Asset Pricing: Modeling and Estimation by B.Philipp Kellerhals

By B.Philipp Kellerhals

The smooth box of asset pricing asks for sound pricing versions grounded at the conception of economic economies a l. a. Ingersoll (1987) as weIl as for accu­ fee estimation suggestions a l. a. Hamilton (1994b) by way of empirical inferences of the desired version. the assumption in the back of this ebook available is to supply the reader with a canonical framework that exhibits the right way to bridge the space among the continuous-time pricing perform in monetary engineering and the capital marketplace info unavoidably purely to be had at discrete time periods. 3 significant monetary markets are to be tested for which we pick out the fairness marketplace, the bond marketplace, and the electrical energy marketplace. In every one mar­ ket we derive new valuation types to cost chosen monetary tools in continuous-time. the choice criterium for selecting a continuous-time version­ ing framework is the richness of the stochastic concept on hand for non-stop­ time strategies with Merton's pioneering contributions to monetary economics, accumulated in Merton (1992). The continuous-time framework, reviewed and as­ sessed through Sundaresan (2000), permits us to acquire analytical pricing formulae that might be unavailable in a discrete time atmosphere. in spite of the fact that, on the time of enforcing the derived theoretical pricing versions on marketplace info, that's unavoidably sampled at discrete time durations, we paintings with so-called specific discrete time equivalents a l. a. Bergstrom (1984). We convey the best way to very easily paintings inside astate area framework which we derive in a common surroundings as weIl as explicitly for every of the 3 applications.

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3 (Optimal Estimator). 9 The corresponding MSE is given by i. e. in this case the mean square error matrix is equal to the variance- covariance matrix. e. the information set F s = {ys, . ,y2, yd, we denote the conditional expectation of ~t given Fs in the further analysis for convenience by JE [~tIFs] == ~tIs. For the second conditional moment we will further use Cov [~tIFs] == Etls, the conditional variance-covariance matrix of ~t given F s . 1 Filtering Objective Having gone through the necessary preliminaries, we will see in this section that the KaIman filter is a set of equations which allows an estimator to be 8 9 See, für example, Jazwinski (1970, p.

G o 52 . , . , . , . , 104 156 208 260 Fig. 1. ROC Taiwan Fund (ROC) holding in a fund, the investors need to sell their shares to other investors for the market price instead of selling and redeeming them at or near their net asset value as with open-end funds. Thus, closed-end funds are endowed with an inelastic supply of shares. Considering the closed-end funds in our sample3 we can identify three different patterns of empirical premia behavior over time: (i) Premia which change from positive to negative values over the examined period of time, (ii) mainly positive premia over time, and (iii) negative premia or discounts for the major part of the sample.

14 Further, we constrain our analysis of Kalman filters on algorithms that are derived frorn the Taylor series expansions, Le. we only deal with extended Kalman filters. For the exposition of the extended Kalman filter algorithms we work with the following general state space model. 12 13 14 Note that these are then formally indexed with t - 1, since we denote the actual information we are working with by the time index t. See, for example, Anderson and Moore (1979) and Tanizaki (1996). For a detailed comparison of different non-linear filtering algorithms see Tanizaki (1996).

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