problem of the discrete arithmetic average Asian call option while the discrete dividends follow geometric Brownian motion. The volatility of the dividends model depends on the Markov-Modulated process. The binomial tree method, in which a more accurate factor has been used, is applied to solve the corresponding pricing problem. Finally, a numerical example with simulations is presented to demonstrate the effectiveness of the proposed method.

PENERAPAN METODE BINOMIAL TREE DALAM MENGESTIMASI HARGA KONTRAK OPSI TIPE AMERIKA

Binomial tree is a method that can be used to determine price option contracts. In this method, the stock price movement is presented in the form of a tree with each branch representing the probability of the stock price to move up or move down. The purpose of this paper was to determine the price of the options contracts with the American type on Binomial Tree method and compare the three methods that is variance matching, proportional , and risk neutral of determining the value of price option contracts used in Binomial Tree method with Black-Schole method. The result of this research was the value of the options contract using the variance matching more similar with the value of the Black-Scholes contract.