This paper considered the problem of hedging a European call (put) option for a diffusion model where the asset price is influenced by n uncertain factors. The market is thus incomplete implying that perfect hedging i...This paper considered the problem of hedging a European call (put) option for a diffusion model where the asset price is influenced by n uncertain factors. The market is thus incomplete implying that perfect hedging is not possible. To derive a hedging strategy, it follows the approach based on the idea of hedging under a mean-variance criterion suggested by Schweizer. A very simple solution of this hedging problem by using the numeraire method was presented and some examples with explicit solutions were given.展开更多
Employee stock options （ESOs） have become an integral component of compensation in the US. In view of their significant cost to firms, the Financial Accounting Standards Board （FASB） has mandated expensing ESOs si...Employee stock options （ESOs） have become an integral component of compensation in the US. In view of their significant cost to firms, the Financial Accounting Standards Board （FASB） has mandated expensing ESOs since 2004. The main difficulty of ESO valuation lies in the uncertain timing of exercises, and a number of contractual restrictions of ESOs further complicate the problem. We present a valuation framework that captures the main characteristics of ESOs. Specifically, we incorporate the holder＇s risk aversion, and hedging strategies that include both dynamic trading of a correlated asset and static positions in market-traded options. Their combined effect on ESO exercises and costs are evaluated along with common features like vesting periods, job termination risk and multiple exercises. This leads to the study of a joint stochastic control and optimal stopping problem. We find that ESO values are much less than the corresponding Black-Scholes prices due to early exercises, which arise from risk aversion and job termination risk; whereas static hedges induce holders to delay exercises and increase ESO costs.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
This paper studies the impact of the reference point on a hedger＇s decision based upon prospect theory and experimental evidence on how prior outcomes affect risky choice. The authors show that in the futures market,...This paper studies the impact of the reference point on a hedger＇s decision based upon prospect theory and experimental evidence on how prior outcomes affect risky choice. The authors show that in the futures market, a hedger who does not adjust his reference point timely would increase his positions continually as his accumulated losses increase, and finally become a speculator. Numerical simulation results under the normal distribution also lend support to the results. The model can help explain why the hedging behavior of firms turns into speculative activities and can offer some new insights into hedging behavior.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
In this paper, a model for multi-period bank hedging with interest rate futures is set up. Formulas for the optimal dynamic multi-period bank and static bank hedge ratio are derived. The described model offers the pot...In this paper, a model for multi-period bank hedging with interest rate futures is set up. Formulas for the optimal dynamic multi-period bank and static bank hedge ratio are derived. The described model offers the potential benefits of： （1） although these formulas are developed for the case of direct sheet balance multi-period hedging, the framework used is sufficiently flexible so that these formulas can be applied to bank loan or deposit multi-period hedging situations respectively. （2） Periodic modification and updating of the interest rate futures position, as suggested by interest rates, throughout the bank hedging horizons. （3） This paper examines a situation in which the return of loan, the interest rate of deposit and the equity capital of bank, and interest rate futures prices are cointergrated, Multi-period bank hedging formulas are derived under three-dimensional stochastic volatility model. However, empirical research is required for validating this model.展开更多
基金National Natural Science Foundation ofChina( 10 1710 66) and Shanghai Key Project( 0 2 DJ14 0 63 )
文摘This paper considered the problem of hedging a European call (put) option for a diffusion model where the asset price is influenced by n uncertain factors. The market is thus incomplete implying that perfect hedging is not possible. To derive a hedging strategy, it follows the approach based on the idea of hedging under a mean-variance criterion suggested by Schweizer. A very simple solution of this hedging problem by using the numeraire method was presented and some examples with explicit solutions were given.
文摘Employee stock options （ESOs） have become an integral component of compensation in the US. In view of their significant cost to firms, the Financial Accounting Standards Board （FASB） has mandated expensing ESOs since 2004. The main difficulty of ESO valuation lies in the uncertain timing of exercises, and a number of contractual restrictions of ESOs further complicate the problem. We present a valuation framework that captures the main characteristics of ESOs. Specifically, we incorporate the holder＇s risk aversion, and hedging strategies that include both dynamic trading of a correlated asset and static positions in market-traded options. Their combined effect on ESO exercises and costs are evaluated along with common features like vesting periods, job termination risk and multiple exercises. This leads to the study of a joint stochastic control and optimal stopping problem. We find that ESO values are much less than the corresponding Black-Scholes prices due to early exercises, which arise from risk aversion and job termination risk; whereas static hedges induce holders to delay exercises and increase ESO costs.
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This research is supported by the National Natural Science Foundation under Grant No.70221001
文摘This paper studies the impact of the reference point on a hedger＇s decision based upon prospect theory and experimental evidence on how prior outcomes affect risky choice. The authors show that in the futures market, a hedger who does not adjust his reference point timely would increase his positions continually as his accumulated losses increase, and finally become a speculator. Numerical simulation results under the normal distribution also lend support to the results. The model can help explain why the hedging behavior of firms turns into speculative activities and can offer some new insights into hedging behavior.
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.
基金This project is supported by National Natural Science Foundation of China （70873014）
文摘In this paper, a model for multi-period bank hedging with interest rate futures is set up. Formulas for the optimal dynamic multi-period bank and static bank hedge ratio are derived. The described model offers the potential benefits of： （1） although these formulas are developed for the case of direct sheet balance multi-period hedging, the framework used is sufficiently flexible so that these formulas can be applied to bank loan or deposit multi-period hedging situations respectively. （2） Periodic modification and updating of the interest rate futures position, as suggested by interest rates, throughout the bank hedging horizons. （3） This paper examines a situation in which the return of loan, the interest rate of deposit and the equity capital of bank, and interest rate futures prices are cointergrated, Multi-period bank hedging formulas are derived under three-dimensional stochastic volatility model. However, empirical research is required for validating this model.
