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We propose a Markov regime switching GARCH model with multivariate normal tempered stable innovation to accommodate fat tails and other stylized facts in returns of financial assets. The model is used to simulate sample paths as input for portfolio optimization with risk measures, namely, conditional value at risk and conditional drawdown. The motivation is to have a portfolio that avoids left tail events by combining models that incorporates fat tail with optimization that focuses on tail risk. In-sample test is conducted to demonstrate goodness of fit. Out-of-sample test shows that our approach yields higher performance measured by Sharpe-like ratios than the market and equally weighted portfolio in recent years which includes some of the most volatile periods in history. We also find that suboptimal portfolios with higher return constraints tend to outperform optimal portfolios.
We study portfolio optimization of four major cryptocurrencies. Our time series model is a generalized autoregressive conditional heteroscedasticity (GARCH) model with multivariate normal tempered stable (MNTS) distributed residuals used to capture t
This paper develops the first closed-form optimal portfolio allocation formula for a spot asset whose variance follows a GARCH(1,1) process. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize the expecte
We present a multigrid iterative algorithm for solving a system of coupled free boundary problems for pricing American put options with regime-switching. The algorithm is based on our recently developed compact finite difference scheme coupled with H
When applying Value at Risk (VaR) procedures to specific positions or portfolios, we often focus on developing procedures only for the specific assets in the portfolio. However, since this small portfolio risk analysis ignores information from assets
In this paper, we study a free boundary problem, which arises from an optimal trading problem of a stock that is driven by a uncertain market status process. The free boundary problem is a variational inequality system of three functions with a degen