Finding semiparametric bounds for option prices is a widely studied pricing technique.We obtain closed-form semiparametric bounds of the mean and variance for the pay-off of two exotic(Collar and Gap) call options giv...Finding semiparametric bounds for option prices is a widely studied pricing technique.We obtain closed-form semiparametric bounds of the mean and variance for the pay-off of two exotic(Collar and Gap) call options given mean and variance information on the underlying asset price.Mathematically,we extended domination technique by quadratic functions to bound mean and variances.展开更多
The paper is on toxic foreign exchange options problem which occurred in Poland just prior to and after the outbreak of the recent crisis. Especially Polish enterprises were severely stricken by transactions on fx and...The paper is on toxic foreign exchange options problem which occurred in Poland just prior to and after the outbreak of the recent crisis. Especially Polish enterprises were severely stricken by transactions on fx and interest rate derivatives contracted with their banks. Poland was the only EU country which did not precipitate into recession during the financial crisis beginning in 2008. However, the toxic fx and interest rate derivatives transmitted the shockwaves from global financial markets into Poland. Huge dimensions of losses resulted in conflicts between banks and their customers, who claimed just being cheated by the financial institutions. The article deeply researches into reasons for such developments on Polish fx over-the-counter derivatives market. As a case study, an authentic strategy has been presented. The contract was concluded between the construction company and one of the biggest commercial banks in Poland. Because the case study may be representative for many other cases, the analysis includes exact pricing of option strategy and therefore reveals inequality of the contract. The consequences of non-implementing the MiFID directive in the context of derivatives offering to non-financial customers were also touched in the paper.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
This paper establishes a lattice Boltzmann method (LBM) with two amending functions for solving partial differential equations (PDEs) arising in Asian and lookback options pricing. The time evolution of stock pric...This paper establishes a lattice Boltzmann method (LBM) with two amending functions for solving partial differential equations (PDEs) arising in Asian and lookback options pricing. The time evolution of stock prices can be regarded as the movement of randomizing particles in different directions, and the discrete scheme of LBM can be interpreted as the binomial models. With the Chapman-Enskog multi-scale expansion, the PDEs are recovered correctly from the continuous Boltzmann equation and the computational complexity is O(N), where N is the number of space nodes. Compared to the traditional LBM, the coefficients of equilibrium distribution and amending functions are taken as polynomials instead of constants. The stability of LBM is studied via numerical examples and numerical comparisons show that the LBM is as accurate as the existing numerical methods for pricing the exotic options and takes much less CPU time.展开更多
We consider a strictly pathwise setting for Delta hedging exotic options,based on Follmer’s pathwise It¨o calculus.Price trajectories areˆd-dimensional continuous functions whose pathwise quadratic variations an...We consider a strictly pathwise setting for Delta hedging exotic options,based on Follmer’s pathwise It¨o calculus.Price trajectories areˆd-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix.The existence of Delta hedging strategies in this pathwise setting is established via existence results for recursive schemes of parabolic Cauchy problems and via the existence of functional Cauchy problems on path space.Our main results establish the nonexistence of pathwise arbitrage opportunities in classes of strategies containing these Delta hedging strategies and under relatively mild conditions on the local volatility matrix.展开更多
基金supported by National Science Foundation of the United States (Grant Nos.DMS-0720977 and DMS-0805929)
文摘Finding semiparametric bounds for option prices is a widely studied pricing technique.We obtain closed-form semiparametric bounds of the mean and variance for the pay-off of two exotic(Collar and Gap) call options given mean and variance information on the underlying asset price.Mathematically,we extended domination technique by quadratic functions to bound mean and variances.
文摘The paper is on toxic foreign exchange options problem which occurred in Poland just prior to and after the outbreak of the recent crisis. Especially Polish enterprises were severely stricken by transactions on fx and interest rate derivatives contracted with their banks. Poland was the only EU country which did not precipitate into recession during the financial crisis beginning in 2008. However, the toxic fx and interest rate derivatives transmitted the shockwaves from global financial markets into Poland. Huge dimensions of losses resulted in conflicts between banks and their customers, who claimed just being cheated by the financial institutions. The article deeply researches into reasons for such developments on Polish fx over-the-counter derivatives market. As a case study, an authentic strategy has been presented. The contract was concluded between the construction company and one of the biggest commercial banks in Poland. Because the case study may be representative for many other cases, the analysis includes exact pricing of option strategy and therefore reveals inequality of the contract. The consequences of non-implementing the MiFID directive in the context of derivatives offering to non-financial customers were also touched in the paper.
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The authors were grateful to the anonymous referees for their valuable suggestions that led to a greatly improved paper. This work was supported by the National Natural Science Foundation of China (Grant No. 11171274) and the Program for New Century Excellent Talents in University (Grant No. NCET-12-0922).
文摘This paper establishes a lattice Boltzmann method (LBM) with two amending functions for solving partial differential equations (PDEs) arising in Asian and lookback options pricing. The time evolution of stock prices can be regarded as the movement of randomizing particles in different directions, and the discrete scheme of LBM can be interpreted as the binomial models. With the Chapman-Enskog multi-scale expansion, the PDEs are recovered correctly from the continuous Boltzmann equation and the computational complexity is O(N), where N is the number of space nodes. Compared to the traditional LBM, the coefficients of equilibrium distribution and amending functions are taken as polynomials instead of constants. The stability of LBM is studied via numerical examples and numerical comparisons show that the LBM is as accurate as the existing numerical methods for pricing the exotic options and takes much less CPU time.
基金support by Deutsche Forschungsgemeinschaft through the Research Training Group RTG 1953.
文摘We consider a strictly pathwise setting for Delta hedging exotic options,based on Follmer’s pathwise It¨o calculus.Price trajectories areˆd-dimensional continuous functions whose pathwise quadratic variations and covariations are determined by a given local volatility matrix.The existence of Delta hedging strategies in this pathwise setting is established via existence results for recursive schemes of parabolic Cauchy problems and via the existence of functional Cauchy problems on path space.Our main results establish the nonexistence of pathwise arbitrage opportunities in classes of strategies containing these Delta hedging strategies and under relatively mild conditions on the local volatility matrix.