Current office hours:  Th 11:00 am-12:00 pm  

           You can also make an appointment: hongkun@math.umass.edu                                                   

        Text Book:   Tomas Bjork: Arbitrage theory in continuous time. (Oxford), 3rd ed, 2003;

        Reference  Book:  S. Shreve, Stochastic Calculus for Finance II: Continuous-Time Models, Springer, 2004;

                   Reference  Book:   Shiryaev, A: Essentials of Stochastic Finance. (World Scienti c, Singapore), 1999.

        Prerequisites:   797SC or approved by the instructor

        Yahoo finance:    finance.yahoo.com

        Google finance:    https://www.google.com/finance

         
       Course Description:  

This is a one-year long topic course which consists of two parts: (I) Stochastic Calculus (II) Applications in Finance and Risk Management.

The purpose of this topic class is to expose our graduate students to the mathematical concepts and techniques used in the study of time series in financial industry, network and engineering. We will investigate the time series that arise in the area of applications, focusing on modeling and risk management. Examples include portfolio selection option pricing, arbitrage, single-agent optimization, the Fundamental Theorem of Asset Pricing, and the Black-Scholes formula. In the Spring Semester of 2017, we will cover applications to finance mathematics and risk management of financial securities. Extremal events appear in very different areas such as insurance, finance, telecommunications, hydrology, meteorology, and engineering, and make daily headlines in the media. The course gives an introduction to the modern extreme value theory and extreme value statistics, which enables students to model extremes in these areas. We will study 1) Continuous time models. Admissible strategies. Pricing and hedging in Markovian models. The Black-Scholes model. Local and stochastic volatility models. Interest rate models. Arbitrage Pricing Theory using martingale approach, Hedging and completeness, Parity relations and Delta Hedging, Currency derivatives, Barrier options, Optimal investment, and pricing of other popular derivatives. 2) Extreme Value Theory and its application to risk management of financial securities and portfolios. Software like Splus and R will be used in some of the excercises.

Some references: (1) Mikosch,T., Elementary Stochastic Calculus with Finance in View, World Scientific 1998.

(2) Shreve, S., Stochastic Calculus and Finance, Lecture notes, 1997.

(3) Steele, J.M., Stochastic Calculus and Financial Applications, Springer 2000.

(4) Fries, C.P., Mathematical Finance: Theory, Modeling and Implementation, 2006.

(5) Kuo, H.-H., Introduction to Stochastic Integration, Springer 2006.

(6) Varadhan,S.R.S., Stochastic Processes, Lecture notes, AMS 2007.

(7) Quastel,J., Notes for Stochastic calculus for Mathematical Finance, University of Toronto, http://www.math.toronto.edu/quastel/fin.h

(8) P. Embrechts, C. Klueppelberg, T. Mikosch. Modelling Extremal Events for Finance and Insurance. Springer, Heidelberg, 1997. 9th Printing 2012

        Home work assignment: There will be excercises throughtout the semester, and a take-home final exam.