3.Strategies of the Options

X p e rT
c e rT
X p e rT c e rT S e rT X p e rT X p e rT
ST
long p short c
S e rT
（2）Inverse Conversion ( 反向转换套利 )
construct a portfolio as follows: enter into a Future ( Forward ) contract at a short position with the exercise price S ; sell a put option with the price p ; buy a call option with the price c ; both the option strike prices are the same . then at the expiration date T , if the price of the asset is ST , the profit function for this Inverse Conversion will be :
Remark: If the prices of the Call and the Put are proper , the following “ put – call parity ” will be valid :
c p S X e rT
That means , in the perfect financial market , the profit of such a Conversion is zero ! Real purpose: We can obtain the profit without any risk from such a portfolio , if the price of Call is too high or the price of Put is too low .
contract at a long position with the exercise price S . Then at the expiration date T , if the price of the asset is ST , the profit function for this Long Future will be :
( ST ) ST S e rT , ( r interest rate ) ~ Equilubrium point ( 盈亏平衡点 )： ST S e rT ; the maximal loss ( 最大亏损值 ) ： S e rT ,
the maximal profit ( 最大盈余值 )： unlimited , if ST → +∞
Equilubrium point : the maximal loss： the maximal profit：

~ ST X c e rT ;
unlimited , if ST → +∞
c e rT ,
c e rT
X c erT
ST
X
short c
（5） Long Put
( ST ) ST S e rT , ( r interest rate ) ~ ST S e rT ; Equilubrium point ( 盈亏平衡点 )： the maximal loss ( 最大亏损值 ) ： unlimited , if ST → +∞
the maximal profit ( 最大盈余值 )：

X p e rT
X p e rT X p e rT
ST
long p
（6） Short Put
( 看跌期权空头 ) ： sell a put option with the price p , the expiration date T ，the strike ( exercise ) price X . then at the expiration date T , if the price of the asset is ST , the profit function for this Short Put will be :

S e rT
p e rT S e rT c e rT X p e rT
X p e rT X
c erT
long c
short p
ST
X p e rT
3. Synthetic Strategies ( 合成头寸组合技巧 )
(1) Synthetic Long Future ( 更多获利、更少亏损的 “期货 ” 多 操作方法：买入看涨期权，价格为 c ; 与此同时再卖出看跌期权， 头) 价格为 p ; 使看涨与看跌的执行价相同 到期日的资产价格如果为 ST , 则该头寸的相应利润函数为：
then at the expiration date T , if the price of the asset is ST , the profit function for this Long Call will be :
( ST ) max( ST X ,0) c e rT , ( r interest rate ) ~ Equilubrium point : ST X c e rT ; the maximal loss： c e rT ,

long s
ST
S e rT
S e rT
（2）Short Future （期货空头 ) ：enter into a Future ( Forward )
contract at a short position with the exercise price S .
then at the expiration date T , if the price of the asset is ST , the profit function for this Short Future will be :
§. Strategies of the Options （期权交易策略 ） 一. Basic Strategies Ref. Fundamentals of Futures and Options Markets , Jon c. Hull
Chap.9
1. Six Basic Positions and their profit functions （1） Long Future（期货多头 ) ： enter into a Future ( Forward )
the maximal profit：

unlimited ,
if ST → +∞
long c
X
X c erT c erT
ST
（4） Short Call ( 看涨期权空头 ) ： sell a call option with the price c , the expiration date T ，the strike ( exercise ) price X .
( ST ) max( X ST ,0) p e rT , ( r interest rate ) ~ rT Equilubrium point : ST X p e ; the maximal loss： p e rT , the maximal profit： X p e rT

short p
p e rT
X p e rT
ST
X
X p e rT
2. Conversion Strategy ( 转换套利策略 ) （1）Conversion ( 正向转换套利 ) construct a portfolio as follows: enter into a Future ( Forward ) contract at a long position with the exercise price S ; buy a put option with the price p ; sell a call option with the price c ; both the option strike prices are the same . then at the expiration date T , if the price of the asset is ST , the profit function for this Conversion will be :
( ST ) [ ST S e rT ] [ max( X ST ,0) p e rT ] [max( ST X ,0) c e rT ] p e rT c e rT X S e rT ( nothing to do with ST ！)
Remark : If the prices of the Call and the Put are proper , the following “ put – call parity ” will be valid :
c p S X e
பைடு நூலகம்T
That means , in the perfect financial market , the profit of such an Inverse Conversion is zero ! Real purpose : We can obtain the profit without any risk from such a portfolio , if the price of Put is too high or the price of Call is too low .