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Analytical and Iterative Solutions in Finance

Learn about analytical and iterative methods to estimate volatilities and solve problems in finance. Discover Excel tools like Goal Seek and Solver for complex equations with unknowns. Share your opinions in the class demo. Dive into the world of finance with critical thinking.

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Analytical and Iterative Solutions in Finance

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Presentation Transcript

  1. IT & Finance Stefano Grazioli

  2. Critical Thinking • Last homework! • Collabwill be the main means of communication between us. • Next Time: Bitcoin • Easy meter

  3. The Hedge Tournament • SOFTWARE CLINIC WILL OPEN THURSDAY • Updates on Collab • Receiving help will become VERY hard the closer we get to the HT • At least one meeting per team between now and HT • 30 min max • Sign up sheets outside my door • You team may appear only once to avoid hoarding

  4. Estimating Volatilities Via Iterative Methods Implicit volatilities, Goal seek and Solver

  5. Analytical Solutions • Preferred way to solve problems“given that y=f(x) and that we know y, find x” • Example: I = C [(1+r)t -1] • If we know thatI = $ 218.99 (and t=10 and C = $1000)what is r? • Analytical solution: r = (I/C+1)1/t – 1then you plug in the numbers, and find out that r = 2%

  6. Analytical Solutions Are Not Always Available • Too complicated, or not known • In these cases we can try iterative solutions • Ideal for computer implementation

  7. Iterative Solutions Continuing the previous example • Pick an arbitrary solution value (e.g., r = 1%) and compute the formula: I = C [(1+r)t -1] • Try another solution value (e.g., r=1.1%) and compute the formula • If the value of I obtained in step 2 is closer to the known value of I ($218.99) than the value of I obtained in step (1), keep increasing the value of r, else reduce it. • Keep on going until you find an r that generates a value of I close enough to the target I

  8. Iterative Solutions • Very powerful techniques BUT • Often approximations • Not guaranteed to find a solution • Might miss solutions in case there is more than one

  9. Excel Tools • Goal seekif you have an equation with one unknown “X” and one known “Y” – as in the example • Goal is a constant • No constraints • Solverif you have an equation with more than one unknowns “X”s and one known Y – e.g., suppose that we did not know t andr (and we had at least two Ys) • Constant, min and max • Constraints

  10. Implicit Volatility Demo

  11. Your Opinion Matters • A couple of things that you have learned from the class • Is the class getting you to think on your own • What can be improved • Attitude towards the HT

  12. WINIT What Is NewIn Technology?

  13. Smart Hedger Demo

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