论文标题
仿射跳转模型的渐近微笑
Asymptotic Smiles for an Affine Jump-Diffusion Model
论文作者
论文摘要
在本文中，我们研究了仿射跳扩散模型隐含波动性的渐近行为。让日志股票价格低于风险中立的措施遵循仿射跳转模型，我们表明，可以通过求解一组普通的微分方程来获得对数股票价格的明确形式生成量。通过应用Gärtner-ellis定理，得出了对数股票价格的大型大偏差原则。我们表征了在大偏差原理中使用速率函数在大成熟度和大损坏方面中隐含波动率的渐近行为。还研究了黑色 - 甲状腺的渐近造成固定成熟度，大污垢和固定性成熟度的渐进性。提供数值结果以验证理论工作。
In this paper, we study the asymptotic behaviors of implied volatility of an affine jump-diffusion model. Let log stock price under risk-neutral measure follow an affine jump-diffusion model, we show that an explicit form of moment generating function for log stock price can be obtained by solving a set of ordinary differential equations. A large-time large deviation principle for log stock price is derived by applying the Gärtner-Ellis theorem. We characterize the asymptotic behaviors of the implied volatility in the large-maturity and large-strike regime using rate function in the large deviation principle. The asymptotics of the Black-Scholes implied volatility for fixed-maturity, large-strike and fixed-maturity, small-strike regimes are also studied. Numerical results are provided to validate the theoretical work.
