Pricing and hedging autocallable products by Markov chain approximation

We propose a unified pricing framework based on continuous-time Markov chain (CTMC) approximation for autocallable structured products. Our method is applicable to a variety of asset price models, including one-dimensional Markov jump-diffusions (the coefficients can be time dependent), regime-switching models, and stochastic local volatility (SLV) models. For SLV models, we develop a hybrid Markov chain approximation scheme that significantly improves the existing CTMC approximation method. We test our pricing method under various popular models and show that it is computationally efficient. To hedge autocallable products, we consider a dynamic hedging approach in the presence of transaction costs. To address the problem that the product’s delta can become too large near the barriers, we apply payoff modification and barrier shifting techniques. We determine the optimal size of adjustments that minimize conditional value-at-risk (CVaR) of the hedging loss using stochastic gradient descent. Empirical experiments demonstrate the effectiveness of our approach in reducing CVaR of the hedging loss.