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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