A new evaluation of mean value for fuzzy numbers and its application to American put option under uncertainty

Yoshida, Yūji; Yasuda, Masami; Nakagami, Jun-ichi; Kurano, Masami

doi:10.1016/j.fss.2003.11.022

Cited by 73 publications

(29 citation statements)

References 17 publications

(31 reference statements)

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“…From financial model research, Jorg Kienitz et al (2012) [28] performed key analysis regarding how the quasi-random number and Brownian Bridge approach can be used to improve Monte Carlo method, and they applied the improved calculation method in option pricing. However, there are relatively few studies regarding American option pricing theory under a fuzzy environment based on numerical approaches, for example, Yoshida et al (2006) [29] based on Black-Scholes model constructed an American option pricing model which set the underlying price as fuzzy variable and through numerical simulation to verify the proposed model effectiveness. Rather, most of existing literature provides analysis based on the binomial tree method, such as Silvia Muzzioli et al (2008) [30] treat the volatility as a fuzzy number and used the multiple-period binomial tree method to obtain risk-neutral valuations of American options.…”

Section: Literature Reviewmentioning

confidence: 99%

Fuzzy Levy-GJR-GARCH American Option Pricing Model Based on an Infinite Pure Jump Process

Zhang

Watada

2018

IEICE Trans. Inf. & Syst.

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SUMMARYThis paper focuses mainly on issues related to the pricing of American options under a fuzzy environment by taking into account the clustering of the underlying asset price volatility, leverage effect and stochastic jumps. By treating the volatility as a parabolic fuzzy number, we constructed a Levy-GJR-GARCH model based on an infinite pure jump process and combined the model with fuzzy simulation technology to perform numerical simulations based on the least squares Monte Carlo approach and the fuzzy binomial tree method. An empirical study was performed using American put option data from the Standard & Poor's 100 index. The findings are as follows: under a fuzzy environment, the result of the option valuation is more precise than the result under a clear environment, pricing simulations of short-term options have higher precision than those of medium-and long-term options, the least squares Monte Carlo approach yields more accurate valuation than the fuzzy binomial tree method, and the simulation effects of different Levy processes indicate that the NIG and CGMY models are superior to the VG model. Moreover, the option price increases as the time to expiration of options is extended and the exercise price increases, the membership function curve is asymmetric with an inclined left tendency, and the fuzzy interval narrows as the level set α and the exponent of membership function n increase. In addition, the results demonstrate that the quasi-random number and Brownian Bridge approaches can improve the convergence speed of the least squares Monte Carlo approach. key words: American option, fuzzy set theory, fuzzy simulation technology, Levy process, GJR-GARCH model, least squares Monte Carlo approach, binomial tree method, quasi-random number, Brownian Bridge approach

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Section: Literature Reviewmentioning

confidence: 99%

Fuzzy Levy-GJR-GARCH American Option Pricing Model Based on an Infinite Pure Jump Process

Zhang

Watada

2018

IEICE Trans. Inf. & Syst.

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“…Therefore, using fuzzy analysis to study such problems as default probability or derivatives pricing has practical needs. There have existed some literatures about option pricing in fuzzy random environments, such as, Yoshida 12 introduced the fuzzy logic to the stochastic financial model, and derived a new model on European options with uncertainty of both randomness and fuzziness, Wu 13 pointed out that owing to the fluctuation of financial market from time to time, the volatility and stock price may occur imprecisely in the real world, therefore, he employed the extension principle in fuzzy sets theory to the Black-Scholes formula, and derived a new model on European options, and turned the European call and put option price into a fuzzy number, Xu et al 14 pointed out that the rate of Poisson process and jump sequence in the Merton's normal jump-diffusion model cannot be expected in a precise sense, so they presented a fuzzy normal jump-diffusion model for European option pricing, with uncertainty of both randomness and fuzziness in the jumps, and obtained the crisp weighted possibilistic mean normal jump-diffusion model, the related researches can also be see in literatures [15][16][17][18] . However, as far as we know, there are few about credit risk analysis and derivatives pricing model under fuzzy environments.…”

Section: Co-published By Atlantis Press and Taylor And Francismentioning

confidence: 99%

A New Default Intensity Model with Fuzziness and Hesitation

Wu¹,

Zhuang²,

Li³

2016

IJCIS

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With the increased financial market volatility, corporate defaults will suffer from the double impact of the external shocks and internal contagion effects. In the existing stochastic default intensity models, the valuation of sensitivity parameters requires a lot of historical data, however, the limited market data does not guarantee the accuracy of parameter estimation, meanwhile, due to the people have a lot of fuzziness and hesitation judgements on the default process, it is necessary for us to let the corresponding random parameter of the default intensity to be a triangular intuitionistic fuzzy interval value. In this paper, we propose a new default intensity model based on the external shocks and internal contagion effects, and introduce the triangular intuitionistic fuzzy numbers into the credit default swaps (CDS) pricing modeling to describe the fuzziness and hesitation of the default process. In the end, we get a new fuzzy form pricing formula for CDS, and by the simulation analysis, we obtain that, all kinds of fuzziness and hesitation of the market have significant impact on credit spreads, and a model result with a consideration of the fair price of CDS in a fuzzy random environment including a pure random environment result. Compared with the existing stochastic model, these proper interval results can offer the investors more flexible options and can more reflect the impact of market environment on credit spreads.

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“…The operations are carried out by a sequential for loop that iterates over the set of α-cuts. We decided not to spread the loop among different threads in GPU code, since most applications in real life do not involve more than three to four degrees of uncertainty in their data model [3], [6], [17], [21], [23]. This number is way too low to exploit thread level parallelism (TLP).…”

Section: Implementation Detailsmentioning

confidence: 99%

“…This particular kind of uncertainty is best modelled using fuzzy numbers, as they allow to deal with such type of quantifiers [24]. The fuzzy approach has been successfully applied in finance [23], transportation [3], supply chain management [6], load flow [17], [21]... for configuring expert systems to run under uncertainty scenarios. A fuzzy arithmetic based on the α-cut approach can be implemented using interval arithmetic [10], however this can be cumbersome in terms of computation intensity, as each fuzzy operation requires at least two interval operations to be computed.…”

Section: Introductionmentioning

confidence: 99%

FuzzyGPU: A Fuzzy Arithmetic Library for GPU

Defour

Marín

2014

2014 22nd Euromicro International Conference on Parallel, Distributed, and Network-Based Processing

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Abstract-Data are traditionally represented using native format such as integer or floating-point numbers in various flavor. However, some applications rely on more complex representation format. This is the case when uncertainty needs to be apprehended. Fuzzy arithmetic is one of the major tools to address this problem, but the execution time of basic operations such as addition or multiplication makes its usage prohibitive. In this article, thanks to a new representation format and modern GPU characteristics we show that it is possible to greatly reduce the execution time of those operations. These techniques have been implemented in fuzzyGPU, a freely distributed library of common operations over fuzzy number.

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A new evaluation of mean value for fuzzy numbers and its application to American put option under uncertainty

Cited by 73 publications

References 17 publications

Fuzzy Levy-GJR-GARCH American Option Pricing Model Based on an Infinite Pure Jump Process

Fuzzy Levy-GJR-GARCH American Option Pricing Model Based on an Infinite Pure Jump Process

A New Default Intensity Model with Fuzziness and Hesitation

FuzzyGPU: A Fuzzy Arithmetic Library for GPU

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