Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of Europ...Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.展开更多
Spatio-temporal variability and dynamics in Sahelian agro-pastoral zones make each local situation a special case. These specificities must be considered to guide the dissemination of agricultural options with a view ...Spatio-temporal variability and dynamics in Sahelian agro-pastoral zones make each local situation a special case. These specificities must be considered to guide the dissemination of agricultural options with a view to sustainable development. The territorial scale of municipalities is not sufficient for this necessary contextualization;the scale of the “village terroir” seems to be a better option. This is the hypothesis we put forward in the framework of the Global Collaboration for Resilient Food Systems program (CRFS), i.e. local context is spatially defined by village terroir. The study is based on data collected through participatory mapping and surveys in “village terroirs” in three regions of Niger (Maradi, Dosso and Tillabéri). Then the links between farm managers and their cultivated land, as well as the spatio-temporal dynamics of local context are analyzed. This study provides evidence of the existence and functional usefulness of the village terroir for farmers, their land management and their activities. It demonstrates the usefulness of contextualizing agricultural options at this scale. Their analysis elucidates the links between “terroirs village” and the specific functioning of the agrosocio-ecosystems acting on each of them, thus laying the systemic and geographical foundations for a model of the spatio- temporal dynamics of “village terroirs”. This initial work has opened up new perspectives in modeling and sustainable development.展开更多
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
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
Based on the analog between the stochastic dynamics and quantum harmonic oscillator,we propose a market force driving model to generalize the Black-Scholes model in finance market.We give new schemes of option pricing...Based on the analog between the stochastic dynamics and quantum harmonic oscillator,we propose a market force driving model to generalize the Black-Scholes model in finance market.We give new schemes of option pricing,in which we can take various unexpected market behaviors into account to modify the option pricing.As examples,we present several market forces to analyze their effects on the option pricing.These results provide us two practical applications.One is to be used as a new scheme of option pricing when we can predict some hidden market forces or behaviors emerging.The other implies the existence of some risk premium when some unexpected forces emerge.展开更多
This paper studies the multi-dimensional Black-Scholes model of security valnation. The extension of the Black-Scholes model implies; the partial differential equation derived from an absence of arbitrage which the au...This paper studies the multi-dimensional Black-Scholes model of security valnation. The extension of the Black-Scholes model implies; the partial differential equation derived from an absence of arbitrage which the authors solve by using the Feynmeu-Kac Formula. Then they compute its special example by solving the multi-variable partial differential equation.展开更多
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
In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging e...In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging error due to discrete-time trading when the true strategy is known for the trader, is investigated. The result provides new statistical tools to study and detect the effect of the long-memory and the Hurst parameter for the error of discrete time hedging.展开更多
In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation （PDE） was invesigated in a fixed domain for valuing two assets of American （call-max/put-min） options...In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation （PDE） was invesigated in a fixed domain for valuing two assets of American （call-max/put-min） options. From the viscosity solution of a PDE, a unique viscosity solution was obtained for the semilinear Black-Scholes PDE.展开更多
文摘Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.
文摘Spatio-temporal variability and dynamics in Sahelian agro-pastoral zones make each local situation a special case. These specificities must be considered to guide the dissemination of agricultural options with a view to sustainable development. The territorial scale of municipalities is not sufficient for this necessary contextualization;the scale of the “village terroir” seems to be a better option. This is the hypothesis we put forward in the framework of the Global Collaboration for Resilient Food Systems program (CRFS), i.e. local context is spatially defined by village terroir. The study is based on data collected through participatory mapping and surveys in “village terroirs” in three regions of Niger (Maradi, Dosso and Tillabéri). Then the links between farm managers and their cultivated land, as well as the spatio-temporal dynamics of local context are analyzed. This study provides evidence of the existence and functional usefulness of the village terroir for farmers, their land management and their activities. It demonstrates the usefulness of contextualizing agricultural options at this scale. Their analysis elucidates the links between “terroirs village” and the specific functioning of the agrosocio-ecosystems acting on each of them, thus laying the systemic and geographical foundations for a model of the spatio- temporal dynamics of “village terroirs”. This initial work has opened up new perspectives in modeling and sustainable development.
文摘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.
文摘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.
文摘Based on the analog between the stochastic dynamics and quantum harmonic oscillator,we propose a market force driving model to generalize the Black-Scholes model in finance market.We give new schemes of option pricing,in which we can take various unexpected market behaviors into account to modify the option pricing.As examples,we present several market forces to analyze their effects on the option pricing.These results provide us two practical applications.One is to be used as a new scheme of option pricing when we can predict some hidden market forces or behaviors emerging.The other implies the existence of some risk premium when some unexpected forces emerge.
文摘This paper studies the multi-dimensional Black-Scholes model of security valnation. The extension of the Black-Scholes model implies; the partial differential equation derived from an absence of arbitrage which the authors solve by using the Feynmeu-Kac Formula. Then they compute its special example by solving the multi-variable partial differential equation.
文摘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.
基金Supported by the National Natural Science Foundation of China(11671115)the Natural Science Foundation of Zhejiang Province(LY14A010025)
文摘In this paper we investigate asymptotic behavior of error of a discrete time hedging strategy in a fractional Black-Scholes model in the sense of Wick-ItS-Skorohod integration. The rate of convergence of the hedging error due to discrete-time trading when the true strategy is known for the trader, is investigated. The result provides new statistical tools to study and detect the effect of the long-memory and the Hurst parameter for the error of discrete time hedging.
基金Project supported by the National Natural Science Foundation of China (Grant No.10271072)
文摘In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation （PDE） was invesigated in a fixed domain for valuing two assets of American （call-max/put-min） options. From the viscosity solution of a PDE, a unique viscosity solution was obtained for the semilinear Black-Scholes PDE.
