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The study analyses stochastic differential equations by showing Ito's lemma and solving the geometric Brown process. Interest rate model is also treated by using the drift condition and affine term structure by analyzing the liquidity and risk premium. Option pricing model is faced by using discretized methods and expected value for vanilla and exotic options with implications for hedging strategies, simulated result is presented with VBA code. Structural model is also considered by using a time dependent default barrier. Portfolio optimization is presented as well with Bayesians applications for smart beta. The percentile of the daily return is also analyzed with implications for the tails risks by using a mixture of normal distribution.