Quanto options allow the buyer to exchange the foreign currency payoff into the domestic currency at a fixed exchange rate. We investigate quanto options with multiple underlying assets valued in different foreign cur...Quanto options allow the buyer to exchange the foreign currency payoff into the domestic currency at a fixed exchange rate. We investigate quanto options with multiple underlying assets valued in different foreign currencies each with a different strike price in the payoff function. We carry out a comparative performance analysis of different stochastic volatility (SV), stochastic correlation (SC), and stochastic exchange rate (SER) models to determine the best combination of these models for Monte Carlo (MC) simulation pricing. In addition, we test the performance of all model variants with constant correlation as a benchmark. We find that a combination of GARCH-Jump SV, Weibull SC, and Ornstein Uhlenbeck (OU) SER performs best. In addition, we analyze different discretization schemes and their results. In our simulations, the Milstein scheme yields the best balance between execution times and lower standard deviations of price estimates. Furthermore, we find that incorporating mean reversion into stochastic correlation and stochastic FX rate modeling is beneficial for MC simulation pricing. We improve the accuracy of our simulations by implementing antithetic variates variance reduction. Finally, we derive the correlation risk parameters Cora and Gora in our framework so that correlation hedging of quanto options can be performed.展开更多
This work provides a new method for pricing options under the generalized stochastic volatility models with Jacobi stochastic correlation.Our method is based on the observation that the generalized models belong to th...This work provides a new method for pricing options under the generalized stochastic volatility models with Jacobi stochastic correlation.Our method is based on the observation that the generalized models belong to the class of polynomial diffusions and therefore the option prices can be efficiently computed via orthogonal polynomial expansions.We take the Heston and Schöbel-Zhu models with stochastic correlation as two specific examples and are able to derive the analytical formulas for the option prices.We also illustrate the accuracy of the proposed method through a number of numerical experiments.展开更多
It is important to consider the changing states in hedging.The Markov regime-switching dynamic correlation multivariate stochastic volatility( MRS-DC-MSV) model was proposed to solve this issue. DC-MSV model and MRS-D...It is important to consider the changing states in hedging.The Markov regime-switching dynamic correlation multivariate stochastic volatility( MRS-DC-MSV) model was proposed to solve this issue. DC-MSV model and MRS-DC-MSV model were used to calculate the time-varying hedging ratios and compare the hedging performance. The Markov chain Monte Carlo( MCMC) method was used to estimate the parameters. The results showed that,there were obviously two economic states in Chinese financial market. Two models all did well in hedging,but the performance of MRS-DCMSV model was better. It could reduce risk by nearly 90%. Thus,in the hedging period,changing states is a factor that cannot be neglected.展开更多
This paper studies the multi-period mean-variance(MV)asset-liability portfolio management problem(MVAL),in which the portfolio is constructed by risky assets and liability.It is worth mentioning that the impact of gen...This paper studies the multi-period mean-variance(MV)asset-liability portfolio management problem(MVAL),in which the portfolio is constructed by risky assets and liability.It is worth mentioning that the impact of general correlation is considered,i.e.,the random returns of risky assets and the liability are not only statistically correlated to each other but also correlated to themselves in different time periods.Such a model with a general correlation structure extends the classical multiperiod MVAL models with assumption of independent returns.The authors derive the explicit portfolio policy and the MV efficient frontier for this problem.Moreover,a numerical example is presented to illustrate the efficiency of the proposed solution scheme.展开更多
In this paper the Kiefer-Wolfowitz (KW) procedure for searching the extremum of the regression function as well as the Robbins-Monro (RM) procedure for solving the regression equation are modified in order that they c...In this paper the Kiefer-Wolfowitz (KW) procedure for searching the extremum of the regression function as well as the Robbins-Monro (RM) procedure for solving the regression equation are modified in order that they can be applied to the case when the measurement errors form an ARMA process. Simple conditions are given to guarantee their convergence to the extremum and the root of regression function respectively by using a new approach combining both the probabilistic method and the ordinary differential equation (ODE) method. The results given here are better than the well-known ones even if the measurement error is the martingale difference sequence.展开更多
文摘Quanto options allow the buyer to exchange the foreign currency payoff into the domestic currency at a fixed exchange rate. We investigate quanto options with multiple underlying assets valued in different foreign currencies each with a different strike price in the payoff function. We carry out a comparative performance analysis of different stochastic volatility (SV), stochastic correlation (SC), and stochastic exchange rate (SER) models to determine the best combination of these models for Monte Carlo (MC) simulation pricing. In addition, we test the performance of all model variants with constant correlation as a benchmark. We find that a combination of GARCH-Jump SV, Weibull SC, and Ornstein Uhlenbeck (OU) SER performs best. In addition, we analyze different discretization schemes and their results. In our simulations, the Milstein scheme yields the best balance between execution times and lower standard deviations of price estimates. Furthermore, we find that incorporating mean reversion into stochastic correlation and stochastic FX rate modeling is beneficial for MC simulation pricing. We improve the accuracy of our simulations by implementing antithetic variates variance reduction. Finally, we derive the correlation risk parameters Cora and Gora in our framework so that correlation hedging of quanto options can be performed.
文摘This work provides a new method for pricing options under the generalized stochastic volatility models with Jacobi stochastic correlation.Our method is based on the observation that the generalized models belong to the class of polynomial diffusions and therefore the option prices can be efficiently computed via orthogonal polynomial expansions.We take the Heston and Schöbel-Zhu models with stochastic correlation as two specific examples and are able to derive the analytical formulas for the option prices.We also illustrate the accuracy of the proposed method through a number of numerical experiments.
基金National Natural Science Foundation of China(No.71401144)
文摘It is important to consider the changing states in hedging.The Markov regime-switching dynamic correlation multivariate stochastic volatility( MRS-DC-MSV) model was proposed to solve this issue. DC-MSV model and MRS-DC-MSV model were used to calculate the time-varying hedging ratios and compare the hedging performance. The Markov chain Monte Carlo( MCMC) method was used to estimate the parameters. The results showed that,there were obviously two economic states in Chinese financial market. Two models all did well in hedging,but the performance of MRS-DCMSV model was better. It could reduce risk by nearly 90%. Thus,in the hedging period,changing states is a factor that cannot be neglected.
基金partially supported by the National Natural Science Foundation of China under Grant Nos.72201067,12201129,and 71973028the Natural Science Foundation of Guangdong Province under Grant No.2022A1515010839+1 种基金the Project of Science and Technology of Guangzhou under Grant No.202102020273the Opening Project of Guangdong Province Key Laboratory of Computational Science at Sun Yat-sen University under Grant No.2021004。
文摘This paper studies the multi-period mean-variance(MV)asset-liability portfolio management problem(MVAL),in which the portfolio is constructed by risky assets and liability.It is worth mentioning that the impact of general correlation is considered,i.e.,the random returns of risky assets and the liability are not only statistically correlated to each other but also correlated to themselves in different time periods.Such a model with a general correlation structure extends the classical multiperiod MVAL models with assumption of independent returns.The authors derive the explicit portfolio policy and the MV efficient frontier for this problem.Moreover,a numerical example is presented to illustrate the efficiency of the proposed solution scheme.
文摘In this paper the Kiefer-Wolfowitz (KW) procedure for searching the extremum of the regression function as well as the Robbins-Monro (RM) procedure for solving the regression equation are modified in order that they can be applied to the case when the measurement errors form an ARMA process. Simple conditions are given to guarantee their convergence to the extremum and the root of regression function respectively by using a new approach combining both the probabilistic method and the ordinary differential equation (ODE) method. The results given here are better than the well-known ones even if the measurement error is the martingale difference sequence.
