Hedge Simulation under Different Interpolation Methods
LABORATORY FOR QUANTITATIVE RISK CONTROL
Title: Hedge Simulation of Multi-Curve Interest Rate Products under Different Interpolation Methods
Responsible: Christoph Plum
Superviser: Christian Fries
Dates: WS 13/14 - SS 2014
Abstract: The major objective of this thesis is to compare the hedge performance of hedge portfolios constructed via multi-curve interest rate curves with different interpolation methods. We focus on the swap market after the beginning of the credit crunch in 2007, making it indispensable to distinguish between discount and forward curves as well as among forward curves with different maturities. The interpolation methods examined cover piecewise constant, linear and several cubic spline interpolations recommended by scientific papers. They are applied to different entities as the yield of the discount factor or the discount factor itself for instance. We introduce the hedge error as practical quality criterion and compare the different curve construction methods using two different hedging algorithms: a short-term buy-and-sell and a long-term buy-and-hold strategy. As they are also implemented in Java, a wide range of numerical experiments is performed on historical market data. We find that the hedge simulation works well both in the single- and in the multi-curve setting. However, in the latter case the analysis is considerably more elaborate. The selected lattice of market data plays an important role for the forward curve calibration as well as for the performance of the hedge simulation under different interpolation methods. The analysis is rounded off by several experiments regarding the stability of the hedge error.