快速均值回复随机波动率模型下的条件期望模拟
Simulation of conditional expectations under fast mean-reverting stochastic volatility models
摘要：
在这篇简短的论文中，我们研究了一个大型系统的随机过程的模拟，一个共同的驱动噪声和快速均值回复随机波动。该模型可用于描述大量金融实体的公司价值。然后，我们寻求一个有效的估计的违约概率，表明公司的价值低于一定的阈值，条件公共因子。我们考虑近似包含快速波动率的系数被某些遍历平均数（一种大数定律）所取代，并研究校正项（中心极限定理型）。这些近似的准确性进行评估的路径损失和支付函数的估计，因为它们出现在篮子信用衍生品的数值模拟。
英文摘要：
In this short paper, we study the simulation of a large system of stochastic processes subject to a common driving noise and fast mean-reverting stochastic volatilities. This model may be used to describe the firm values of a large pool of financial entities. We then seek an efficient estimator for the probability of a default, indicated by a firm value below a certain threshold, conditional on common factors. We consider approximations where coefficients containing the fast volatility are replaced by certain ergodic averages (a type of law of large numbers), and study a correction term (of central limit theorem-type). The accuracy of these approximations is assessed by numerical simulation of pathwise losses and the estimation of payoff functions as they appear in basket credit derivatives.
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