In order to price European contingent claim in a class of fractional Black-Scholes market,where the prices of assets follow a Wick-It stochastic differential equation driven by the fractional Brownian motion and mar...In order to price European contingent claim in a class of fractional Black-Scholes market,where the prices of assets follow a Wick-It stochastic differential equation driven by the fractional Brownian motion and market coefficients are deterministic functions,the pricing formula of European call option was explicitly derived by the method of the stochastic calculus of the fractional Brownian motion.A result about fractional Clark derivative was also obtained.展开更多
The method for pricing the option in a market with interval number factors is proposed. The no-arbitrage principle in the interval number valued market and the rule to judge the reasonability of a price interval are g...The method for pricing the option in a market with interval number factors is proposed. The no-arbitrage principle in the interval number valued market and the rule to judge the reasonability of a price interval are given. Using the method, the price interval where the riskless interest and the volatility under B-S setting is given. The price interval from binomial tree model when the key factors u, d, R are all interval numbers is also discussed.展开更多
The cross-fertilization between artificial intelligence and computational finance has resulted in some of the most active research areas in financial engineering. One direction is the application of machine learning t...The cross-fertilization between artificial intelligence and computational finance has resulted in some of the most active research areas in financial engineering. One direction is the application of machine learning techniques to pricing financial products, which is certainly one of the most complex issues in finance. In the literature, when the interest rate,the mean rate of return and the volatility of the underlying asset follow general stochastic processes, the exact solution is usually not available. In this paper, we shall illustrate how genetic algorithms (GAs), as a numerical approach, can be potentially helpful in dealing with pricing. In particular, we test the performance of basic genetic algorithms by using it to the determination of prices of Asian options, whose exact solutions is known from Black-Scholesoption pricing theory. The solutions found by basic genetic algorithms are compared with the exact solution, and the performance of GAs is ewluated accordingly. Based on these ewluations, some limitations of GAs in option pricing are examined and possible extensions to future works are also proposed.展开更多
基金National Natural Science Foundation of China(No.10826098)Natural Science Foundation of Anhui Province,China(No.090416225)Anhui Natural Science Foundation of Universities,China(No.KJ2010A037)
文摘In order to price European contingent claim in a class of fractional Black-Scholes market,where the prices of assets follow a Wick-It stochastic differential equation driven by the fractional Brownian motion and market coefficients are deterministic functions,the pricing formula of European call option was explicitly derived by the method of the stochastic calculus of the fractional Brownian motion.A result about fractional Clark derivative was also obtained.
文摘The method for pricing the option in a market with interval number factors is proposed. The no-arbitrage principle in the interval number valued market and the rule to judge the reasonability of a price interval are given. Using the method, the price interval where the riskless interest and the volatility under B-S setting is given. The price interval from binomial tree model when the key factors u, d, R are all interval numbers is also discussed.
文摘The cross-fertilization between artificial intelligence and computational finance has resulted in some of the most active research areas in financial engineering. One direction is the application of machine learning techniques to pricing financial products, which is certainly one of the most complex issues in finance. In the literature, when the interest rate,the mean rate of return and the volatility of the underlying asset follow general stochastic processes, the exact solution is usually not available. In this paper, we shall illustrate how genetic algorithms (GAs), as a numerical approach, can be potentially helpful in dealing with pricing. In particular, we test the performance of basic genetic algorithms by using it to the determination of prices of Asian options, whose exact solutions is known from Black-Scholesoption pricing theory. The solutions found by basic genetic algorithms are compared with the exact solution, and the performance of GAs is ewluated accordingly. Based on these ewluations, some limitations of GAs in option pricing are examined and possible extensions to future works are also proposed.
