期权定价模型(证券投资学,南京审计学院 张维)

证券投资学

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第23讲1、关注最近的国际资本市场2、期权定价模型

期权定价理论(OPT)二项式期权定价模型；

Black-Scholes模型

Myron Scholes and Fischer Black

It was an ordinary autumn afternoon in Belmont, Mass. 1969, when Fischer Black, a 31 year old independent finance contractor, and Myron Scholes a 28 year old assistant professor of finance, at MIT hit upon an idea that would change financial history. Black had been working for Arthur D. Little in Cambridge, Mass., when he met a colleague who had devised a model for pricing securities and other assets. With his Harvard Ph.D. in applied mathematics just five years old, Black's interest was sparked. His colleague's model focused on stocks, so Black turned his attention to options, which were not widely traded at the time.

By 1973, the tandem team of Fischer Black and Myron Scholes had written the first draft of a paper that outlined an analytic model that would determine the fair market value for European type call options on non-payout assets. They submitted their work to the Journal of Political Economy for publication, who promptly responded by rejecting their paper. Convinced that their ideas had merit, they sent a copy to the Review of Economics and Statistics, where it elicited the same response. After making some revisions based on extensive comments from Merton Miller (Nobel Laureate from the University of Chicago) and Eugene Fama, of the University of Chicago, they resubmitted their paper to the Journal of Political Economy, who finally accepted it. From the moment of its publication in 1973, the Black and Scholes Option Pricing Model has earned a position among the most widely accepted of all financial models.8

Modern option pricing techniques, with roots in stochastic calculus, are often considered among the most mathematically complex of all applied areas of finance. These modern techniques derive their impetus from a formal history dating back to 1877, when Charles Castelli wrote a book entitled The Theory of Options in Stocks and Shares. Castelli's book introduced the public to the hedging and speculation aspects of options, but lacked any monumental theoretical base. Twenty three years later, Louis Bachelier offered the earliest known analytical valuation for options in his mathematics dissertation at the Sorbonne.9

He was on the right track, but he used a process to generate share price that allowed both negative security prices and option prices that exceeded the price of the underlying asset. Bachelier's work interested a professor at MIT named Paul Samuelson, who in 1955, wrote an unpublished paper entitled "Brownian Motion in the Stock Market". During that same year, Richard Kruizenga, one of Samuelson's students, cited Bachelier's work in his dissertation entitled "Put and Call Options: A Theoretical and Market Analysis". In 1962, another dissertation, this time by A. James Boness

, focused on options. In his work, entitled "A Theory and Measurement of Stock Option Value", Boness developed a pricing model that made a significant theoretical jump from that of his predecessors. More significantly, his work served as a precursor to that of Fischer Black and Myron Scholes, who in 1973 introduced their landmark option pricing model.

Since 1973, the original Black and Scholes Option Pricing Model has been the subject of much attention. Many financial scholars have expanded upon the original work. In 1973, Robert Merton relaxed the assumption of no pidends. In 1976, Jonathan Ingerson went one step further and relaxed the the assumption of no taxes or transaction costs. In 1976, Merton responded by removing the restriction of constant interest rates. The results of all of this attention, that originated in the autumn of 1969, are alarmingly accurate valuation models for stock options.

关于期权的基本涵义 提问测试？

The idea of options is certainly not new. Ancient Romans, Grecians, and Phoenicians traded options against outgoing cargoes from their local seaports. When used in relation to financial instruments, options are generally defined as a "contract between two parties in which one party has the right but not the obligation to do something, usually to buy or sell some underlying asset". Having rights without obligations has financial value, so option holders must purchase these rights, making them assets. This asset derives their value from some other asset, so they are called derivative assets.

Call options are contracts giving the option holder the right to buy something, while put options, conversely entitle the holder to sell something. Payment for call and put options, takes the form of a flat, up-front sum called a premium. Options can also be associated with bonds (i.e. convertible bonds and callable bonds), where payment occurs in installments over the entire life of the bond, but this paper is only concerned with traditional put and call options.

二项式期权定价模型

假定现在要确定某个买进期权在到期之 前某个时期的价值。同时，进一步假定 与期权相对应的股票在当时的价格为每 股50元，但有可能上升到75元或下跌到 25元。在假定借贷利率为25%。那么， 在这些条件下，一个执行价格为50元的 买进期权，其价值是多少呢？15

投资组合

t=0时资 金流入

t=1资金流入 S1=25元 0 +25 -25 S2=75元 -50 -75 -25

出售2个买入期权 购买1股股票 借入20元

+2C -50 +20

合计

0

016