Financial Mathematics

At the end of the course students should be able to: - Compute present and future values of cash-flow streams to compute the net present values of different real and financial investments. - Have a basic knowledge of the functioning of financial markets and of the way in which investment decisions are made. - Understand the risk-return tradeoff. Understand how diversification affects risk. - Have a clear understanding of the difference between systematic and diversifiable risk and know how to measure each. - Understand how interest rates are set and the principles of valuation of fixed income securities. - Know the basic types of derivatives and understand why and how they are used in risk management.

1. Introduction to Financial Mathematics a. Time Value of Money b. Future and Present Value c. The frequency of compounding. Effective Annual Interest Rate (EAR) 2. Annuities and Perpetuities a. Concept of annuity b. Ordinary Annuity, Annuity Due c. Perpetuity 3. Loan Amortization a. French loan b. American loan c. Constant principal paid off loan 4. Discounted cash flow valuation a. Payback period b. Net Present Value (NPV) c. Internal Rate of return (IRR) 5. Interest and Bond Valuation a. Yield curves and forward rates b. Bond Valuation and Bond Yields c. Annual and Semi-Annual Coupon Bonds 6. Stocks and their Valuation a. Common Stocks and Preferred Stocks b. Constant Growth Stocks c. Valuing Stocks Expected to Grow at a Non-Constant Rate 7. Risk and Return a. Mathematical representation of a portfolio b. The Graphical Relation between Risk and Rates of Return c. Portfolio theory and asset allocation. 8. The Capital Asset Pricing Model (CAPM) a. The CAPM b. The CML and the SML c. Portfolio beta 9. Financial Derivatives a. The main types of derivatives b. Valuing forward contracts. The futures price. c. Valuing Options. Binomial model

Learning activities in year 2020/2021 str based on a bimodal system: lectures will be given on an online basis, onsite teaching when it comes to the reduced groups. 1.- Theory (online)- Sessions. The instructor of the course teach the basic concepts of the topic. Classnotes are provided to the students. 2.- Solution to exercises. The student must solve the test to assess his/her degree of knowledge of the different concepts. This part comprises the individual work of the student at home. 3.- Exercises - Sessions (onsite). The instructor of these sessions solves the exercise sets provided to the students.