Asian options are the popular second generation derivative products and embedded in many structured notes to enhance upside performance.The embedded options,as a result,usually have a long duration.The movement of int...Asian options are the popular second generation derivative products and embedded in many structured notes to enhance upside performance.The embedded options,as a result,usually have a long duration.The movement of interest rates becomes more important in pricing such long-dated options.In this paper,the pricing of Asian options under stochastic interest rates is studied.Assuming Hull and White model for the interest rates,a closed-form formula for geometric-average options is derived.As a by-product,pricing formula is also given for plan-vanilla options under stochastic interest rates.展开更多
Abstract Option pricing problem plays an extremely important role in quantitative finance. In com- plete market, Black-Scholes-Merton theory has been central to the development of financial engineering as both discipl...Abstract Option pricing problem plays an extremely important role in quantitative finance. In com- plete market, Black-Scholes-Merton theory has been central to the development of financial engineering as both discipline and profession. However, in incomplete market, there are not any replicating port- folios for those options, and thus, the market traders cannot apply the law of one price for obtaining a unique solution. Fortunately, the authors can get a fair price via local-equilibrium principle. In this paper, the authors apply the stochastic control theory to price the exotic option-barrier options, and analyze the relationship between the price and the current positions. The authors get the explicit expression for the market price of the risk. The position effect plays a significant role in option pricing, because it can tell the trader how many and which direction to trade with the market in order to reach the local equilibrium with the market.展开更多
Pricing variance swaps under stochastic volatility has been an important subject pursued recently. Various approaches have been proposed, mainly due to the substantially increased trading activities of volatility-rela...Pricing variance swaps under stochastic volatility has been an important subject pursued recently. Various approaches have been proposed, mainly due to the substantially increased trading activities of volatility-related derivatives in the past few years. In this note, the authors develop analytical method for pricing variance swaps under stochastic volatility with an Ornstein-Uhlenbeck(OU) process. By using Fourier transform algorithm, a closed-form solution for pricing variance swaps with stochastic volatility is obtained, and to give a comparison of fair strike value based on the discrete model, continuous model, and the Monte Carlo simulations.展开更多
A new point of view of robust statistics based on a geometrical approach is tackled in this paper. Estimation procedures are carried out from a new robust cost function based on a chaining of elementary convex norms. ...A new point of view of robust statistics based on a geometrical approach is tackled in this paper. Estimation procedures are carried out from a new robust cost function based on a chaining of elementary convex norms. This chain is randomly articulated in order to treat more efficiently natural outliers in data-set. Estimated parameters are considered as random fields and each of them, named articulated estimator random field （AERF） is a manifold or stratum of a stratified space with Riemannian geometry properties, From a high level excursion set, a probability distribution model Mata is presented and a system model validation geometric criterion （SYMOVAGEC） for system model structures Msys based on Rieeian scalar curvatures is proposed. Numerical results are drawn in a context of system identification.展开更多
This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal ...This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and terminal wealth, and the uncertain prospects are ranked according to a multiple-priors model of Chen and Epstein(2002). The price is determined by two optimal stochastic control problems(mixed with optimal stopping time in the case of American option) of forward-backward stochastic differential equations.By means of backward stochastic differential equation and partial differential equation methods, we show that both bid and ask prices are closely related to the Black-Scholes risk-neutral price with modified dividend rates.The two prices will actually coincide with each other if there is no trading constraint or the model uncertainty disappears. Finally, two applications to European option and American option are discussed.展开更多
The pricing and hedging problem of foreign currency option with higher borrowing rate is discussed.The method to obtain the price and hedging portfolio of currency option is based on backward stochastic differential e...The pricing and hedging problem of foreign currency option with higher borrowing rate is discussed.The method to obtain the price and hedging portfolio of currency option is based on backward stochastic differential equations(BSDE for short) theory and Malliavin calculus technique.The sensitivity of the model parameters is also considered and some numerical simulations are given to illustrate our conclusion.展开更多
文摘Asian options are the popular second generation derivative products and embedded in many structured notes to enhance upside performance.The embedded options,as a result,usually have a long duration.The movement of interest rates becomes more important in pricing such long-dated options.In this paper,the pricing of Asian options under stochastic interest rates is studied.Assuming Hull and White model for the interest rates,a closed-form formula for geometric-average options is derived.As a by-product,pricing formula is also given for plan-vanilla options under stochastic interest rates.
基金supported by the National Natural Science Foundation of China under Grant No.9732007CB814901
文摘Abstract Option pricing problem plays an extremely important role in quantitative finance. In com- plete market, Black-Scholes-Merton theory has been central to the development of financial engineering as both discipline and profession. However, in incomplete market, there are not any replicating port- folios for those options, and thus, the market traders cannot apply the law of one price for obtaining a unique solution. Fortunately, the authors can get a fair price via local-equilibrium principle. In this paper, the authors apply the stochastic control theory to price the exotic option-barrier options, and analyze the relationship between the price and the current positions. The authors get the explicit expression for the market price of the risk. The position effect plays a significant role in option pricing, because it can tell the trader how many and which direction to trade with the market in order to reach the local equilibrium with the market.
基金supported by the National Social Science Fund of China under Grant No.14ATJ005Anhui Provincial Natural Science Foundation under Grant Nos.1308085MF93 and 1408085MKL84the National Natural Science Foundations of China under Grant No.11401556
文摘Pricing variance swaps under stochastic volatility has been an important subject pursued recently. Various approaches have been proposed, mainly due to the substantially increased trading activities of volatility-related derivatives in the past few years. In this note, the authors develop analytical method for pricing variance swaps under stochastic volatility with an Ornstein-Uhlenbeck(OU) process. By using Fourier transform algorithm, a closed-form solution for pricing variance swaps with stochastic volatility is obtained, and to give a comparison of fair strike value based on the discrete model, continuous model, and the Monte Carlo simulations.
文摘A new point of view of robust statistics based on a geometrical approach is tackled in this paper. Estimation procedures are carried out from a new robust cost function based on a chaining of elementary convex norms. This chain is randomly articulated in order to treat more efficiently natural outliers in data-set. Estimated parameters are considered as random fields and each of them, named articulated estimator random field （AERF） is a manifold or stratum of a stratified space with Riemannian geometry properties, From a high level excursion set, a probability distribution model Mata is presented and a system model validation geometric criterion （SYMOVAGEC） for system model structures Msys based on Rieeian scalar curvatures is proposed. Numerical results are drawn in a context of system identification.
基金supported by National Natural Science Foundation of China(Grant Nos.11271143,11371155 and 11326199)University Special Research Fund for Ph D Program(Grant No.20124407110001)+1 种基金National Natural Science Foundation of Zhejiang Province(Grant No.Y6110775)the Oxford-Man Institute of Quantitative Finance
文摘This paper considers utility indifference valuation of derivatives under model uncertainty and trading constraints, where the utility is formulated as an additive stochastic differential utility of both intertemporal consumption and terminal wealth, and the uncertain prospects are ranked according to a multiple-priors model of Chen and Epstein(2002). The price is determined by two optimal stochastic control problems(mixed with optimal stopping time in the case of American option) of forward-backward stochastic differential equations.By means of backward stochastic differential equation and partial differential equation methods, we show that both bid and ask prices are closely related to the Black-Scholes risk-neutral price with modified dividend rates.The two prices will actually coincide with each other if there is no trading constraint or the model uncertainty disappears. Finally, two applications to European option and American option are discussed.
基金supported by the National Nature Science Foundation of China(11221061,61174092,11126214,11126208)the National Science Fund for Distinguished Young Scholars of China(11125102)the Fundamental Research Funds for the Central Universities(2010QS05)
文摘The pricing and hedging problem of foreign currency option with higher borrowing rate is discussed.The method to obtain the price and hedging portfolio of currency option is based on backward stochastic differential equations(BSDE for short) theory and Malliavin calculus technique.The sensitivity of the model parameters is also considered and some numerical simulations are given to illustrate our conclusion.
