Pricing, hedging and testing risky assets in financial markets
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State price density (SPD) and stochastic discount factor (SDF) are important elements in asset pricing. In this thesis, I first propose to use projection pursuit regression (PPR) and local polynomial regression (LPR) to estimate the SPD of interest rates nonparametrically. By using a similar approach, I also estimate the delta values in the interest rate options and discusses how to delta-hedge these options. Unlike SPD measured in a risk-neutral economy, SDF is implied by an asset pricing model. It displays which prices are reasonable given the returns in the current period. Hansen and Jagannathan (1997) develop the Hansen-Jagannathan distance (HJ-distance) to measure pricing errors produced by SDF. While the HJ-distance has several desirable properties, Ahn and Gadarowski (2004) find that the specification test based on the HJ-distance overrejects correct models too severely in commonly used sample size to provide a valid test. This thesis proposes to improve the finite sample properties of the HJ-distance test by applying the shrinkage method (Ledoit and Wolf, 2003) to compute its weighting matrix.