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
The primary goal of this paper is to price European options in the Merton＇s frame- work with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial mar...The primary goal of this paper is to price European options in the Merton＇s frame- work with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial market, the average jump rate and jump sizes cannot be recorded or collected accurately. So the main idea of this paper is to model the rate as a triangular fuzzy number and jump sizes as fuzzy random variables and use the property of fuzzy set to deduce two different jump-diffusion models underlying principle of rational expectations equilibrium price. Unlike many conventional models, the European option price will now turn into a fuzzy number. One of the major advantages of this model is that it allows investors to choose a reasonable European option price under an acceptable belief degree. The empirical results will serve as useful feedback information for improvements on the proposed model.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
We use an actuarial approach to estimate the valuation of the reload option for a non-tradable risk asset under the jump-diffusion processes and Hull-White interest rate. We verify the validity of the actuarial approa...We use an actuarial approach to estimate the valuation of the reload option for a non-tradable risk asset under the jump-diffusion processes and Hull-White interest rate. We verify the validity of the actuarial approach to the European vanilla option for non-tradable assets. The formulas of the actuarial approach to the reload option are derived from the fair premium principle and the obtained results are arbitrage. Numerical experiments are conducted to analyze the effects of different parameters on the results of valuation as well as their differences from those obtained by the no-arbitrage approach. Finally, we give the valuations of the reload options under different parameters.展开更多
In this paper, we present a stock model with Markov switching in the uncertainty markets, where the parameters of drift and volatility change according to the states of a Markov process. To price the option, we firstl...In this paper, we present a stock model with Markov switching in the uncertainty markets, where the parameters of drift and volatility change according to the states of a Markov process. To price the option, we firstly establish a risk-neutral probability based on the uncertain measure given by Liu. Then a closed form of the European option pricing formula is obtained by applying the Laplace transforms and the inverse Laplace transforms.展开更多
For a non-Gaussian Levy model, it is shown that if the model exists a trivial arbitrage-free interval, option pricing by mean correcting method is always arbitrage-free, and if the arbitrage-free interval is non-trivi...For a non-Gaussian Levy model, it is shown that if the model exists a trivial arbitrage-free interval, option pricing by mean correcting method is always arbitrage-free, and if the arbitrage-free interval is non-trivial, this pricing method may lead to arbitrage in some cases. In the latter case, some necessary and sufficient conditions under which option price is arbitrage-free are obtained.展开更多
This paper studies the first passage time problem for a reflected two-sided jump-diffusion risk model with the jumps having a hyper-Erlang distribution.The authors give the explicit closed-form expression for the join...This paper studies the first passage time problem for a reflected two-sided jump-diffusion risk model with the jumps having a hyper-Erlang distribution.The authors give the explicit closed-form expression for the joint Laplace transform of the first passage time and the overshoot for the reflected process.Finally,the formula is applied to the ruin problem under the barrier dividend strategy and the pricing of the Russian option.展开更多
In this paper, under the assumption that the exchange rate follows the extended Vasicek model, the pricing of the reset option in FBM model is investigated. Some interesting themes such as closed-form formulas for the...In this paper, under the assumption that the exchange rate follows the extended Vasicek model, the pricing of the reset option in FBM model is investigated. Some interesting themes such as closed-form formulas for the reset option with a single reset date and the phenomena of delta of the reset jumps existing in the reset option during the reset date are discussed. The closed-form formulae of pricing for two kinds of power options are derived in the end.展开更多
The purpose of this article is to study the rational evaluation of European options price when the underlying price process is described by a time-change Levy process. European option pricing formula is obtained under...The purpose of this article is to study the rational evaluation of European options price when the underlying price process is described by a time-change Levy process. European option pricing formula is obtained under the minimal entropy martingale measure （MEMM） and applied to several examples of particular time-change Levy processes. It can be seen that the framework in this paper encompasses the Black-Scholes model and almost all of the models proposed in the subordinated market.展开更多
The mean correcting martingale measure for the stochastic process defined as the exponential of an additive process is constructed. Necessary and sufficient conditions for the existence of mean correcting martingale a...The mean correcting martingale measure for the stochastic process defined as the exponential of an additive process is constructed. Necessary and sufficient conditions for the existence of mean correcting martingale are also obtained. The investigation of this paper will establish a unified way that is applicable both to the case of Ldvy processes and that of the sums of independent random variables. As an application, we present the necessary and sufficient conditions that the discounted stock price process is a martingale.展开更多
Option pricing problem is one of the central issue in the theory of modern finance.Uncertain currency model has been put forward under the foundation of uncertainty theory as a tool to portray the foreign exchange rat...Option pricing problem is one of the central issue in the theory of modern finance.Uncertain currency model has been put forward under the foundation of uncertainty theory as a tool to portray the foreign exchange rate in uncertain finance market.This paper uses uncertain differential equation involved by Liu process to dispose of the foreign exchange rate.Then an American barrier option of currency model in uncertain environment is investigated.Most important of all,the authors deduce the formulas to price four types of American barrier options for this currency model in uncertain environment by rigorous derivation.展开更多
A novel option pricing method based on Fourier-cosine series expansion was proposed by Fang and Oosterlee. Developing their idea, three new option pricing methods based on Fourier, Fourier-cosine and Fourier-sine seri...A novel option pricing method based on Fourier-cosine series expansion was proposed by Fang and Oosterlee. Developing their idea, three new option pricing methods based on Fourier, Fourier-cosine and Fourier-sine series expansions are presented in this paper, which are more efficient when the option prices are calculated with many strike prices. A series of numerical experiments under different exp-L^vy models are also given to compare these new methods with the Fang and Oosterlee＇s method and other methods.展开更多
In this paper,a rough Heston model with variable volatility of volatility(vol-of-vol)is derived by modifying the generalized nonlinear Hawkes process and extending the scaling techniques.Then the nonlinear fractional ...In this paper,a rough Heston model with variable volatility of volatility(vol-of-vol)is derived by modifying the generalized nonlinear Hawkes process and extending the scaling techniques.Then the nonlinear fractional Ric-cati equation for the characteristic function of the asset log-price is derived.The existence,uniqueness and regularity of the solution to the nonlinear fractional Riccati equation are proved and the equation is solved by the Adams methods.Finally the Fourier-cosine methods are combined with the Adams methods to price the options.展开更多
We derive methods for risk-neutral pricing of multi-asset options,when log-returns jointly follow a multivariate tempered stable distribution.These lead to processes that are more realistic than the better known Brown...We derive methods for risk-neutral pricing of multi-asset options,when log-returns jointly follow a multivariate tempered stable distribution.These lead to processes that are more realistic than the better known Brownian motion and stable processes.Further,we introduce the diagonal tempered stable model,which is parsimonious but allows for rich dependence between assets.Here,the number of parameters only grows linearly as the dimension increases,which makes it tractable in higher dimensions and avoids the so-called“curse of dimensionality.”As an illustration,we apply the model to price multi-asset options in two,three,and four dimensions.Detailed goodness-of-fit methods show that our model fits the data very well.展开更多
The problem of general exchange option pricing on jump-diffusion model is presented, we use the methods of the change of numeraire and martingale measure, and get the analytic solution of above option.
基金Supported by the National Natural Science Foundation of China(11201221)Supported by the Natural Science Foundation of Jiangsu Province(BK2012468)
文摘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.
基金Supported by the Key Grant Project of Chinese Ministry of Education(309018)National Natural Science Foundation of China(70973104 and 11171304)the Zhejiang Natural Science Foundation of China(Y6110023)
文摘The primary goal of this paper is to price European options in the Merton＇s frame- work with underlying assets following jump-diffusion using fuzzy set theory. Owing to the vague fluctuation of the real financial market, the average jump rate and jump sizes cannot be recorded or collected accurately. So the main idea of this paper is to model the rate as a triangular fuzzy number and jump sizes as fuzzy random variables and use the property of fuzzy set to deduce two different jump-diffusion models underlying principle of rational expectations equilibrium price. Unlike many conventional models, the European option price will now turn into a fuzzy number. One of the major advantages of this model is that it allows investors to choose a reasonable European option price under an acceptable belief degree. The empirical results will serve as useful feedback information for improvements on the proposed model.
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.
基金Supported by the National Natural Science Foundation of China(No.11571365,11171349)
文摘We use an actuarial approach to estimate the valuation of the reload option for a non-tradable risk asset under the jump-diffusion processes and Hull-White interest rate. We verify the validity of the actuarial approach to the European vanilla option for non-tradable assets. The formulas of the actuarial approach to the reload option are derived from the fair premium principle and the obtained results are arbitrage. Numerical experiments are conducted to analyze the effects of different parameters on the results of valuation as well as their differences from those obtained by the no-arbitrage approach. Finally, we give the valuations of the reload options under different parameters.
文摘In this paper, we present a stock model with Markov switching in the uncertainty markets, where the parameters of drift and volatility change according to the states of a Markov process. To price the option, we firstly establish a risk-neutral probability based on the uncertain measure given by Liu. Then a closed form of the European option pricing formula is obtained by applying the Laplace transforms and the inverse Laplace transforms.
基金Supported by National Natural Science Foundation of China(Grant No.11171101)National Social Science Fund of China(Grant No.11BTJ011)Research Projects of Humanities and Social Sciences Foundation of Ministry of Education of China(Grant No.12YJAZH173)1)
文摘For a non-Gaussian Levy model, it is shown that if the model exists a trivial arbitrage-free interval, option pricing by mean correcting method is always arbitrage-free, and if the arbitrage-free interval is non-trivial, this pricing method may lead to arbitrage in some cases. In the latter case, some necessary and sufficient conditions under which option price is arbitrage-free are obtained.
基金supported by the Natural Science Foundation of China under Grant Nos.11301369,11401419the Natural Science Foundation of Jiangsu Province under Grant Nos.BK20130260,BK20140279
文摘This paper studies the first passage time problem for a reflected two-sided jump-diffusion risk model with the jumps having a hyper-Erlang distribution.The authors give the explicit closed-form expression for the joint Laplace transform of the first passage time and the overshoot for the reflected process.Finally,the formula is applied to the ruin problem under the barrier dividend strategy and the pricing of the Russian option.
文摘In this paper, under the assumption that the exchange rate follows the extended Vasicek model, the pricing of the reset option in FBM model is investigated. Some interesting themes such as closed-form formulas for the reset option with a single reset date and the phenomena of delta of the reset jumps existing in the reset option during the reset date are discussed. The closed-form formulae of pricing for two kinds of power options are derived in the end.
文摘The purpose of this article is to study the rational evaluation of European options price when the underlying price process is described by a time-change Levy process. European option pricing formula is obtained under the minimal entropy martingale measure （MEMM） and applied to several examples of particular time-change Levy processes. It can be seen that the framework in this paper encompasses the Black-Scholes model and almost all of the models proposed in the subordinated market.
基金Supported by the Foundation for Innovative Research Groups of the National Natural Science Foundation of China(71221061)National Natural Science Foundation of China(11171101)+3 种基金National Social Science Fund of China(11BTJ01115BJY122)Social Sciences Foundation of Ministry of Education of China(12YJAZH173)Aid program for Science and Technology Innovative Research Team in Higher Educational Institutions of Hunan Province
文摘The mean correcting martingale measure for the stochastic process defined as the exponential of an additive process is constructed. Necessary and sufficient conditions for the existence of mean correcting martingale are also obtained. The investigation of this paper will establish a unified way that is applicable both to the case of Ldvy processes and that of the sums of independent random variables. As an application, we present the necessary and sufficient conditions that the discounted stock price process is a martingale.
基金supported by the Natural Science Foundation of Hebei Province under Grant No.F2020202056the Key Project of Hebei Education Department under Grant No.ZD2020125the Social Science Foundation of Hebei Province under Grant No.HB18GL036。
文摘Option pricing problem is one of the central issue in the theory of modern finance.Uncertain currency model has been put forward under the foundation of uncertainty theory as a tool to portray the foreign exchange rate in uncertain finance market.This paper uses uncertain differential equation involved by Liu process to dispose of the foreign exchange rate.Then an American barrier option of currency model in uncertain environment is investigated.Most important of all,the authors deduce the formulas to price four types of American barrier options for this currency model in uncertain environment by rigorous derivation.
基金Supported by the Research Grant of University of Macao (Grants Nos.UL020/08-Y3/MAT/JXQ01/FSTRG058/09-10S/DD/FST)
文摘A novel option pricing method based on Fourier-cosine series expansion was proposed by Fang and Oosterlee. Developing their idea, three new option pricing methods based on Fourier, Fourier-cosine and Fourier-sine series expansions are presented in this paper, which are more efficient when the option prices are calculated with many strike prices. A series of numerical experiments under different exp-L^vy models are also given to compare these new methods with the Fang and Oosterlee＇s method and other methods.
基金supported by National Natural Science Foundation of China (No. 12171 122)Shenzhen Science and Technology Program (No. RCJC20210609103755110)+1 种基金Fundamental Research Project of Shenzhen (No. JCYJ20190806143201649)supported by National Natural Science Foundation of China (Grant No. 12071373).
文摘In this paper,a rough Heston model with variable volatility of volatility(vol-of-vol)is derived by modifying the generalized nonlinear Hawkes process and extending the scaling techniques.Then the nonlinear fractional Ric-cati equation for the characteristic function of the asset log-price is derived.The existence,uniqueness and regularity of the solution to the nonlinear fractional Riccati equation are proved and the equation is solved by the Adams methods.Finally the Fourier-cosine methods are combined with the Adams methods to price the options.
文摘We derive methods for risk-neutral pricing of multi-asset options,when log-returns jointly follow a multivariate tempered stable distribution.These lead to processes that are more realistic than the better known Brownian motion and stable processes.Further,we introduce the diagonal tempered stable model,which is parsimonious but allows for rich dependence between assets.Here,the number of parameters only grows linearly as the dimension increases,which makes it tractable in higher dimensions and avoids the so-called“curse of dimensionality.”As an illustration,we apply the model to price multi-asset options in two,three,and four dimensions.Detailed goodness-of-fit methods show that our model fits the data very well.
文摘The problem of general exchange option pricing on jump-diffusion model is presented, we use the methods of the change of numeraire and martingale measure, and get the analytic solution of above option.
