# Binary options binom, Binomial options pricing model - Wikipedia

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Published12 Mar Abstract Randomized binomial tree and methods for pricing American options were studied.

### Understanding the Binomial Option Pricing Model

Firstly, both the completeness and the no-arbitrage conditions in the randomized binomial tree market were proved. Secondly, the description of the node was given, and the cubic polynomial relationship between the number of nodes and the time steps was also obtained.

Then, the characteristics of paths and storage structure of the randomized binomial tree were depicted. Then, the procedure and method for pricing American-style options were given in a random binomial tree market.

The binomial option pricing model is an options valuation method developed in The binomial option pricing model uses an iterative procedure, allowing for the specification of nodes, or points in time, during the time span between the valuation date and the option's expiration date. Key Takeaways The binomial option pricing model values options using an iterative approach utilizing multiple periods to value American options. With the model, there are two possible outcomes with each iteration—a move up or a move down that follow a binomial tree. The model is intuitive and is used more frequently in practice than the well-known Black-Scholes model.

Finally, a numerical example pricing the American option was illustrated, and the sensitivity analysis of parameter was carried out. The results show that the impact of the occurrence probability of the random binomial tree environment on American option prices is very significant.

### American Binary Option Pricing: 3 Period Binomial Tree Model

With the traditional complete market characteristics of random binary and a stronger ability to describe, at the same time, maintaining a computational feasibility, randomized binomial tree is a kind of promising method for pricing financial derivatives. Introduction Cox et al. As Binomial option pricing method is simple and flexible to price all kinds of complex derivatives, and easy to realize the computer programming, it has become one of the mainstream methods of pricing derivatives, and also one of the frontiers and hot researches on pricing derivatives for decades.

Benninga and Wiener and Tian researched the relative properties of the binary tree and priced complex financial derivatives by binary tree to improve the computational efficiency of binary tree algorithm [ 45 ]. Rubinstein [ 6 ] expanded the built Edgeworth binary tree with random distribution of Edgeworth, which effectively involved the information of randomly distributed skewness and kurtosis, and made binary tree approach nonnormal distribution when applied to option pricing.

Walsh [ 7 ] proved the effectiveness of binary tree algorithm via the study of the convergence and convergence speed problems of binary method from the theoretical point of view.

Gerbessiotis [ 8 ] gave a parallel binomial option pricing method with independent architecture, studied algorithm parameter adjustment method of achieving the optimal theory acceleration, and verified the feasibility and effectiveness of the algorithm under different parallel computing environments. Georgiadis [ 9 ] tested that there is no so-called closed-form solution when pricing options with binary tree method.

Simonato [ 10 ] posed Johnson binary tree based on the approximation to Johnson distribution of the random distribution, overcoming some possible problems in Edgeworth binary tree that the combination of skewness and kurtosis cannot constitute qualified random distribution.

## Binomial options pricing model - Wikipedia

Due to the theory that Hermite orthogonal polynomials can approximate random distribution with the arbitrary precision, Leccadito et al. Cui et al. Wen et al.

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- Binomial Option Pricing Model Definition

Yuen et al. Aluigi et al. Jimmy [ 19 ] proposed robust binomial lattices for pricing derivatives where probabilities can be chosen to match local densities.

### Binomial options pricing model

However, in the traditional binary tree market, if the formed combination of the upward movement is seen as a market environment known by the binary theory; determines the unique market volatilitythere is only an environment in the traditional binary tree market and at each node the binary tree moved upward or downward only once it means that market volatility is the same at any time.

However, this assumption is far from the reality of the financial markets, because the stock prices will respond immediately to the various information from domestic and abroad, and thus it is very sensitive.

For example, a sudden change in the risk-free interest rate, the conflict with its neighbor countries, good performance of the rival company, a new CEO, and other random emergency information will lead to great fluctuation in stock prices.

In reality, companies hardly change their valuations on a day-to-day basis, but their stock prices and valuations change nearly every second. This difficulty in reaching a consensus about correct pricing for any tradable asset leads to short-lived arbitrage opportunities. But a lot of successful investing boils down to a simple question of present-day valuation— what is the right current price today for an expected future payoff? Binominal Options Valuation In a competitive market, to avoid arbitrage opportunities, assets with identical payoff structures must have the same price. Valuation of options has been a challenging task and pricing variations lead to arbitrage opportunities.

Ganikhodjaev and Bayram and Kamola and Nasir [ 20 — 22 ] put forward the random binary tree applied to European option pricing. In this binary options binom binary tree market, there are at least two market environments, one of which represents the normal state of the market while the other is the abnormal state of the market. Therefore, the first market environment which represents the normal state of the market corresponds to smaller market volatility and larger probability and the second market environment has larger market volatility and smaller probability.

The contribution of this paper is studying the related properties of random binary tree from the viewpoint of complete market and the number of nodes, giving the storage structure of random binary, describing the path characteristics of random binary tree, and researching the American option pricing problem under the random binary market.

The other sections of this paper are as follows. In Section 2we introduce random binary tree and its properties; the American option pricing problem under random binary environment is studied in Section 3 binary options binom In Section 4we demonstrate the effectiveness of the algorithm through a numerical binary options binom and study the parameters sensitivity of relevant model.

Randomized Binary Tree 2. Random Walks in an Independent Environment Solomon [ 23 ] is the first person to study random walks in an independent environment in the integer field.

Letfor all be a sequence of independent and identically distributed random variables; then the random walks in an independent environment in the integer domain are a random sequencewhere.