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<p>Empirical evidence suggests that asset prices exhibit mean reversion, stochastic volatility, and jumps; however, most option-pricing studies focus on tractable affine models. This paper develops a pricing framework for a more flexible non-affine model that combines mean reversion with stochastic volatility and jumps. Since the governing partial integro-differential equation does not have a closed-form solution, we propose an efficient, high-order Chebyshev pseudospectral scheme. The method accurately prices both European and American options, as verified against Monte Carlo benchmarks. A key advantage is that it computes the early-exercise boundary for American options directly, allowing for an analysis of how this boundary varies with the underlying price and volatility as maturity approaches.</p>

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Chebyshev Pseudospectral Method for Option Valuation Under the Mean Reversion, Jumps, and Non-Affine Stochastic Volatility Model

  • 期刊论文

  • 发表日期：

    2026年6月20日

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  • Ting-Fu Chen,
  • Tzyy-Leng Horng

摘要

Empirical evidence suggests that asset prices exhibit mean reversion, stochastic volatility, and jumps; however, most option-pricing studies focus on tractable affine models. This paper develops a pricing framework for a more flexible non-affine model that combines mean reversion with stochastic volatility and jumps. Since the governing partial integro-differential equation does not have a closed-form solution, we propose an efficient, high-order Chebyshev pseudospectral scheme. The method accurately prices both European and American options, as verified against Monte Carlo benchmarks. A key advantage is that it computes the early-exercise boundary for American options directly, allowing for an analysis of how this boundary varies with the underlying price and volatility as maturity approaches.