13 research outputs found
Consistent Re-Calibration of the Discrete-Time Multifactor Vasi\v{c}ek Model
The discrete-time multifactor Vasi\v{c}ek model is a tractable Gaussian spot
rate model. Typically, two- or three-factor versions allow one to capture the
dependence structure between yields with different times to maturity in an
appropriate way. In practice, re-calibration of the model to the prevailing
market conditions leads to model parameters that change over time. Therefore,
the model parameters should be understood as being time-dependent or even
stochastic. Following the consistent re-calibration (CRC) approach, we
construct models as concatenations of yield curve increments of Hull-White
extended multifactor Vasi\v{c}ek models with different parameters. The CRC
approach provides attractive tractable models that preserve the no-arbitrage
premise. As a numerical example, we fit Swiss interest rates using CRC
multifactor Vasi\v{c}ek models.Comment: 29 pages, 16 figures, 2 table
Hedging of long term zero-coupon bonds in a market model with reinvestment risk
We present a computational methodology to value and hedge long term zero-coupon bonds trading in short and medium term ones. For this purpose we develop a discrete time stochastic yield curve model with limited availability of maturity dates at a fixed time point and newly issued bonds at future time points. This involves reinvestment risk and there is no perfect hedging strategy available for long term liabilities. We calibrate the model to market data and describe optimal hedging strategies under a given risk tolerance. These considerations provide a natural extrapolation of the yield curve beyond the last liquid maturity date, and a framework which allows to value long term insurance liabilities, for instance, under Solvency 2. Moreover, we determine the optimal trading strategy replicating the liabilities under the given risk tolerance
Affine representations of fractional processes with applications in mathematical finance
Hedging of long term zero-coupon bonds in a market model with reinvestment risk
We present a computational methodology to value and hedge long term zero-coupon bonds trading in short and medium term ones. For this purpose we develop a discrete time stochastic yield curve model with limited availability of maturity dates at a fixed time point and newly issued bonds at future time points. This involves reinvestment risk and there is no perfect hedging strategy available for long term liabilities. We calibrate the model to market data and describe optimal hedging strategies under a given risk tolerance. These considerations provide a natural extrapolation of the yield curve beyond the last liquid maturity date, and a framework which allows to value long term insurance liabilities, for instance, under Solvency 2. Moreover, we determine the optimal trading strategy replicating the liabilities under the given risk tolerance.ISSN:2190-9733ISSN:2190-974
Model risk in portfolio optimization
We consider a one-period portfolio optimization problem under model uncertainty. For this purpose, we introduce a measure of model risk. We derive analytical results for this measure of model risk in the mean-variance problem assuming we have observations drawn from a normal variance mixture model. This model allows for heavy tails, tail dependence and leptokurtosis of marginals. The results show that mean-variance optimization is seriously compromised by model uncertainty, in particular, for non-Gaussian data and small sample sizes. To mitigate these shortcomings, we propose a method to adjust the sample covariance matrix in order to reduce model risk