Continuous Time Asset Pricing lies at the heart of the modern theory of financial engineering . In this course, we distinguish between complete markets, in which there is a unique no-arbitrage price, and incomplete markets, where absence of arbitrage is not sufficient to obtain uniqueness of prices. We focus mostly on the framework of Brownian Motion driven models. The benchmark model will be the Black-Scholes-Merton pricing model, but we will also cover more general models, such as local and stochastic volatility models. We will discuss both the Partial Differential Equations approach, and the Martingale approach. They are related through the notion of the Feynman-Kac theorem. We also discuss optimal portfolio investment in the above mentioned models, and discuss relationship to pricing and risk management.
Risk Management is a topic of fundamental importance in financial markets. Quantitative risk management frameworks must be able to identify, quantify, and mitigate risks. There are various sources of risk faced by market participants, including market, credit, liquidity, and operational risk. The global 2007-2009 financial crisis has led to numerous regulatory reforms, which required banks to comply with more stringent capital requirements, including value at risk, expected shortfall, and maximum shortfalls. It also led to the introduction of financial utilities, such as clearinghouses, which collect all risk in the system and insulate each party against the default of the other. This course deals with quantitative modeling and measuring of risk. You will learn how to design risk management procedure which accounts for correlated risk sources, and how to simulate systems to evaluate the resulting risk. We introduce financial instruments that are used to mitigate risk, such as credit default swaps. Time allowing, we also discuss topics of recent interest in the financial industry and the regulatory environment, including systemic risk measures, liquidity coverage ratio requirements to deal with liquidity risk, and procedures to assess funding risk.