{"id":22551777,"url":"https://github.com/tatevkaren/finance-projects","last_synced_at":"2025-06-11T05:38:14.085Z","repository":{"id":113747854,"uuid":"326000920","full_name":"TatevKaren/Finance-Projects","owner":"TatevKaren","description":"Case Studies in Finance: Stock Price Valuation using Black-Scholes using Brownian Motions, Investment Project comparing Stocks and Bonds, Determining Pension Fund's Premium. 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Whether this amount will be returned and whether it will accrue a return depends on the performance of two indices, namely the FTSE100 and the SP500. We will consider the pay-off in-depth in\n\nModel formulation in terms of Stochastic Differential Equations (SDE)'s assuming the model of geometric Brownian Motion\n\u003cp align=\"left\"\u003e\n\u003cimg src=\"Model_intermsof_SDE.png?raw=true\"\n  alt=\"\"\n  width=\"430\" height=\"100\"\u003e\n\u003c/p\u003e\n\u003cp align=\"left\"\u003e\n\u003cimg src=\"Model_intermsof_SDE2.png?raw=true\"\n  alt=\"\"\n  width=\"350\" height=\"100\"\u003e\n\u003c/p\u003e\n\n## Snapshots for data visualization\n\u003cp align=\"left\"\u003e\n\u003cimg src=\"InvestmentProjectBNPParibas_figure1.png?raw=true\"\n  alt=\"\"\n  width=\"400\" height=\"150\"\u003e\n\u003c/p\u003e\n\u003cimg src=\"InvestmentProjectBNPParibas_figure2.png?raw=true\"\n  alt=\"\"\n  width=\"400\" height=\"150\"\u003e\n\u003c/p\u003e\n\n\n# 2: Black-Scholes SDE Price Evaluation\nFile name: Quantitative_Finance_BlackScholes_SDE_Case_Study.pdf\n\n\nThe SDE investor follows: \n\u003cp align=\"left\"\u003e\n\u003cimg src=\"SDE_Wealth_of_investor_follows.png?raw=true\"\n  alt=\"\"\n  width=\"350\" height=\"100\"\u003e\n\u003c/p\u003e\nBlack-Scholes world with following setting:\n\u003cp align=\"left\"\u003e\n\u003cimg src=\"Assumed_BlackScholes_setting.png?raw=true\"\n  alt=\"\"\n  width=\"300\" height=\"100\"\u003e\n\u003c/p\u003e\nMean and the variance of the Brownian Motion:\n\u003cp align=\"left\"\u003e\n\u003cimg src=\"Mean_Variance_BrownianMotion.png?raw=true\"\n  alt=\"\"\n  width=\"350\" height=\"100\"\u003e\n\u003c/p\u003e\n\nFollowing topics are included in this analysis:\n - Black-Scholes \n - Stochastic Differential Dquation (SDE)\n - Geometric Brownian Motion\n - Itˆo’s lemma\n - Monet Carlo Simulation\n - Euler's Scheme, One-sided Bump-and-Reprice method\n - Closed-form derrivatives, sensitivity\n - Constant Relative Risk Aversion \n\n\n# 3: Expected Premium Analysis for a Pension Fund\n**Code:** LI_ExpectedNetPremiumPensionFund.m , LI_ExpectedNetPremiumPensionFund2.m, LI_ExpectedSurvivalRates.m, LI_Simulation_Ages.m\n\n**Data:** qxt.mat\n\n**Paper:** LI_ExpectedNetPremium_PensionFund.pdf\n\nPopulation grows older this results in problems for pension funds. This use-case shows how one can randomly generate the ages of the pension fund customers and calculate the expected pension costs for the pension fund and the expected premium they need to charge to the customers in order to run no losses.\n\u003cp align=\"left\"\u003e\n\u003cimg src=\"LossFunction_of_PensionFund.png?raw=true\"\n  alt=\"\"\n  width=\"400\" height=\"100\"\u003e\n\u003c/p\u003e\n\n\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ftatevkaren%2Ffinance-projects","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Ftatevkaren%2Ffinance-projects","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Ftatevkaren%2Ffinance-projects/lists"}