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We propose a new class of models for pricing generalized variance swaps. We assume that, in the most general form, the process for the asset price is a function of a general time-homogeneous diffusion process belonging to a symmetric pricing semigroup, time changed by a composition of a Lévy subordinator and an absolutely continuous process. We derive the analytical pricing formulas for various types of generalized variance swaps based on eigenfunction expansion method. We also numerically implement the model and test its sensitivity to some of the key parameters of the model.

When the broken rotor bar (BRB) fault occurs in induction motors, the amplitude of stator fundamental current is modulated by fault components, forming the current envelope with a particular frequency, which can be considered as a powerful criterion for BRB detection. However, it is relatively difficult to extract especially at time-varying loads due to the nonstationary characteristics. Thus, a novel envelope extraction method (EEM) combining fast Fourier transform and sliding overlapping window is proposed and the overall performance is tested by simulation. The results show that the method is capable to effectively extract the current envelope, but the extraction accuracy is unsatisfied due to the spectrum leakage in the case of non-integer periodic truncation. The technique of discrete spectrum correction is then introduced into EEM to improve its extraction accuracy, and then, an improved EEM (IEEM) is proposed and then tested by simulation. The results show that the IEEM is able to eliminate the impact of non-integer periodic truncation, effectively and accurately extract the current envelope. Finally, the two methods are applied in BRB fault online detection of 1.1 and 2.2 kW induction motors at time-varying loads. The corresponding experimental results demonstrate its validity and universality again.

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In this paper, we introduce the stochastic correlation processes for modeling the credit spread. We first model the components of spread process as correlated Ornstein-Uhlenbeck processes and correlation as Jacobi process. Using the properties of Jacobi process, we are able to obtain the analytical solutions for the credit spread option prices. To further enhance the model's ability to capture the abrupt changes in the observed correlation time series, we construct a new model where the correlation is modeled by a Jacobi process time change by Lévy subordinators. We employ the eigenfunction expansion methods to obtain the closed-form solutions for the option prices. Our empirical study indicates the time changed Jacobi process fits the correlation series significantly better than the Jacobi process.