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摘要：Options are financial derivatives for avoiding market risk. Many theories and practices show that as long as investors choose reasonable numbers of securities and their derivatives, they will obtain risk-free interest rate which resulting in risk-free returns. This combination depends on the pricing of derivative securities.

Background
In early 1970, Black and Scholes (1973) researched the changing regularity of stock price by using the hedging theory, and they successfully derived the stochastic partial differential equations of price of stock options without dividend. It then provides a strong guarantee to price options accurately and reasonably. And this excellent finding significantly advances the stability and development of financial derivatives market.

Black-Scholes option pricing model has the following advantages: First, it supplies the notion of risk-neutral (also called no-risk-preference).This model gets rid of risk preference parameters and greatly simplifies the complexity of analyzing the price of financial derivatives. Second, the model creatively develops that it’s possible for the investor to limit the risk while chase higher returns; and it creates a new financial derivatives - the standard options. Control risk is one of the most important significances of the Black-Scholes option pricing model. After the 1970s, the development of world economic has speeded up and the tide of world economic integration has been accelerated. Both the volatility of exchange rate and interest rate are more frequent with great high range. Therefore, the market risk is increasing. Control and reduce risk became more and more important for all investors. Black-Scholes pricing model not only proposed options which can control/reduce the risks, but also opened up a road for the mathematics to be used in the economic field to create more and more tools for controlling/reducing risk. Black-Scholes pricing model suggests that people’s collective behavior satisfies a certain of mathematical laws under certain conditions. This inference breaks the traditional the old ideas that human behavior can not be quantified described. Through quantitative analysis using mathematical tools, investors can better control their trading risks, and it’s possible for the management to manage the risk and reduce the risk of the whole market. Black-Scholes pricing model has laid a good foundation for the derivatives market's rapid development, and it also made derivative financial instruments good approaches for investment, financing and preventing risk.

The rise and development of option pricing theory has promoted the development of the options market greatly. It avoids people’s subjective blindness in option pricing and ensures that both sides of the transaction can trade fairly and reasonably. And it provides an effective way for them to hedge their risks when facing the changing market situation. Option pricing theory provided us with an idea of dealing with random phenomena, so that it’s a good idea to solve the similar problems with random perturbations.

Reference
Almendral, A. and C. W. Oosterlee (2005). "Numerical valuation of options with jumps in the underlying." Applied Numerical Mathematics 53(1): 1-18.

Black, F. and Scholes, M.S. (1973), ‘The pricing of options and corporate liabilities’, Journal of Political Economy 81, 637-654.

Christensen, M. M. and C. Munk (2004). A Note on the Numerical Solution of the Black-Scholes-Merton PDE, Technical report, Department of Finance and Accounting, University of Southern Denmark.

Cox, J. C., S. A. Ross, et al. (1979). "Option pricing: A simplified approach* 1." Journal of Financial Economics 7(3): 229-263.

Dong, G. N. "Numerical Solutions of Financial P本论文由英语论文网提供整理，提供论文代写，英语论文代写，代写论文，代写英语论文，代写留学生论文，代写英文论文，留学生论文代写相关核心关键词搜索。