This chapter focuses on switching diffusions with two-time scales. It consists of two parts. The first part considers a stochastic volatility model using regime-switching diffusions with fast mean reversion. It develops asymptotic expansions for option pricing and establishes the asymptotic error bounds for these expansions. The second part of the chapter considers the states of the discrete event process belonging to several “ergodic” classes that are weakly connected. The underlying switching diffusion is shown to be positive recurrent under mild conditions.

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Two-Time-Scale Switching Diffusions

  • Hai-Dang Nguyen,
  • George Yin,
  • Chao Zhu

摘要

This chapter focuses on switching diffusions with two-time scales. It consists of two parts. The first part considers a stochastic volatility model using regime-switching diffusions with fast mean reversion. It develops asymptotic expansions for option pricing and establishes the asymptotic error bounds for these expansions. The second part of the chapter considers the states of the discrete event process belonging to several “ergodic” classes that are weakly connected. The underlying switching diffusion is shown to be positive recurrent under mild conditions.