Lookback options are path-dependent options. In general, the binomial tree methods, as the most popular approaches to pricing options, involve a path dependent variable as well as the underlying asset price for lookba...Lookback options are path-dependent options. In general, the binomial tree methods, as the most popular approaches to pricing options, involve a path dependent variable as well as the underlying asset price for lookback options. However, for floating strike lookback options, a single-state variable binomial tree method can be constructed. This paper is devoted to the convergence analysis of the single-state binomial tree methods both for discretely and continuously monitored American floating strike lookback options. We also investigate some properties of such options, including effects of expiration date, interest rate and dividend yield on options prices, properties of optimal exercise boundaries and so展开更多
Solution of the system stochastic differential equations in multi dimensional case using Monte Carlo method had many useful features in compare with the other computational methods. One of them is the solution of boun...Solution of the system stochastic differential equations in multi dimensional case using Monte Carlo method had many useful features in compare with the other computational methods. One of them is the solution of boundary value problems to be found at just one point, if required (with associated saving in computation), whereas deterministic methods necessarily find the solution at large number of points simultaneously. This property can be particularly useful in problems such option pricing, where the value of an option is required only at the time of striking, and for the state of the market at that time. In this work we consider a European multi-asset options which mathematically described by the system of stochastic differential equations. We will apply Monte Carlo method for the solution of that system which is the price of Multi-asset rainbow options.展开更多
In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were disc...In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were discussed as examples. The problem is a parabolic one on a finite domain whose equation degenerates into ordinary differential equations on the boundaries. A fully discrete scheme was established by using the Legendre spectral method in space and the Crank-Nicolson finite difference scheme in time. The stability and convergence of the scheme were analyzed. Numerical results show that the method can keep the spectral accuracy in space for such degenerate problems.展开更多
As a kind of weak-path dependent options, barrier options are an important kind of exotic options. Because the pricing formula for pricing barrier options with discrete observations cannot avoid computing a high dimen...As a kind of weak-path dependent options, barrier options are an important kind of exotic options. Because the pricing formula for pricing barrier options with discrete observations cannot avoid computing a high dimensional integral, numerical calculation is time-consuming. In the current studies, some scholars just obtained theoretical derivation, or gave some simulation calculations. Others impose underlying assets on some strong assumptions, for example, a lot of calculations are based on the Black-Scholes model. This thesis considers Merton jump diffusion model as the basic model to derive the pricing formula of discrete double barrier option;numerical calculation method is used to approximate the continuous convolution by calculating discrete convolution. Then we compare the results of theoretical calculation with simulation results by Monte Carlo method, to verify their efficiency and accuracy. By comparing the results of degeneration constant parameter model with the results of previous models we verified the calculation method is correct indirectly. Compared with the Monte Carlo simulation method, the numerical results are stable. Even if we assume the simulation results are accurate, the time consumed by the numerical method to achieve the same accuracy is much less than the Monte Carlo simulation method.展开更多
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
Limitations exist in applying discounted cash flow and analogy sales methods to evaluate mining titles. In order to find a more appropriate way of evaluating mining titles, the Black-Scholes model is discussed in this...Limitations exist in applying discounted cash flow and analogy sales methods to evaluate mining titles. In order to find a more appropriate way of evaluating mining titles, the Black-Scholes model is discussed in this paper. The authors pay particular attention to the determination of the time to maturity of the option on the basis of characteristics of the mining industry, pointing out that a reasonable time to maturity of the option should be the remaining time after deducting the essential time, needed by exploitation of the mineral resources within the mining property, from the life of the mining title. Several conclusions, related to the exercise of mineral resource management, are drawn from a case study analysis; extending the life of a mining title within a certain range could increase the revenue to the seller of the mining title. Application of the Black-Scholes model to evaluate mining titles would encourage an expansion of the scale of production.展开更多
An efficient and accurate numerical method, which is called the CONV method, was proposed by Lord et al in [1] to price Bermudan options. In this paper, this method is applied to price Bermudan barrier options in whic...An efficient and accurate numerical method, which is called the CONV method, was proposed by Lord et al in [1] to price Bermudan options. In this paper, this method is applied to price Bermudan barrier options in which the monitored dates may be many times more than the exercise dates. The corresponding algorithm is presented to practical option pricing. Numerical experiments show that this algorithm works very well for different exponential Lévy asset models.展开更多
In this article, we derive a boundary element formulation for the pricing of barrier option. The price of a barrier option is modeled as the solution of Black-Scholes’ equation. Then the problem is transformed to a b...In this article, we derive a boundary element formulation for the pricing of barrier option. The price of a barrier option is modeled as the solution of Black-Scholes’ equation. Then the problem is transformed to a boundary value problem of heat equation with a moving boundary. The boundary integral representation and integral equation are derived. A boundary element method is designed to solve the integral equation. Special quadrature rules for the singular integral are used. A numerical example is also demonstrated. This boundary element formulation is correct.展开更多
A compound option is simply an option on an option. In this short paper, by using a martingale technique, we obtain an analytical formula for pricing compound European call options. Numerical results are given to expl...A compound option is simply an option on an option. In this short paper, by using a martingale technique, we obtain an analytical formula for pricing compound European call options. Numerical results are given to explain some economic phenomenon.展开更多
基金Supported by National Science Foundation of China
文摘Lookback options are path-dependent options. In general, the binomial tree methods, as the most popular approaches to pricing options, involve a path dependent variable as well as the underlying asset price for lookback options. However, for floating strike lookback options, a single-state variable binomial tree method can be constructed. This paper is devoted to the convergence analysis of the single-state binomial tree methods both for discretely and continuously monitored American floating strike lookback options. We also investigate some properties of such options, including effects of expiration date, interest rate and dividend yield on options prices, properties of optimal exercise boundaries and so
文摘Solution of the system stochastic differential equations in multi dimensional case using Monte Carlo method had many useful features in compare with the other computational methods. One of them is the solution of boundary value problems to be found at just one point, if required (with associated saving in computation), whereas deterministic methods necessarily find the solution at large number of points simultaneously. This property can be particularly useful in problems such option pricing, where the value of an option is required only at the time of striking, and for the state of the market at that time. In this work we consider a European multi-asset options which mathematically described by the system of stochastic differential equations. We will apply Monte Carlo method for the solution of that system which is the price of Multi-asset rainbow options.
文摘In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were discussed as examples. The problem is a parabolic one on a finite domain whose equation degenerates into ordinary differential equations on the boundaries. A fully discrete scheme was established by using the Legendre spectral method in space and the Crank-Nicolson finite difference scheme in time. The stability and convergence of the scheme were analyzed. Numerical results show that the method can keep the spectral accuracy in space for such degenerate problems.
文摘As a kind of weak-path dependent options, barrier options are an important kind of exotic options. Because the pricing formula for pricing barrier options with discrete observations cannot avoid computing a high dimensional integral, numerical calculation is time-consuming. In the current studies, some scholars just obtained theoretical derivation, or gave some simulation calculations. Others impose underlying assets on some strong assumptions, for example, a lot of calculations are based on the Black-Scholes model. This thesis considers Merton jump diffusion model as the basic model to derive the pricing formula of discrete double barrier option;numerical calculation method is used to approximate the continuous convolution by calculating discrete convolution. Then we compare the results of theoretical calculation with simulation results by Monte Carlo method, to verify their efficiency and accuracy. By comparing the results of degeneration constant parameter model with the results of previous models we verified the calculation method is correct indirectly. Compared with the Monte Carlo simulation method, the numerical results are stable. Even if we assume the simulation results are accurate, the time consumed by the numerical method to achieve the same accuracy is much less than the Monte Carlo simulation method.
基金National Natural Science Foundations of China(Nos.11471175,11171221)
文摘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.
基金Project 50074031 supported by National Natural Science Foundation of China
文摘Limitations exist in applying discounted cash flow and analogy sales methods to evaluate mining titles. In order to find a more appropriate way of evaluating mining titles, the Black-Scholes model is discussed in this paper. The authors pay particular attention to the determination of the time to maturity of the option on the basis of characteristics of the mining industry, pointing out that a reasonable time to maturity of the option should be the remaining time after deducting the essential time, needed by exploitation of the mineral resources within the mining property, from the life of the mining title. Several conclusions, related to the exercise of mineral resource management, are drawn from a case study analysis; extending the life of a mining title within a certain range could increase the revenue to the seller of the mining title. Application of the Black-Scholes model to evaluate mining titles would encourage an expansion of the scale of production.
文摘An efficient and accurate numerical method, which is called the CONV method, was proposed by Lord et al in [1] to price Bermudan options. In this paper, this method is applied to price Bermudan barrier options in which the monitored dates may be many times more than the exercise dates. The corresponding algorithm is presented to practical option pricing. Numerical experiments show that this algorithm works very well for different exponential Lévy asset models.
文摘In this article, we derive a boundary element formulation for the pricing of barrier option. The price of a barrier option is modeled as the solution of Black-Scholes’ equation. Then the problem is transformed to a boundary value problem of heat equation with a moving boundary. The boundary integral representation and integral equation are derived. A boundary element method is designed to solve the integral equation. Special quadrature rules for the singular integral are used. A numerical example is also demonstrated. This boundary element formulation is correct.
基金The research is supported by the research grant RG081/04-05S/JXQ/FST from University of Macauthe grant 050/2005/A from FDCT
文摘A compound option is simply an option on an option. In this short paper, by using a martingale technique, we obtain an analytical formula for pricing compound European call options. Numerical results are given to explain some economic phenomenon.
