Browsing by Author "Yang, Fan"

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    Essays on asset pricing.
    (2011-06) Yang, Fan
    My dissertation investigates two important puzzles in derivatives markets. In Chapter one, I identify a “slope” factor in the cross section of commodity futures returns. Low-basis commodity futures have higher loadings on this factor than highbasis commodity futures. This slope factor and a level factor — an index of commodity futures — jointly explain most of the average futures returns in commodity futures portfolios sorted by basis. The risk price of this new factor is about 10% per annum. More importantly, I find that this factor is highly correlated with investment shocks, which represent the technological progress in producing new capital. Then, I investigate a competitive dynamic equilibrium model of commodity production to endogenize this correlation. The model reproduces the cross-sectional futures returns. Other major implications of the model are supported by data as well. Chapter two is coauthored with Pierre Collin-Dufresne and Robert Goldstein. We investigate a structural model of market and firm-level dynamics in order to jointly price long-dated S&P 500 options and tranche spreads on the five-year CDX index. We demonstrate the importance of calibrating the model to match the entire term structure of CDX index spreads because it contains pertinent information regarding the timing of expected defaults and the specification of idiosyncratic dynamics. Our model matches the time series of tranche spreads well, both before and during the financial crisis, thus offering a resolution to the puzzle reported by Coval, Jurek and Stafford (2009a).
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    Likelihood ratio tests for high-dimensional normal distributions.
    (2011-12) Yang, Fan
    For a random sample of size n obtained from p-variate normal distributions, we consider the likelihood ratio tests (LRT) for their means and covariance matrices. Most of these test statistics have been extensively studied in the classical multivariate analysis and their limiting distributions under the null hypothesis were proved to be a Chi-Square distribution under the assumption that n goes to infinity while p remains fixed. In our research, we consider the high-dimensional case where both p and n go to infinity and their ratio p/n converges to a constant y in (0, 1]. We prove that the likelihood ratio test statistics under this assumption will converge in distribution to a normal random variable and we also give the explicit forms of its mean and variance. We run simulation study to show that the likelihood ratio test using this new central limit theorem outperforms the one using the traditional Chi-square approximation for analyzing high-dimensional data.
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    A Personalized Recommender System with Correlation Estimation
    (2018-05) Yang, Fan
    Recommender systems aim to predict users’ ratings on items and suggest certain items to users that they are most likely to be interested in. Recent years there has been a lot of interest in developing recommender systems, especially personalized recommender systems to efficiently provide personalized services and increase conversion rates in commerce. Personalized recommender systems identify every individual’s preferences through analyzing users’ behavior, and sometimes also analyzing user and item feature information. Existing recommender system methods typically ignore the correlations between ratings given by a user. However, based on our observation the correlations can be strong. We propose a new personalized recommender system method that takes into account the correlation structure of ratings by a user. General precision matrices are estimated for the ratings of each user and clustered among users by supervised clustering. Moreover, in the proposed model we utilize user and item feature information, such as the demographic information of users and genres of movies. Individual preferences are estimated and grouped over users and items to find similar individuals that are close in nature. Computationally, we designed an algorithm applying the difference of convex method and the alternating direction method of multipliers to deal with the nonconvexity of the loss function and the fusion type penalty respectively. Theoretical rate of convergence is investigated for our new method. We also show theoretically that incorporating the correlation structure gives higher asymptotic efficiency of the estimators compared to ignoring it. Both simulation studies and Movielens data indicate that our method outperforms existing competitive recommender system methods.