A General Benchmark Model for Stochastic Jump Sizes

This paper extends the benchmark framework of Platen (2002) by introducing a sequence of incomplete markets, having uncertainty driven by a Wiener process and a marked point process. By introducing an idealized market, in which all relevant economical variables are observed, but may not all be traded, a generalized growth optimal portfolio (GOP) is obtained and calculated explicitly. The problem of determining the GOP is solved in a general setting which extends existing treatments and provides a clear link to the market prices of risk. The connection between traded securities, arbitrage and market incompleteness is analyzed. This provides a framework for analyzing the degree of incompleteness associated with jump processes, a problem well-known from insurance and credit risk modeling. By staying under the empirical measure, the resulting benchmark model has potential advantages for various applications in finance and insurance.

Sharpe Ratio Maximization and Expected Utility when Asset Prices have Jumps

We analyze portfolio strategies which are locally optimal, meaning that they maximize the Sharpe ratio in a general continuous time jump-diffusion framework. These portfolios are characterized explicitly and compared to utility based strategies. In the presence of jumps, maximizing the Sharpe ratio is shown to be generally inconsistent with maximizing expected utility, but this is shown to depend strongly on market completeness and whether event risk is priced.

The Implied-Realized Volatility Relation with Jumps in Underlying Asset Prices

Recent developments allow a nonparametric separation of the continuous sample path component and the jump component of realized volatility. The jump component has very different time series properties than the continuous component, and accounting for this allows improved forecasting of future realized volatility. We investigate the potential forecasting role of implied volatility backed out from option prices in the presence of these new separate realized volatility components. We show that implied volatility has incremental information relative to both the continuous and jump components of realized volatility when forecasting subsequently realized return volatility, and it appears to be an unbiased forecast. Furthermore, implied volatility has predictive power for future values of each component of realized volatility separately, showing in particular that even the jump component of realized volatility is, to some extent, predictable.Bipower variation, implied volatility, instrumental variables, jumps, options, realized volatility, stock prices, vector autoregressive model, volatility forecasting

The Information Content of Treasury Bond Options Concerning Future Volatility and Price Jumps

We study the relation between realized and implied volatility in the bond market. Realized volatility is constructed from high-frequency (5-minute) returns on 30 year Treasury bond futures. Implied volatility is backed out from prices of associated bond options. Recent nonparametric statistical techniques are used to separate realized volatility into its continuous sample path and jump components, thus enhancing forecasting performance. We generalize the heterogeneous autoregressive (HAR) model to include implied volatility as an additional regressor, and to the separate forecasting of the realized components. We also introduce a new vector HAR (VecHAR) model for the resulting simultaneous system, controlling for possible endogeneity of implied volatility in the forecasting equations. We show that implied volatility is a biased and inefficient forecast in the bond market. However, implied volatility does contain incremental information about future volatility relative to both components of realized volatility, and even subsumes the information content of daily and weekly return based measures. Perhaps surprisingly, the jump component of realized bond return volatility is, to some extent, predictable, and bond options appear to be calibrated to incorporate information about future jumps in Treasury bond prices, and hence interest rates.Bipower variation, bond futures options, HAR, Heterogeneous Autoregressive Model, implied volatility, jumps, realized volatility, VecHAR, volatility forecasting