In this paper I replicate Clewlow and Strickland's control variates methods based on Greek letters method to test if it can improve the simulation efficiency. First, I use Black Scholes Merton formula for option pricing as a benchmark, to compare with the European call option price from Monte Carlo methods. Then I use Greek letters as control variates to reduce sample standard deviation and improve the efficiency of the Monte Carlo simulation. The whole process is programming in C++. C++ is a

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... mpiled language which can generate machine code from source code and provide a shorter running time. This paper is based on ideas from Implementing Derivatives Models by Clewlow and Strickland, On The Simulation of Contingent Claims by Clewlow and Carverhill, Chapter 4, and Derivatives Markets by McDonald, Chapter 12, 13, 19.