论文标题
用随机漂移和扩散校准局部波动率模型
Calibrating Local Volatility Models with Stochastic Drift and Diffusion
论文作者
论文摘要
我们提出了三种模型的蒙特卡洛校准算法：具有随机利率的局部波动性，随机利率的随机局部波动性，确定利率确定性利率，最后是随机利率的随机局部波动性。对于每个模型，我们包括相应SDE系统的详细推导，并列出所需的输入数据和校准步骤。我们提供的条件下，鉴于欧洲期权价格，随机利率模型参数和相关性，可以存在地方波动。这些模型是在外汇设置中摆放的。汇率的漂移项为两个随机短率的差异，即国内和外国，每个差额由G1 ++工艺建模。对于随机波动率，我们通过CIR过程对汇率的方差进行建模。我们包括测试以显示所提出算法的收敛性和准确性。
We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and finally stochastic local volatility with stochastic interest rates. For each model, we include detailed derivations of the corresponding SDE systems, and list the required input data and steps for calibration. We give conditions under which a local volatility can exist given European option prices, stochastic interest rate model parameters, and correlations. The models are posed in a foreign exchange setting. The drift term for the exchange rate is given as a difference of two stochastic short rates, domestic and foreign, each modeled by a G1++ process. For stochastic volatility, we model the variance for the exchange rate by a CIR process. We include tests to show the convergence and the accuracy of the proposed algorithms.
