Course 2024-2025 a.y.

• Valuation and replication of American and path-dependent options via lattice methods.
• Valuation and replication of basket options in a multidimensional diffusive framework. Currency markets and quanto options.
• Valuation of European options in the jump-diffusion model.
• Monte Carlo methods in financial engeneering: efficiency and bias. Simulation of asset prices. Derivatives valuation. Variance reduction techniques. Valuation of the Greeks.
• Introduction to VBA: routines, functions, plots, arrays, user forms. Comparison with Python.

• Select the proper techniques to address path-dependency and American exercise features of financial derivatives.
• Implement multivariate diffusive models to account for the covariance structure among financial assets;  price and hedge basket derivative securities.
• Use jump diffusive models for financial assets and price by no-arbitrage European derivatives on these underlyings.
• Master Monte Carlo methods to simulate asset prices, evaluate derivatives and their greeks, enhance the accuracy of the estimate.

Solve core computational issues in financial engeneering as:

• Price and replicate path-dependent and American options with trees.
• Evaluate multiasset derivatives via Monte Carlo methods.
• Enhance the accuracy of their Monte Carlo estimate via suitable variance reduction techniques.
• Compute Greeks with various Monte Carlo methods.
• Develop algorithms in VBA and Python.
• Prepare an executive report on one of the aformentioned topics.

• Lectures
• Practical Exercises
• Individual works / Assignments
• Collaborative Works / Assignments

Theory classes outline the pricing and hedging problems in different enviroments (discrete-time and continuous-time uni- and multivariate market models) and provide technical solutions for them. The most significant applications will be implemented during the lab sessions.
 

Students will be introduced to VBA (Visual Basic for Applications) and Python, and tutored in the implementation of the alghorithms in the lab sessions. However VBA is not mandatory: students proficient with Python, R or MatLab are allowed to use their preferred language instead of VBA for the assignment.
 

The assignment can be shared by a student group, or can be done individually. Attending students only present their preliminary results during the last class of the course. Presentations offer the chance to get comments and feedback by instructors and colleagues and are not graded. However, presentations allow students to test their ability in delivering technical presentations.

The assessment consists of a brief written individual exam and an assignment.

The brief written individual exam counts 70% and consists of open and closed questions on the main arguments of the classes.

One (open) question  requires to compute the price and/or the replicating strategy of a financial derivative. The other open/closed questions verify students  have acquired the necessary knowledge of the theory topics. A detailed list of the theory topics required for the exam will be distributed by the end of the course.

The assignment counts 30% and consists in writing a code to solve a selected problem as, for example, the evaluation of a particular path-dependent option, and a brief report on the related numerical/financial issues. Students can choose to code with VBA, Python or any other preferred language (e.g. R, MatLab). The list of assignment titles and instructions are provided during the course. The assignment can be done in groups or individually, and is due the same day of the written exam.  The assignment grade is valid until the end of the academic year.

The assignment allows students to deepen their knowledge on the specific selected topic, by writing a code, analyzing the numerical and financial critical issues, and by preparing a technical report. The assignment verifies the coding ability of the students, and their ability to price and replicate derivatives with trees, or Monte Carlo methods.

Lecture notes, slides, and codes distributed by the instructors via BBoard.

A book closely aligned with our program for the continuous-time portion is "Monte Carlo Methods for Financial Engineering," by P. Glassermann, Springer ed.  

This book is fully optional, as all material is covered in the lecture notes, yet it offers insight into the level and the arguments of the course.