Nonparametric predictive inference for American option pricing based on the binomial tree model

He, Ting; Coolen, Frank P. A.; Coolen‐Maturi, Tahani

doi:10.1080/03610926.2020.1764040

Cited by 5 publications

(12 citation statements)

References 22 publications

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“…E(g(S t ) = sup p∈ E p (g(S t ))), (6) where  is a set of classical, precise probability distributions corresponding to the NPI approach for Bernoulli data, 4 and E p is the expected value corresponding to a specific precise probability distribution p ∈ . By applying this method to price exotic options, the investor is offered a price interval, of which the maximum buying price is its lower bound and the minimum selling price is its upper bound: call option:…”

Section: E(g(s Tmentioning

confidence: 99%

“…The NPI method has been utilized to price these vanilla options in incomplete markets, and showed good performance 5,6 . There is a common characteristic of all vanilla options, which is a monotonic payoff in the binomial tree.…”

Section: Introductionmentioning

confidence: 99%

“…3 Coolen presented the NPI method for Bernoulli random quantities to calculate the upper and lower probabilities, 4 and this has been applied to the vanilla option pricing procedure combined with the binomial tree model. 5,6 The development of the NPI methods for vanilla options offers the maximum buying price and the minimum selling price as the bounds of the predictive price results, based only on historical data. To set up the binomial tree, we follow the same assumptions about underlying asset price movements in the model proposed by Cox, Ross, and Rubinsein (CRR), 7 by supposing the prices of the underlying asset are a sequence of random quantities, with the movement factors u for upward movement and d for downward movement.…”

Section: Introductionmentioning

confidence: 99%

“…For American options, there is no closed formula to price the option like the classic CRR model, but we have presented the mathematical description of the American option backward optimization method on the basis of the NPI method 6 . At each time step, the option price

V_{t}^{i}

, where t denotes the time step and i denotes the ordered node at time t , is derived by comparing the instant value and the discount exception from the next time step.…”

Section: Introductionmentioning

confidence: 99%

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

Coolen

Coolen‐Maturi

2022

Appl Stoch Models Bus & Ind

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This 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.

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Section: E(g(s Tmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

V_{t}^{i}

, where t denotes the time step and i denotes the ordered node at time t , is derived by comparing the instant value and the discount exception from the next time step.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Coolen

Coolen‐Maturi

2022

Appl Stoch Models Bus & Ind

Self Cite

View full text Add to dashboard Cite

show abstract

“…Coolen et al (2018) presented a new approach to quantify the credit risk by using the NPI method based on the ROC analysis. The implements of the NPI method for the vanilla option pricing well perform when there are less certain information of the underlying asset (He et al, 2019); (He et al, 2020).…”

Section: Introductionmentioning

confidence: 99%

Nonparametric Predictive Inference for Asian options

2020

Preprint

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Asian option, as one of the path-dependent exotic options, is widely traded in the energy market, either for speculation or hedging. However, it is hard to price, especially the one with the arithmetic average price. The traditional trading procedure is either too restrictive by assuming the distribution of the underlying asset or less rigorous by using the approximation. It is attractive to infer the Asian option price with few assumptions of the underlying asset distribution and adopt to the historical data with a nonparametric method. In this paper, we present a novel approach to price the Asian option from an imprecise statistical aspect. Nonparametric Predictive Inference (NPI) is applied to infer the average value of the future underlying asset price, which attempts to make the prediction reflecting more uncertainty because of the limited information. A rational pairwise trading criterion is also proposed in this paper for the Asian options comparison, as a risk measure. The NPI method for the Asian option is illustrated in several examples by using the simulation techniques or the empirical data from the energy market.

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Comparison of American, European, and Exotic Options and Pricing Methods

Wang

2024

Advances in Economics, Business and Management Research

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As a matter of fact, the valuation of options is a fundamental element of financial markets and investment in general especially in recent years. With this in mind, this study provides an overview and analysis of three commonly used options as well as the methods used to price them. To be specific, these options include the Binomial tree model, the Black-Scholes Model, and Monte Carlo simulations. Additionally, recent research on option pricing is presented, highlighting various aspects such as flexibility, pricing premiums, market predictability strategy, and investor suitability. At the same time, this study examines the constraints of existing research and identifies prospective domains for further study. According to the analysis, the main aim of this study is to introduce and contrast three different choices along with their respective pricing systems. In the meantime, it also aims to extend current research concerns and provide guidance to future researchers, which shed light on guiding further exploration of option pricing.

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Nonparametric predictive inference for American option pricing based on the binomial tree model

Abstract: Nonparametric predictive inference for American option pricing based on the binomial tree model.', Communications in statistics theory and methods. .

Cited by 5 publications

References 22 publications

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

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

Nonparametric Predictive Inference for Asian options

Comparison of American, European, and Exotic Options and Pricing Methods

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