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Stochastic Financial Mathematics Exchange Rates and Volatility - PowerPoint PPT Presentation

May 07, 2023 •276 likes •358 views

Stochastic Financial Mathematics Exchange Rates and Volatility Andrey Sarantsev Aleksey Eremenko Objective Use Sage to manipulate currency data Analyze results Five currencies used: Euro, UK Pound, Chinese Yuan, Japanese Yen,

  1. Stochastic Financial Mathematics Exchange Rates and Volatility Andrey Sarantsev Aleksey Eremenko

  2. Objective ● Use Sage to manipulate currency data ● Analyze results ● Five currencies used: Euro, UK Pound, Chinese Yuan, Japanese Yen, Russian Ruble

  3. Method ● Define n -long set S of exchange rates ● State that for some x k +1 ( x ( k + 1 ) ) S ( k + 1 ) = S ( k ) e x ( k + 1 ) = ln ( S ( k + 1 ) ● Equivalently, ) S ( k ) ● Assume set of x are independent, identically distributed RVs (Normal) ● Able to calculate variance of subset of x ● What does this variance mean?

  4. Moving Variance ● Note this is Empirical Variance ● Subset of x -set length m ● Data limitations (days) ● Meaningful results ● Why moving variance?

  5. EUR – green, GBP – blue, Yuan – black, JPY - red, RUB - yellow

  6. Chinese Yuan

  7. Varying Window Sizes

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