金融数学小型研讨会（地点：数学楼三楼会议室）
报告一
报告人：梁进（教授），单位：同济大学威尼斯人
报告时间：2017年4月15日 14：00-14：40
题目： 信用等级变换的自由边界模型的一些发展
摘要：报告信用等级变换的自由边界模型的一些最新进展，包括考虑多信用等级、宏观状态转换、首次穿过违约边界、随机利率等情形，以及在信用衍生品如CDS，CCIRS，可转债课赎回债券上的应用。
报告二
报告人：许威（教授），单位：同济大学威尼斯人
报告时间：2017年4月15日 14：40-15：20
题目： Moment Matching Machine Learning Methods for Risk Management of Large Variable Annuity Portfolios
摘要：Variable annuity (VA) with embedded guarantees have rapidly grown in popularity around the world in recent years. Valuation of VAs has been studied extensively in past
decades. However, most of the studies focus on a single contract. These methods can be extended neither to valuate nor to manage the risk of a large variable annuity portfolio
due to the computational complexity. In this paper, we propose an efficient moment matching machine learning method to solve this problem. This method is proved to be a good candidate for risk management in terms of the speed of and the complexity of computing the annual dollar deltas, VaRs and CVaRs for a large variable annuity portfolio whose contracts are over a period of 25 years. There are two stages for our method. First, we select a small number of contracts and propose a moment matching Monte Carlo method based on the Johnson curve, rather
than the well known nested simulations, to compute the annual dollar deltas, VaRs and CVaRs for each selected contract. Then, these computed results are used as a training set for well known machine learning methods, such as regression tree , neural network and so on. Afterwards, the annual dollar deltas, VaRs and CVaRs for the entire portfolio {/em are predicted} through the trained machine learning method. Compared to other existing methods, our method is very efficient and accurate. Finally, our test results support our claims.
报告三
报告人：马成虎（教授），单位：复旦大学管理学院
报告时间：2017年4月15日 15：20-16：00
题目：“European Options：The DNA in Finance ”
Abstract: In this presentation I shall provide a survey on the information content of European options for revealing both the fundamental and the technical aspects of the underlying securities. We shall identify the role of European options for revealing the term structure of interest rates, futures price, future volatility (VIX), investors' aggregated preference/sentiment, and more generally the risk-neutral pricing kernel in an arbitrage free market environment. An option-based asset pricing model will be also presented.
The presentation is largely based on my recently published books:
《金融经济学原理》，清华大学出版社，2016
“Advanced Asset Pricing Theory", Imperial College Press: London， 2011
报告四
报告人：徐承龙（教授），单位：同济大学威尼斯人
报告时间：2017年4月15日 16：00-16：40 Abstract: This paper constructs an efficient hybrid Monte Carlo variance reduction method for pricing European options driven by Levy process. The hybrid variance reduction method combines conditional Monte Carlo(CMC) and importance sampling(IS) technique. Owing to the structure of movement of asset price and Black-Scholes formula, we formulate the conditional expectation of the European option price under Levy process and then the IS method is used to reduce simulation variance greatly. Since the conditional expectation formula is smooth with respect to(w.r.t) the concerned parameters, the Greeks, which means the gradient of the option price to the parameters, can be calculated conveniently and efficiently. Furthermore, we proposed a very efficient prediction-correction algorithm to determine the optimal parameters in the importance sampling measure based on the moments match idea and iteration correction algorithm. Numerical examples confirm that our hybrid acceleration method has reasonable variance reduction effect and the prediction-correction algorithm determining the optimal parameters in the importance sampling measure can save a lot of time cost than the traditional Newton's iteration method. Some theoretical results are also given such as convergence of sample average approximation (SAA) method and the existence and uniqueness of the optimal problem determining the parameters in the importance sampling measure.