--------------------------------------------------- # # # Chapter 1: Trading Strategies # # # --------------------------------------------------- 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.

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