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Black-Scholes Option Pricing Model Modified to Admit a Miniscule Drift Can Reproduce the Volatility Smile
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作者 Matthew C. Modisett James A. Powell 《Applied Mathematics》 2012年第6期597-605,共9页
This paper develops a closed-form solution to an extended Black-Scholes (EBS) pricing formula which admits an implied drift parameter alongside the standard implied volatility. The market volatility smiles for vanilla... This paper develops a closed-form solution to an extended Black-Scholes (EBS) pricing formula which admits an implied drift parameter alongside the standard implied volatility. The market volatility smiles for vanilla call options on the S&P 500 index are recreated fitting the best volatility-drift combination in this new EBS. Using a likelihood ratio test, the implied drift parameter is seen to be quite significant in explaining volatility smiles. The implied drift parameter is sufficiently small to be undetectable via historical pricing analysis, suggesting that drift is best considered as an implied parameter rather than a historically-fit one. An overview of option-pricing models is provided as background. 展开更多
关键词 option pricing black-scholes VOLATILITY SMILE
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NEW METHOD TO OPTION PRICING FOR THE GENERAL BLACK-SCHOLES MODEL-AN ACTUARIAL APPROACH
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作者 闫海峰 刘三阳 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第7期826-835,共10页
Using physical probability measure of price process and the principle of fair premium, the results of Mogens Bladt and Hina Hviid Rydberg are generalized. In two cases of paying intermediate divisends and no intermedi... Using physical probability measure of price process and the principle of fair premium, the results of Mogens Bladt and Hina Hviid Rydberg are generalized. In two cases of paying intermediate divisends and no intermediate dividends, the Black_Scholes model is generalized to the case where the risk_less asset (bond or bank account) earns a time_dependent interest rate and risk asset (stock) has time_dependent the continuously compounding expected rate of return, volatility. In these cases the accurate pricing formula and put_call parity of European option are obtained. The general approach of option pricing is given for the general Black_Scholes of the risk asset (stock) has the continuously compounding expected rate of return, volatility. The accurate pricing formula and put_call parity of European option on a stock whose price process is driven by general Ornstein_Uhlenback (O_U) process are given by actuarial approach. 展开更多
关键词 option pricing Black_Scholes model fair premium O_U process
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SIMPLEST DIFFERENTIAL EQUATION OF STOCK PRICE,ITS SOLUTION AND RELATION TO ASSUMPTION OF BLACK-SCHOLES MODEL
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作者 云天铨 雷光龙 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第6期654-658,共5页
Two kinds of mathematical expressions of stock price, one of which based on certain description is the solution of the simplest differential equation (S.D.E.) obtained by method similar to that used in solid mechanics... Two kinds of mathematical expressions of stock price, one of which based on certain description is the solution of the simplest differential equation (S.D.E.) obtained by method similar to that used in solid mechanics,the other based on uncertain description (i.e., the statistic theory)is the assumption of Black_Scholes's model (A.B_S.M.) in which the density function of stock price obeys logarithmic normal distribution, can be shown to be completely the same under certain equivalence relation of coefficients. The range of the solution of S.D.E. has been shown to be suited only for normal cases (no profit, or lost profit news, etc.) of stock market, so the same range is suited for A.B_ S.M. as well. 展开更多
关键词 stock market option pricing Black_Scholes model probability and certainty differential equation
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Critical Exercise Price for American Floating Strike Lookback Option in a Mixed Jump-Diffusion Model 被引量:4
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作者 YANG Zhao-qiang 《Chinese Quarterly Journal of Mathematics》 2018年第3期240-259,共20页
This paper studies the critical exercise price of American floating strike lookback options under the mixed jump-diffusion model. By using It formula and Wick-It-Skorohod integral, a new market pricing model estab... This paper studies the critical exercise price of American floating strike lookback options under the mixed jump-diffusion model. By using It formula and Wick-It-Skorohod integral, a new market pricing model established under the environment of mixed jumpdiffusion fractional Brownian motion. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given, then the American floating strike lookback options factorization formula is obtained, the results is generalized the classical Black-Scholes market pricing model. 展开更多
关键词 MIXED JUMP-DIFFUSION fractional BROWNIAN motion Wick-Ito-Skorohod integral market pricing model option factorization CRITICAL exercise price
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PRICING CATASTROPHE OPTIONS WITH COUNTERPARTY CREDIT RISK IN A REDUCED FORM MODEL 被引量:2
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作者 徐亚娟 王过京 《Acta Mathematica Scientia》 SCIE CSCD 2018年第1期347-360,共14页
In this paper, we study the price of catastrophe Options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price proc... In this paper, we study the price of catastrophe Options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price process is modeled through a jump-diffusion process which is correlated to the loss process, the interest rate process and the default intensity process are modeled through the Vasicek model: We derive the closed form formulae for pricing catastrophe options in a reduced form model. Furthermore, we make some numerical analysis on the explicit formulae. 展开更多
关键词 pricing catastrophe option counterparty risk measure change reduced form model
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Pricing Stochastic Barrier Options under Hull-White Interest Rate Model 被引量:1
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作者 潘坚 肖庆宪 《Journal of Donghua University(English Edition)》 EI CAS 2016年第3期433-438,共6页
A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stocha... A barrier option valuation model with stochastic barrier which was regarded as the main feature of the model was developed under the Hull-White interest rate model.The purpose of this study was to deal with the stochastic barrier by means of partial differential equation methods and then derive the exact analytical solutions of the barrier options.Furthermore,a numerical example was given to show how to apply this model to pricing one structured product in realistic market.Therefore,this model can provide new insight for future research on structured products involving barrier options. 展开更多
关键词 stochastic barrier Hull-White interest rate model partial differential equation(PDE) methods option pricing
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Pricing VIX options in a 3/2 plus jumps model
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作者 TAN Xiao-yu WANG Cheng-xiang +1 位作者 HUANG Wen-li LI Sheng-hong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2018年第3期323-334,共12页
This paper proposes and makes a study of a new model(called the 3/2 plus jumps model) for VIX option pricing. The model allows the mean-reversion speed and volatility of volatility to be highly sensitive to the actual... This paper proposes and makes a study of a new model(called the 3/2 plus jumps model) for VIX option pricing. The model allows the mean-reversion speed and volatility of volatility to be highly sensitive to the actual level of VIX. In particular, the positive volatility skew is addressed by the 3/2 plus jumps model. Daily calibration is used to prove that the proposed model preserves its validity and reliability for both in-sample and out-of-sample tests.The results show that the models are capable of fitting the market price while generating positive volatility skew. 展开更多
关键词 pricing VIX options 3/2 plus jumps model positive volatility skew
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A Full Asymptotic Series of European Call Option Prices in the SABR Model with Beta = 1
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作者 Z. Guo H. Schellhorn 《Applied Mathematics》 2019年第6期485-512,共28页
We develop two new pricing formulae for European options. The purpose of these formulae is to better understand the impact of each term of the model, as well as improve the speed of the calculations. We consider the S... We develop two new pricing formulae for European options. The purpose of these formulae is to better understand the impact of each term of the model, as well as improve the speed of the calculations. We consider the SABR model (with &beta;=1) of stochastic volatility, which we analyze by tools from Malliavin Calculus. We follow the approach of Alòs et al. (2006) who showed that under stochastic volatility framework, the option prices can be written as the sum of the classic Hull-White (1987) term and a correction due to correlation. We derive the Hull-White term, by using the conditional density of the average volatility, and write it as a two-dimensional integral. For the correction part, we use two different approaches. Both approaches rely on the pairing of the exponential formula developed by Jin, Peng, and Schellhorn (2016) with analytical calculations. The first approach, which we call “Dyson series on the return’s idiosyncratic noise” yields a complete series expansion but necessitates the calculation of a 7-dimensional integral. Two of these dimensions come from the use of Yor’s (1992) formula for the joint density of a Brownian motion and the time-integral of geometric Brownian motion. The second approach, which we call “Dyson series on the common noise” necessitates the calculation of only a one-dimensional integral, but the formula is more complex. This research consisted of both analytical derivations and numerical calculations. The latter show that our formulae are in general more exact, yet more time-consuming to calculate, than the first order expansion of Hagan et al. (2002). 展开更多
关键词 SABR model Stochastic VOLATILITY Malliavin CALCULUS Exponential Formula option pricing
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Option Pricing and Hedging under a Markov Switching Lévy Process Model
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作者 宋瑞丽 王波 《Chinese Quarterly Journal of Mathematics》 2017年第1期66-78,共13页
In this paper, we consider a Markov switching Lévy process model in which the underlying risky assets are driven by the stochastic exponential of Markov switching Lévy process and then apply the model to opt... In this paper, we consider a Markov switching Lévy process model in which the underlying risky assets are driven by the stochastic exponential of Markov switching Lévy process and then apply the model to option pricing and hedging. In this model, the market interest rate, the volatility of the underlying risky assets and the N-state compensator,depend on unobservable states of the economy which are modeled by a continuous-time Hidden Markov process. We use the MEMM(minimal entropy martingale measure) as the equivalent martingale measure. The option price using this model is obtained by the Fourier transform method. We obtain a closed-form solution for the hedge ratio by applying the local risk minimizing hedging. 展开更多
关键词 Markov chain model MEMM Lévy process option pricing HEDGING
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The SABR Model: Explicit Formulae of the Moments of the Forward Prices/Rates Variable and Series Expansions of the Transition Probability Density and of the Option Prices
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作者 Lorella Fatone Francesca Mariani +1 位作者 Maria Cristina Recchioni Francesco Zirilli 《Journal of Applied Mathematics and Physics》 2014年第7期540-568,共29页
The SABR stochastic volatility model with β-volatility β ? (0,1) and an absorbing barrier in zero imposed to the forward prices/rates stochastic process is studied. The presence of (possibly) nonzero correlation bet... The SABR stochastic volatility model with β-volatility β ? (0,1) and an absorbing barrier in zero imposed to the forward prices/rates stochastic process is studied. The presence of (possibly) nonzero correlation between the stochastic differentials that appear on the right hand side of the model equations is considered. A series expansion of the transition probability density function of the model in powers of the correlation coefficient of these stochastic differentials is presented. Explicit formulae for the first three terms of this expansion are derived. These formulae are integrals of known integrands. The zero-th order term of the expansion is a new integral formula containing only elementary functions of the transition probability density function of the SABR model when the correlation coefficient is zero. The expansion is deduced from the final value problem for the backward Kolmogorov equation satisfied by the transition probability density function. Each term of the expansion is defined as the solution of a final value problem for a partial differential equation. The integral formulae that give the solutions of these final value problems are based on the Hankel and on the Kontorovich-Lebedev transforms. From the series expansion of the probability density function we deduce the corresponding expansions of the European call and put option prices. Moreover we deduce closed form formulae for the moments of the forward prices/rates variable. The moment formulae obtained do not involve integrals or series expansions and are expressed using only elementary functions. The option pricing formulae are used to study synthetic and real data. In particular we study a time series (of real data) of futures prices of the EUR/USD currency's exchange rate and of the corresponding option prices. The website: http://www.econ.univpm.it/recchioni/finance/w18 contains material including animations, an interactive application and an app that helps the understanding of the paper. A more general reference to the work of the authors and of their coauthors in mathematical finance is the website:http://www.econ.univpm.it/recchioni/finance. 展开更多
关键词 SABR Stochastic VOLATILITY models option pricing SPECTRAL DECOMPOSITION FX Data
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Trinomial tree model of the real options approach used in mining investment price forecast and analysis
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作者 Qing-Hua GU Qiong WU Cai-Wu LU 《Journal of Coal Science & Engineering(China)》 2013年第4期573-577,共5页
In order to effectively avoid the defects of a traditional discounted cash flow method, a trinomial tree pricing model of the real option is improved and used to forecast the investment price of mining. Taking Molybde... In order to effectively avoid the defects of a traditional discounted cash flow method, a trinomial tree pricing model of the real option is improved and used to forecast the investment price of mining. Taking Molybdenum ore as an example, a theoretical model for the hurdle price under the optimal investment timing is constructed. Based on the example data, the op- tion price model is simulated. By the model, mine investment price can be computed and forecast effectively. According to the characteristics of mine investment, cut-off grade, reserve estimation and mine life in different price also can be quantified. The result shows that it is reliable and practical to enhance the accuracy for mining investment decision. 展开更多
关键词 real option approach (ROA) trinomial tree model hurdle price price forecast
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Early exercise premium method for pricing American options under the J-model
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作者 Yacin Jerbi 《Financial Innovation》 2016年第1期266-291,共26页
Background:This study develops a new model called J-am for pricing American options and for determining the related early exercise boundary(EEB).This model is based on a closed-form solution J-formula for pricing Euro... Background:This study develops a new model called J-am for pricing American options and for determining the related early exercise boundary(EEB).This model is based on a closed-form solution J-formula for pricing European options,defined in the study by Jerbi(Quantitative Finance,15:2041-2052,2015).The J-am pricing formula is a solution of the Black&Scholes(BS)PDE with an additional function called f as a second member and with limit conditions adapted to the American option context.The aforesaid function f represents the cash flows resulting from an early exercise of the option.Methods:This study develops the theoretical formulas of the early exercise premium value related to three American option pricing models called J-am,BS-am,and Heston-am models.These three models are based on the J-formula by Jerbi(Quantitative Finance,15:2041-2052,2015),BS model,and Heston(Rev Financ Stud,6:327-343,1993)model,respectively.This study performs a general algorithm leading to the EEB and to the American option price for the three models.Results:After implementing the algorithms,we compare the three aforesaid models in terms of pricing and the EEB curve.In particular,we examine the equivalence between J-am and Heston-am as an extension of the equivalence studied by Jerbi(Quantitative Finance,15:2041-2052,2015).This equivalence is interesting since it can reduce a bi-dimensional model to an equivalent uni-dimensional model.Conclusions:We deduce that our model J-am exactly fits the Heston-am one for certain parameters values to be optimized and that all the theoretical results conform with the empirical studies.The required CPU time to compute the solution is significantly less in the case of the J-am model compared with to the Heston-am model. 展开更多
关键词 American option pricing Stochastic volatility model Early exercise boundary Early exercise premium J-law J-process J-formula Heston model
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Application of Binomial Option Pricing Model to the Appraisal of Knowledge Management Investment
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作者 Jing Sui Jinsheng He Jiancheng Yu 《Chinese Business Review》 2005年第3期1-5,共5页
This paper views knowledge management (KM) investment from the angle of real options, and demonstrates the utility of the real options approach to KM investment analysis. First, KM project has characteristics of unc... This paper views knowledge management (KM) investment from the angle of real options, and demonstrates the utility of the real options approach to KM investment analysis. First, KM project has characteristics of uncertainty, irreversibility and choice of timing, which suggests that we can appraise KM investment by real options theory. Second, the paper analyses corresponding states of real options in KM and finance options. Then, this paper sheds light on the way to the application of binomial pricing method to KM investment model, which includes modeling and conducting KM options. Finally, different results are shown of using DCF method and binomial model of option evaluation via a case. 展开更多
关键词 knowledge management real options binomial option pricing model project appraisal
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基于Black-Scholes实物期权定价模型的发电商投资决策分析 被引量:13
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作者 袁德 李宜君 +1 位作者 董全学 刘玮 《电力系统保护与控制》 EI CSCD 北大核心 2008年第12期17-20,共4页
从电源投资建设项目的特点出发,结合电源建设投资的期权特性,得出了与Black—Scholes期权定价模型相对应的电源建设投资实物期权内容。通过建立基于Black-Scholes实物期权定价模型,并将其运用到电源建设投资决策中,避免了传统的电源投... 从电源投资建设项目的特点出发,结合电源建设投资的期权特性,得出了与Black—Scholes期权定价模型相对应的电源建设投资实物期权内容。通过建立基于Black-Scholes实物期权定价模型,并将其运用到电源建设投资决策中,避免了传统的电源投资决策方法依赖项目净现值等缺点。通过算例对电源建设投资项目的期权进行了估价,表明将实物期权理论应用到电源建设投资决策中是可行的。 展开更多
关键词 发电商 black-scholes期权定价模型 实物期权 投资决策
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一种无风险利率时变条件下的Black-Scholes期权定价模型 被引量:9
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作者 任智格 何朗 黄樟灿 《数学杂志》 CSCD 北大核心 2015年第1期203-206,共4页
本文研究了无风险利率改进的Black-Scholes期权定价模型问题.利用指数函数和Ito公式的方法,获得了一种改进的Black-Scholes期权定价模型,推广了现有Black-Scholes期权定价模型的结果.
关键词 black-scholes模型 期权定价 无风险利率 看涨期权
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广义Black-Scholes模型期权定价新方法——保险精算方法 被引量:70
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作者 闫海峰 刘三阳 《应用数学和力学》 EI CSCD 北大核心 2003年第7期730-738,共9页
 利用公平保费原则和价格过程的实际概率测度推广了MogensBladt和TinaHviidRydberg的结果· 在无中间红利和有中间红利两种情况下,把Black_Scholes模型推广到无风险资产(债券或银行存款)具有时间相依的利率和风险资产(股票)也具...  利用公平保费原则和价格过程的实际概率测度推广了MogensBladt和TinaHviidRydberg的结果· 在无中间红利和有中间红利两种情况下,把Black_Scholes模型推广到无风险资产(债券或银行存款)具有时间相依的利率和风险资产(股票)也具有时间相依的连续复利预期收益率和波动率的情况,在此情况下获得了欧式期权的精确定价公式以及买权与卖权之间的平价关系· 给出了风险资产(股票) 展开更多
关键词 期权定价 black-scholes模型 公平保费 O-U过程
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基于Black-Scholes模型的公司资本结构模型 被引量:8
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作者 杨宝臣 刘铮 张彤 《管理科学学报》 1999年第2期66-70,共5页
】对考虑代理成本的公司资本结构问题进行了研究,引入期权理论及其定价模型给出确定这一情况下的公司最优资本结构的方法。
关键词 black-scholes模型 资本结构 代理成本
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修正的Black-Scholes模型下的欧式期权定价 被引量:9
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作者 孙玉东 师义民 《高校应用数学学报(A辑)》 CSCD 北大核心 2012年第1期23-32,共10页
通常情况下,期权定价研究都假定股票价格的波动率和期望收益率为常数.假定波动率和期望收益率为股票价格的一般函数.利用金融市场复制策略及布朗运动的Ito公式,得到欧式未定权益的一般Black-Scholes偏微分方程,并通过求解偏微分方程获... 通常情况下,期权定价研究都假定股票价格的波动率和期望收益率为常数.假定波动率和期望收益率为股票价格的一般函数.利用金融市场复制策略及布朗运动的Ito公式,得到欧式未定权益的一般Black-Scholes偏微分方程,并通过求解偏微分方程获得欧式期权定价公式. 展开更多
关键词 布朗运动 期权定价 修正的black-scholes模型
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关于Black-Scholes期权定价模型的证明 被引量:4
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作者 姜本源 胡煜寒 +1 位作者 付林 高丹霞 《鞍山师范学院学报》 2008年第4期1-4,共4页
lack-Scholes期权定价模型是20世纪70年代以来金融理论发展的最重要的基石,但是在各类文献中却几乎没有关于它的详细、准确的证明.本文将有关文献中出现的错误加以更正,并优化了证明过程,给出一个关于Black-Scholes期权定价模型严格的... lack-Scholes期权定价模型是20世纪70年代以来金融理论发展的最重要的基石,但是在各类文献中却几乎没有关于它的详细、准确的证明.本文将有关文献中出现的错误加以更正,并优化了证明过程,给出一个关于Black-Scholes期权定价模型严格的数学证明. 展开更多
关键词 期权 期权定价模型 偏微分方程
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Modified Differential Transform Method for Solving Black-Scholes Pricing Model of European Option Valuation Paying Continuous Dividends
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作者 AHMAD Manzoor MISHRA Rajshree JAIN Renu 《Journal of Partial Differential Equations》 CSCD 2023年第4期381-393,共13页
.Option pricing is a major problem in quantitative finance.The Black-Scholes model proves to be an effective model for the pricing of options.In this paper a com-putational method known as the modified differential tr... .Option pricing is a major problem in quantitative finance.The Black-Scholes model proves to be an effective model for the pricing of options.In this paper a com-putational method known as the modified differential transform method has been em-ployed to obtain the series solution of Black-Scholes equation with boundary condi-tions for European call and put options paying continuous dividends.The proposed method does not need discretization to find out the solution and thus the computa-tional work is reduced considerably.The results are plotted graphically to establish the accuracy and efficacy of the proposed method. 展开更多
关键词 European option pricing black-scholes equation call option put option modified differential transform method
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