期权价格的性质证明（欧式期权价差与执行价差不等式，欧式期权价格是原生资产的齐一次

定理一    设c是执行价格为K的欧式看涨期权价格，当K1>K2(相同到期日期)时，求证：0<=c2-c1<=K1-K2
定理二    设p是执行价格为K的欧式看跌期权价格，当K1>K2(相同到期日期)时，求证：0<=p1-p2<=K1-K2


定理三    欧式看张(跌)期权的价格是标的资产的齐一次函数，即:    对任意的 α>0，有ct(αSt,αK)=αct(St,K)，看跌类似~（最好无套利思想证明）


灰常感谢~

1,2. construct a bull spread and draw the payoff's figure. Then prove it through the figure. Should be very easy, an entry level mathematical problem

3. consider the payoff function CT(ST,K)=max(ST-K,0). It is a homogenous function (degree 1). Suppose Ct(St,K) is not homogenous, let's say aCt(St,K)>Ct(aSt,aK), you can short "a" share of option Ct(St,K) and long a synthetic option with strike aK and underlying is "a" share of St. At maturity, aCT(ST,K)  should be equal to CT(aST,aK), you make the arbitrage profit aCt(St,K)－Ct(aSt,aK)

@Chemist_MZ

Chemist_MZ 发表于 2014-11-28 09:46
1,2. construct a bull spread and draw the payoff's figure. Then prove it through the figure. Should  ...

灰常感谢，小白学弟才入门，以后多多请教，再次感谢~

Chemist_MZ 发表于 2014-11-28 09:46
1,2. construct a bull spread and draw the payoff's figure. Then prove it through the figure. Should  ...

灰常感谢，小白学弟才入门，以后多多请教，再次感谢~