Properties of interest rate swaps.pdf
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The properties of interest rate swaps
An investigation of the price setting of illiquid interest rates swaps and the perfect hedging portfolios.
Max Lindquist
12/23/2011

Abstract
The main purpose of this thesis is to analyze the properties of various types of simple interest rates swaps, investigate how they depend on the swap rates of the liquid instruments on the market and the OIS-rates, and analyze how an illiquid instrument should be priced and hedged. The price setting tool used by the Fixed Income division at SEB Merchant Banking has been analyzed, and simulations of the hedging portfolios have been done over a time span of one year.
The conclusions have been that it is impossible to hedge against the convex OIS rate dependence of the analyzed swaps and that, thought it might seem like a good idea, a dynamic hedge will lead to a much worse outcome than a static hedge.

[3] Table of Contents
1. Introduction ................................................. 4
2. Theory ....................................................... 5
2.1. Forward Rate Agreements (FRA)...................... 5
2.2. Vanilla Interest Rate Swaps ............................. 5
2.3. Overnight Index Swaps (OISs) ......................... 6
2.4. Rationale for OIS discounting ........................... 7
2.5. Revised Formulas.............................................. 7
3. The Model........................................................... 8
3.1. Constructing the LIBOR and OIS yield curves ...... 8
3.2. The Swaps dependence on the OISs .................. 9
3.3. How to Hedge an Instrument ............................ 10
3.4. Analyzed Instruments ....................................... 12
4. Data .................................................................. 16
5. Results ............................................................... 17
5.1. Intraday ........................................................... 17
5.1.1. Testing the effects from the swap rates.............. 18
5.1.2. Testing the effects from the OIS rates ............... 19
5.1.3. Testing the convexity ...................................... 20
5.1.4. Running the simulation .................................. 21
5.2. Changing Dates ............................................... 23
5.2.1. Testing for all Variables Constant .................... 25
5.2.2. Testing the effects from the swap rates............. 30
5.2.3. Testing the effects from the OIS rates ............... 33
5.2.4. Running the simulation .................................... 35
5.2.5. Analyzing the hedge .................................... 37
5.3. Dynamic Hedging ................................... 43
7. Conclusions .................. 45
8. Reference List ...................................... 46
9. Appendix ......................... 47