This paper presents integral representations for the price of vanilla put options, namely, European and American put options on a basket of two-dividend paying stocks using integral method based on the double Mellin t...This paper presents integral representations for the price of vanilla put options, namely, European and American put options on a basket of two-dividend paying stocks using integral method based on the double Mellin transform. We show that by the decomposition of the integral equation for the price of American basket put option, the integral equation for the price of European basket put option can be obtained directly.展开更多
Background:We investigated the determination of the pledged loan-to-value ratio in an optionpricing environment and mainly articulated the theoretical framework and analytical method.Methods:The basic idea is that the...Background:We investigated the determination of the pledged loan-to-value ratio in an optionpricing environment and mainly articulated the theoretical framework and analytical method.Methods:The basic idea is that the present value of the pledged loan payoff is equal to a put option’s value.While the interest rate is fixed and the loan is without coupon,we analyzed the pledged loan-to-value ratioin the option pricing perspective and got it that the pledged loan-to-value ratio is decided by term,excessreturn,and the value volatility of the pledge.Next,we extended the same work to coupon loan and portfoliopledge circumstances.For zero coupon and fixed interest rate circumstances,we performed a numericalanalysis.Results:Our results indicate the following:the pledged loan-to-value ratio is a convex decreasing function ofthe term;and the pledged loan-to-value ratio is a concave decreasing function of the value volatility of the pledge;and the pledged loan-to-value ratio is a concave increasing function of the risk premium.For floating interest rate circumstances,we should specify the function form between the loan interest and the risk-free rate.Conclusions:The scientific measurement of the pledged loan-to-value ratio means that simple rules of thumb or the VaR method may lead to mispricing,which could create the possibility of arbitrage.In this way,a new direction for trading derivative products of pledges will be provided.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
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
文摘This paper presents integral representations for the price of vanilla put options, namely, European and American put options on a basket of two-dividend paying stocks using integral method based on the double Mellin transform. We show that by the decomposition of the integral equation for the price of American basket put option, the integral equation for the price of European basket put option can be obtained directly.
基金support of National Science Fund of China(No.71003005 and No.71373002).
文摘Background:We investigated the determination of the pledged loan-to-value ratio in an optionpricing environment and mainly articulated the theoretical framework and analytical method.Methods:The basic idea is that the present value of the pledged loan payoff is equal to a put option’s value.While the interest rate is fixed and the loan is without coupon,we analyzed the pledged loan-to-value ratioin the option pricing perspective and got it that the pledged loan-to-value ratio is decided by term,excessreturn,and the value volatility of the pledge.Next,we extended the same work to coupon loan and portfoliopledge circumstances.For zero coupon and fixed interest rate circumstances,we performed a numericalanalysis.Results:Our results indicate the following:the pledged loan-to-value ratio is a convex decreasing function ofthe term;and the pledged loan-to-value ratio is a concave decreasing function of the value volatility of the pledge;and the pledged loan-to-value ratio is a concave increasing function of the risk premium.For floating interest rate circumstances,we should specify the function form between the loan interest and the risk-free rate.Conclusions:The scientific measurement of the pledged loan-to-value ratio means that simple rules of thumb or the VaR method may lead to mispricing,which could create the possibility of arbitrage.In this way,a new direction for trading derivative products of pledges will be provided.
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.
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.
