In the past two decades,we have witnessed the revolutionary period in the trading of financial derivative securities or contingent claims in financial markets around the world.A derivative security may be defined as a security whose value depends on the values of other more basic underlying variables,which may be the prices of traded securities,prices of commodities or stock indices.The two most common derivative securities are futures and options.A forward contract (called a futures contract if traded on exchanges) is an agreement between two parties to buy or sell an asset at a certain time in the future for a predetermined price while an option gives the holder the right (but not the obligation) to buy or sell an asset by a certain date for a predetermined price.There has been a great proliferation in the number and variety of derivative securities and new derivative products are being invented continuously.The construction of the theoretical framework for the pricing of new derivative securities has been one of the major challenges in the field of mathematicl finance.The theoretical studies of financial derivative securities and their risk management have been commonly known as Rocket Science on Wall Street. In this book,we concentrate on the study of pricing models for financial options.Option trading forms an integrated part in portfolio management in financial firms.Indeed,many financial strategies and decisions can be analyzed from the perspective of options.We explore the characteristics of various types of options and discuss the theoretical framework within which the fair prices of options can be determined. In Sec. 1.1,we introduce some basic types of options traded in financial markets and present definitions of terms commonly used in the financial option theory,such as self-financing strategy,arbitrage,hedging,etc.Also,we discuss various trading strategies associated with the use of options and their combinations.In Sec.1.2,we deduce rational boundaries on option values without any assumptions on the stochastic behavior of the prices of the underlying assets.The effects of the early exercise feature and dividend payments on option values are also discussed.It is then followed by the discussion of the assumptions of asset price dynamics and mathematical formulation of stochastic processes,in particular,the Geometric Brownian process.The Ito lemma,the basic tool used for the evaluation of stochastic differentials,is derived.A brief discussion on martingale,a type of stochastic process used to describe "fair" games,is also included.In the last section,we introduce the concepts of riskless hedging and risk neutrality,and present the derivation of the renowned Black-Scholes equation in option pricing theory.One can argue that the fair or arbitrage option price can be interpreted as the discounted expectation of its terminal payoff under an adjusted probability distribution.The adjusted probability distribution is precisely the distribution under which the asset price follows a martingale.Finally,we end the chapter by showing that the position of an option can be replicated by a self-financing dynamic trading strategy with assets and bonds only.The fair price of an option is simply the value of its replicating portfolio. 1.1 Financial options and their trading strategies 1.1.1 Trading strategies involving options
在过去二十年里，我们目睹了全世界金融衍生证券交易的革命时期或金融市场中的未定权益。衍生证券可以被定义为证券，其价值取决于其他更基本的基本变量的价值，这可以是证券交易的价格，商品价格或股票指数。两个最常见的衍生证券是期货和期权。远期合同（如果在交易所交易就是所谓的期货合约）是双方为在今后某一时间以预定的价格购买或出售资产而选择持有人有权（但没有义务）在某一特定日期以预定价格购买或出售资产所达成的协议。各种各样衍生性金融证劵和新的金融衍生产品正在不断的出现。新的衍生证券定价理论框架的建设已经是金融数学理论研究领域的主要挑战之一。金融衍生证券的理论研究和风险控制管理已普遍称为华尔街的火箭科学。 在本书中，我们集中研究金融期权的定价模式。在财政企业中期权交易是投资组合管理中的一个组成部分。确实，许多金融战略和决策可从探讨期权的角度分析。我们探索不同类型的期权和在合理的价格内讨论理论框架就可以得到结论。
1.1 金融期权及其交易策略
1.1.1涉及期权交易策略
