问题 问答题

某无红利支付股票的欧式期权执行价格为29美元,股票现价为30美元,无风险年利率为5%,股票年波动率为25%,期权到期日为4个月。
(1)如果该期权为欧式看涨期权,计算其价格;
(2)如果该期权为欧式看跌期权,计算其价格;
(3)验证看涨看跌期权平价关系是否成立。

答案

参考答案:某无红利支付股票的欧式期权执行价格为29美元,股票现价为30美元,无风险年利率为5%,股票年波动率为25%,期权到期日为4个月。
(1)如果该期权为欧式看涨期权,计算其价格;
(2)如果该期权为欧式看跌期权,计算其价格;
(3)验证看涨看跌期权平价关系是否成立。

解析:[解] 在本题中,S0=30,K=29,r=0.05,σ=0.25,T=0.3333
所以:
d1=[*]=0.4225
d2=[*]=0.2782
N(0.4225)=0.6637,N(0.2782)=0.6096
N(-0.4225)=0.3363,N(-0.2782)=0.3904
因此:
(1)欧式看涨期权的价格为:30×0.6637-29e-0.05×0.3333×0.6096=2.52;
(2)欧式看跌期权的价格为:29e-0.05×0.3333×0.3094-30×0.3363=1.05;
(3)欧式看涨看跌期权平价关系为:p+S0=c+Ke-r(T-t)
将c=2.52,S0=30,K=29,p=1.05,e-r(T-t)=0.9835带入上式,可以发现计算出的欧式看涨看跌期权的价格满足欧式看涨看跌期权平价关系。

单项选择题

For me, scientific knowledge is divided into mathematical sciences, natural sciences or sciences dealing with the natural world (physical and biological sciences), and sciences dealing with mankind (psychology, sociology, all the sciences of cultural achievements, every kind of historical knowledge). Apart from these sciences is philosophy, about which we will talk later. In the first place, all this is pure of theoretical knowledge, sought only for the purpose of understanding, in order to fulfil the need to understand what is intrinsic and consubstantial to man. What distinguishes man from animal is that he knows and needs to know. If man did not know that the world existed, and that the world was of a certain kind, that he was in the world and that he himself was of a certain kind, he wouldn’t be man. The technical aspects or applications of knowledge are equally necessary for man and are of the greatest importance because they also contribute to defining him as man and permit him to pursue a life increasingly more truly human.

But even while enjoying the results of technical progress, he must defend the primacy and autonomy of pure knowledge. Knowledge sought directly for its practical applications will have immediate and foreseeable success, but not the kind of important result whose revolutionary scope is in large part unforeseen, except by the imagination of the Utopians. Let me recall a well-known example. If the Greek mathematicians had not applied themselves to the investigation of conic sections, zealously and without the least suspicion that it might someday be useful, it would not have been possible centuries later to navigate far from shore. The first man to study nature of electricity could not imagine that’ their experiments, carried on because of mere intellectual curiosity, would eventually lead to modern electrical technology, without which we can scarcely conceive of contemporary life. Pure knowledge is valuable for its own sake, because the human spirit cannot resign itself to ignorance. But, in addition, it is the foundation for practical results that would not have been reached if this knowledge had not been sought disinterestedly.

The practical scientist().

A.is a philosopher

B.is interested in the unknown

C.knows the value of what he will discover

D.knows that the world exists

选择题