# Teaching

## Programme Director:

I am the director of the **MSc in Quantitative Finance Programme** at Alliance Manchester Business School, one of four MSc programmes offered by the Accounting and Finance Division. The programme takes place over a period of twelve months and consists of two teaching semesters and an MSc dissertation semester. It attracts about 35-40 students per year. The students come from a variety of backgrounds, ranging from business & economics to technical subjects, such as statistics, mathematics, engineering, and computing. The students take classes in stochastic calculus, asset pricing theory, derivatives, credit risk derivatives, and interest rate derivatives, among others. They also have access to econometrics, survival analysis, and computing (C++ and Matlab) classes.

You can learn more about the MSc in Quantitative Finance Programme HERE.

## Course Director:

I am teaching two courses available to MSc students in AMBS and the School of Mathematics:

**1. Derivative Securities (available to MSc in Finance/Quantitative Finance/Math Finance students)**

The aim of the course is to make students familiar with important derivatives instruments, such as forwards, futures, plain-vanilla options, and exotic options. The courses starts by reviewing material taught in most derivatives classes at the undergraduate level: forwards (introduction, determination of the arbitrage-free forward price, and valuation); futures (introduction, and hedging with futures), and plain-vanilla options (introduction, arbitrage bounds, valuation using trees or continuous-time methods, and delta-hedging). It continues with more advanced material, such as non-Black-Scholes valuation models (e.g., jump-diffusion- or stochastic volatility-models), the valuation of derivatives using Monte Carlo simulation and finite difference methods, exotic options, and Value-at-Risk (VaR).

The course is taught based on Hull's (2017) "Options, Futures, and Other Derivatives."

You can find out more about the course by clicking HERE.

**2. Stochastic Calculus for Finance** **(available exclusively to MSc in Quantitative Finance students)**

The aim of the course is to make students familiar with the mathematical pre-requisites necessary to understand important financial models, such as the Black-Scholes models. The course starts off by introducing infinite probability spaces, talking about experiments, filtrations, and probability measures. It next reviews Brownian motion, studying several of its more important properties, such as quadratic variation. We then look at stochastic calculus concepts, talking about the Ito integral, the Ito-Doeblin formula (which is often called Ito's lemma), and the Levy theorem. In the final parts related to risk-neutral pricing, we review Girsanov's theorem, the central risk-neutral pricing result, and the two fundamental theorems of asset pricing (involving arbitrage and the completeness of markets).

The course is taught based on Shreve's (2004/10) "Stochastic Calculus for Finance II: Continuous-Time Models."

You can find out more about the course by clicking HERE.