Stochastic Calculus for Finance Instructor: Shixiang Xia City University of Hong Kong Semester A, 2023 1/8 Why this course? ▶ We live in a random world • We want to better understand the world around us • And possibly anticipate what might happen in the future ▶ Nowadays many fields use complex models to represent the real world • Those models cannot simply come out of thin air • Must be rigorous and sophisticated • Stochastic calculus provides very useful building blocks ▶ Both finance academia and industry make extensive use of stochastic modeling • One of the (most) central questions in finance: what is the price of an asset? Or relatedly, what is the expected return on an asset? • We will apply stochastic modeling to option pricing 2/8 Why this course? ▶ Stochastic calculus is a valuable skill that can significantly enhance your qualifications for a quant career • Financial modeling: model asset prices, interest rates, volatility, etc, which are essential for pricing derivatives, risk management, and developing trading strategies • Derivatives pricing: derive pricing formulas or develop numerical methods to calculate the fair value of derivatives such as options, futures, and swaps • Risk management: quantify and manage risk in financial portfolios; estimate the potential losses or gains associated with different investment strategies and make informed decisions about risk exposure • Algorithmic trading: identify patterns, trends, or statistical anomalies that may indicate profitable trading opportunities • Calibration and estimation: estimate and calibrate parameters of stochastic models based on observed data, which is important for improving the accuracy of pricing models and risk assessments 3/8 Why this course? ▶ Salary information according to Glassdoor (August, 2023) • Quantitative Analyst: average total pay HK$1,238,500 per year in the Hong Kong Average base pay: HK$900,000 Average additional cash compensation: HK$338,500, with a range from HK$112,500 – HK$775,000 Focus on practical implementation, modeling, and risk management • Quantitative Researcher: average total pay HK$1,880,000 per year in the Hong Kong Average base pay: HK$1,000,000 Average additional cash compensation: HK$880,000, with a range from HK$550,000 – HK$1,600,000 Focus on theoretical research and innovation 4/8 Why this course? ▶ Knowing stochastic calculus is just one component of being a quant; other components include statistical modeling, numerical methods, optimization, and machine learning • Many of these topics will be covered by our program • You may also choose elective courses that include these topics ▶ A strong foundation in stochastic calculus will provide you with a solid framework for understanding and applying these other concepts effectively 5/8 About this course ▶ The course is divided into two parts: discrete time and continuous time ▶ You will be equipped with the following tools • Essential probability tools Required to “understand” the language of math finance probability space, random variable, expectations, filtration, independence, conditional expectations • Essential math finance tools Key ideas and tools in math finance Brownian motion, Itô’s Lemma, stochastic integral, SDE, RN pricing, Black-Scholes pricing formula, option Greeks 6/8 About this course ▶ Contact information • Please send your questions and homework solutions to cityu.teaching+EF5250@gmail.com • Please do not send to my CityU email ▶ Assessment • Problem sets (45%) You need to form a group of 3-4 students for problem sets About 5 assignments in total The lowest homework score will be dropped Significant penalties for late submissions • Peer evaluation (5%) Evaluate your group members’ contributions to problem sets • Final exam (50%) On campus, close book, close notes Details to be announced by the University 7/8 About this course ▶ Textbooks • Required: Stochastic Calculus for Finance I and Stochastic Calculus for Finance II, both by Steven Shreve • Optional: Stochastic Calculus and Financial Applications by J. Michael Steele ▶ Other references • Principles of Mathematical Analysis by Walter Rudin • Asset Pricing and Portfolio Choice Theory by Kerry Back ▶ Other details • Please refer to the syllabus 8/8
