| 1. |
- Lindberg, Carl, 1978
(författare)
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News-generated dependence and optimal portfolios for n stocks in a market of Barndorff-Nielsen and shephard type
- 2006
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Ingår i: Mathematical Finance. - 0960-1627 .- 1467-9965. ; 16:3, s. 549-568
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Tidskriftsartikel (refereegranskat)abstract
- We consider Merton's portfolio optimization problem in a Black and Scholes market with non-Gaussian stochastic volatility of Ornstein-Uhlenbeck type. The investor can trade in n stocks and a risk-free bond. We assume that the dependence between stocks lies in that they partly share the Ornstein-Uhlenbeck processes of the volatility. We refer to these as news processes, and interpret this as that dependence between stocks lies solely in their reactions to the same news. The model is primarily intended for assets that are dependent, but not too dependent, such as stocks from different branches of industry. We show that this dependence generates covariance, and give statistical methods for both the fitting and verification of the model to data. Using dynamic programming, we derive and verify explicit trading strategies and Feynman-Kac representations of the value function for power utility.
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| 2. |
- Lindberg, Carl, 1978
(författare)
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Portfolio Optimization and Statistics in Stochastic Volatility Markets
- 2005
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Large financial portfolios often contain hundreds of stocks. The aim of this thesis is to find explicit optimal trading strategies that can be applied to portfolios of that size for different n-stock extensions of the model by Barndorff-Nielsen and Shephard [3]. A main ambition is that the number of parameters in our models do not grow too fast as the number of stocks n grows. This is necessary to obtain stable parameter estimates when we fit the models to data, and n is relatively large. Stability over the parameter estimates is needed to obtain accurate estimates of the optimal strategies. Statistical methods for fitting the models to data are also given. The thesis consists of three papers. Paper I presents an n-stock extension to the model in [3] where the dependence between different stocks lies strictly in the volatility. The model is primarily intended for stocks that are dependent, but not too dependent, such as stocks from different branches of industry. We develop optimal portfolio theory for the model, and indicate how to do the statistical analysis. In Paper II we extend the model in Paper I further, to model stronger dependence. This is done by assuming that the diffusion components of the stocks contain one Brownian motion that is unique for each stock, and a few Brownian motions that all stocks share. We then develop portfolio optimization theory for this extended model. Paper III presents statistical methods to estimate the model in [3] from data. The model in Paper II is also considered. It is shown that we can divide the centered returns by a constant times the daily number of trades to get normalized returns that are i.i.d. and N(0,1). It is a key feature of the Barndorff-Nielsen and Shephard model that the centered returns divided by the volatility are also i.i.d. and N(0,1). This suggests that we identify the daily number of trades with the volatility, and model the number of trades within the framework of Barndorff-Nielsen and Shephard. Our approach is easier to implement than the quadratic variation method, requires much less data, and gives stable parameter estimates. A statistical analysis is done which shows that the model fits the data well.
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| 3. |
- Lindberg, Carl, 1978
(författare)
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Portfolio optimization when expected stock returns are determined by exposure to risk
- 2009
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Ingår i: Bernoulli. - 1350-7265. ; 15:2, s. 464-474
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Tidskriftsartikel (refereegranskat)abstract
- It is widely recognized that when classical optimal strategies are applied with parameters estimated from data, the resulting portfolio weights are remarkably volatile and unstable over time. The predominant explanation for this is the difficulty of estimating expected returns accurately. In this paper, we modify the n stock Black-Scholes model by introducing a new parametrization of the drift rates. We solve Markowitz' continuous time portfolio problem in this framework. The optimal portfolio weights correspond to keeping 1/n of the wealth invested in stocks in each of the n Brownian motions. The strategy is applied out-of-sample to a large data set. The portfolio weights are stable over time and obtain a significantly higher Sharpe ratio than the classical 1/n strategy.
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| 4. |
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| 5. |
- LINDBERG, CARL, 1978
(författare)
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The estimation of the Barndorff-Nielsen and Shephard model from daily data based on measures of trading intensity
- 2008
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Ingår i: Applied Stochastic Models in Business and Industry. - : Wiley. - 1526-4025 .- 1524-1904. ; 24:4, s. 277-289
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Tidskriftsartikel (refereegranskat)abstract
- We give a method to fit the Barndorff-Nielsen and Shephard model [J. R. Stat. Soe. Ser. B 2001; 63:167-241] to daily data. Many researchers have established a connection between volatility and different measures of trading intensity, such as traded volume or number of trades. We benefit from this connection, and propose to use some measure of trading intensity as the volatility in the model in [J. R. Stat. Soe. Ser. B 2001; 63:167-241] . Our approach gives stable parameter estimates, and it is much easier to implement than the quadratic variation method. The efficiency of our method is illustrated by a statistical analysis on the Ericsson stock from the OMX Stockholmsbörsen during an exceptionally turbulent period of five years. The results indicate a good model fit. Copyright © 2007 John Wiley & Sons, Ltd.
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