**SLIDES**

week1 (simple and compound interest rates)

Slides2 (Net Present Value and Internal Rate of Return)

Slides3 (Annuities, loans and mortgages) —

Complements on the various rates in a mortgage note-mortgages

slides4 (Spot term structure of interest rates)

slides5 (Perfect market, arbitrage and market NPV)

Slides6 (Forward rates, FRAs, Caps/Floor – Swaps) ** **

slides7 (Floating rate loans)

slides8 (Duration) — Assogestioni file on funds classification, in Italian guida-alla-classificazione-2003-

slides9 (Mean-Variance porfolio selection and CAPM)

Slides10 (Option pricing in the binomial model plus put-call parity)

Suggested reading:

- Impact of negative rates https://www.ecb.europa.eu/press/key/date/2016/html/sp160728.en.html
- Hull and White 2013 article on Libor vs OIS discounting: http://www-2.rotman.utoronto.ca/~hull/downloadablepublications/LIBORvsOIS.pdf
- Construction of Overnight Index Swaps discounting curve http://www.eduriskinternational.com/Constructing%20The%20OIS%20Curve.pdf

**DETAILED SYLLABUS**

Sept 14, 2016. Simple and compound interest rate. Compound and discount functions. Continuous compounding. On the slides [week1]; Lovelock [Chap 1 (no counting days convention)]

Sept 15. Financially equivalent rates. Effective Rate. NPV at a flat rate: properties and usage in portfolio choice. IRR: definition, properties. IRR for an investment with periodic, constant interest with par price. On the slides [slides2] ; Lovelock [Chap 2 (rule of 72 excluded)].

Sept 21. Functions IRR and XIRR in Excel. Present value of annuities: ordinary and due. Examples and a simplified Gordon’s model [slides2 and slides3]; Lovelock [Chap 4].

Sept 22. Accumulated principal of an annuity. Loans and mortgages. Amortization: coupon bond and French amortization. [slides 3]; file note-mortgages, and Lovelock [Chap 5 and 6].

Sept 28. Market compound and discount factors. Generalities on market rates and construction of the zero coupon yield curve for short maturities (linear interpolation). Only on the slides [slides4]

Sept 29. Euribors, Eonia. Market compound factors are increasing with the maturities, but rates need not. As long as compound factors are increasing, there is no arbitrage on the market (no matter if the rates are negative). Only in the slides, [slides4 and 5]

Oct 5. Perfect market. Self financing strategies. Arbitrage of type 1 and 2. No arbitrage implies the law of one price. Only in the slides, [slides 5]

Oct 6. Market NPV: definition and proof it is the unique no arbitrage price for the stream of cashflows. Implicit forward rates and first properties. [slides5] and Luenberger Chap 4, [pag 74-75-76]; [slides6]

Oct 12. Analysis of the a posteriori convenience of a forward contract. FRAs and examples [slides6]

Oct 13. Fair FRA rate (theoretically) equals the implicit forward rate. Usage of FRAs. Caplets and floorlets: payoff and usage. [slides6]

Oct 19. Interest Rate Swaps. Description and usage. Comparative advantage argument. [slides6 and from page 147 onwards on Hull ]

Oct 20. Comparative advantage: how to set the fixed rates in the swaps with the bank in such a way that the bank earns a fixed spread. Bootstrap of the yield curve using IRS. Introduction to floating rate loans. [slides6 and slides7]

Oct 26. Floating rate loans. Valuation with and without spread on the floating rate. Examples. [slides7]** UP TO HERE FOR THE MIDTERM.**

Oct 27. Interest rate risk and its components. Price risk and introduction to duration. [slides8]** **

Nov 10. Duration properties and usage [slides8]** **

Nov 11. Mean-variance analysis: introduction to the case of two risky assets (portfolio returns, mean variance of portfolios on the two) (Luenberger and slides9)

Nov 16. Mean-variance analysis, continued. Diversification, MVP and the efficient frontier (Luenberger and slides9)

Nov 17. Mean-variance with N risky assets. MVP and the efficient frontier. Limits for big N: diversification cannot eliminate market risk, only idiosyncratic. (Luenberger and slides9)

Nov 23. Presence of the risk free asset. The CML and the tangent portfolio. Sharpe ratio is a RORAC. Introduction to the CAPM.

Nov 24. The CAPM and the CAPM as a regression model on the market portfolio. Risk adjusted discounting.

Nov 30. The binomial market model (one period case). Derivatives and options, replication. Calculation of the forward price K* of a forward contract.

Dec 1. Risk neutral probabilities and the pricing formula in the binomial model. Put-call parity (see new file slides10). Examples.