[游戏开发]3.3.4 Trading Strategies

1. Single Option Strategies

Covered Call(Long Stock + Short Call)

• $S_T<X$
  • Short call: $c$
  • Long stock: $S_T?S_0$
  • 合计 $c+S_T?S_0$
• $S_T\ge X$
  • Short call: $c?(S_T?X)$
  • Long stock: $S_T?S_0$
  • 合计 $c+X?S_0$

Protective Put(Long Stock + Long Put)

• $S_T\ge X$
  • Long call: $?p$
  • Long stock: $S_T?S_0$
  • 合计 $S_T?S_0?p$
• $S_T<X$
  • Short call: $(X?S_T)?p$
  • Long stock: $S_T?S_0$
  • 合计 $X?S_0?p$

Principal Protected Notes(PPNs)
Principal protected note: a security created from a single option such that the investor benefits from any gain of a specified portfolio without the risk of losses.

• Long a three-year zero-coupon bond that will pay USD 10,000 in three years.
• Long a three-year call option on a portfolio, which is currently worth USD 10,000 with a strike price of USD 10,000.

2. Spread Trading Strategies

画图的时候记得strike price与option price的关系

Bull Call Spread

• Long 1 $Cal{l}_1$ at $X_1$ + Short 1 $Cal{l}_2$ at $X_2$
• $X_1<X_2$
  
  

Bull Put Spread

• Long 1 $pu{t}_1$ at $X_1$ + Short 1 $pu{t}_2$ at $X_2$,
• $X_1<X_2$
  
  

Bear Call Spread

• Short 1 $Cal{l}_1$ at $X_1$ + Long 1 $Cal{l}_2$ at $X_2$
• $X_1<X_2$
  
  

Bear Put Spread

• Short 1 $pu{t}_1$ at $X_1$ + Long 1 $pu{t}_2$ at $X_2$
• $X_1<X_2$
  
  
  Box Spread
• Bull call spread + Bear put spread
  • Strike prices and Times to maturity used for the bull spread are the same as those used for the bear spread.
• Under a no arbitrage assumption, the present value of the pay off will equal the net premium paid.
  

Butterfly Spread(with call options)
Butterfly Spread(with put options)

Calendar Spread(with call/put option)

• Short 1 $T_1$ call/put + Long 1 $T_2$ call/put
• $T_1<T_2$
• Calendar spread has a long and a short position with exercise price, but the maturity of long position is longer than that of short position.
  

3. Combined Strategies

Straddle

• Long 1 call + long 1 put, both at X
  
  

Strangle

• Long 1 call at $X_2$+ long 1 put at $X_1$, usually $X_1<X_2$