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#        Chapter 1: Trading Strategies            #
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Summary: Consider the following trading strategy:


* At start time t_0 buy a number of delta_0 stocks.

* At time t_1, sell these delta_0 stocks and buy a 
  number of delta_1 stocks. Or, more precisely, if 
  delta_1-delta_0 > 0, buy a number of delta_1-delta_0 
  stocks, or, if delta_1-delta_0 < 0, sell a number of 
  delta_1-delta_0 stocks at time t_1. To put it in 
  another way: At time t_1 readjust your stock position 
  such that you hold a number of delta_1 stocks at 
  the end of day t_1.

* At time t_2, sell these delta_1 stocks and buy a 
  number of delta_2 stocks such that your stock position 
  is delta_2 stocks at the end of day t_2.

Do this for all days t_k < t_N:

* At time t_k, sell delta_{k-1} stocks and buy a number 
  of delta_k stocks such that your stock position is 
  delta_k stocks at the end of day t_k.

Finally at t_N close the position:

* At time t_N, sell delta_{N-1} stocks and buy no new 
  stocks such that your stock position is closed at the 
  end of day t_N.


Then, if S_k denotes the closing price of the stock on 
day t_k, this trading strategy has generated the following 
amount of money V_N at time t_N (assume zero interest 
rates):


V_N = V_0 + sum_{k=1}^N delta_{k-1}*(S_k - S_{k-1})     (1)


Formula (1) lies at the bottom of option pricing and 
payoff replication. It is proven in chapter 1 as well as 
its generalization in case of non zero interest rates.


pdf-file: Chapter 1: Trading Strategies


Option Pricing
Time Series Models















Hochschule RheinMain,
Applied Mathematics:


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