*This post is about the final term of the Imperial College Business School 2012-2013 MSc Finance programme. For the earlier posts, please go to the Imperial College category of this blog.*

The summer term ended about two weeks ago with the final exams of the programme. The final term consists exclusively of electives and a research project, which is due for submission in August. MSc Finance students could choose from the following elective courses for the summer term: Cases in Finance and Investments, Credit Risk, Corporate Finance in Regulated Industries, Fixed-Income Securities, Mergers and Acquisitions, Private Equity and Venture Capital, Structured Credit and Equity Products, Behavioural Investment Management and Advanced Options Theory. Students doing the so-called "Applied Financial Research" (AFR) report had to choose up to three electives, depending on the number of courses taken in the spring term, and students doing the bigger traditional "Research Project" (RP) could choose a maximum of two electives. The business school also offered an optional course on programming in VBA, after already having offered a C++ class in the previous term. Since I have been one of the students doing the RP, I had two courses in the final term, namely Fixed-Income Securities and Advanced Options Theory, which are therefore the only ones I can review in this post.

Both of these courses relied heavily on the books by Paul Wilmott, especially Paul Wilmott Introduces Quantitative Finance and The Mathematics of Financial Derivatives. For your information, "PW Introduces..." is almost identical to the more expensive three-volume set Paul Wilmott on Quantitative Finance, the only difference being that the latter contains additional chapters on more specialized cases, so the aforementioned book is absolutely sufficient for studies and probably for practical use, too. I like Wilmott's books very much, because they were not written for hardcore mathematicians or physicists like some other quant finance books but for working finance professionals. They contain the required amount of math and asset pricing theory in continuous time, but all of this is presented in a very intuitive way.

As the name suggests,** Advanced Options Theory** (AOT) was about the evaluation of options. The course focused on the pricing of equity derivatives in a continuous-time framework. Naturally, we had the pleasure of dealing with all kinds of differential equations in each lecture. First, we derived the pricing PDE for derivative securities using the general no-arbitrage method and then went on to different ways of solving such partial differential equations. The solution methods we discussed included Laplace transformation, restating the problem in terms of the heat or diffusion equation, and similarity methods for reducing the dimensionality of the problem. We then went on to numerical solution methods, including finite difference methods, which we discussed in great detail and learned how to implement in the C++ programming language. In the following lectures, exotic options were introduced and priced in the PDE framework. During the remainder of the course, further assumptions of the Black-Scholes model were relaxed. For example, we later assumed interest rates and volatility to be stochastic instead of constant and allowed for the underlying asset price path to be discontinuous by incorporating a jump component.

**Fixed-Income Securities** (FIS) often relied on a set of tools similar to those used in AOT, but I personally think FIS was more challenging. The math itself was not difficult, but many models and techniques just are more abstract for interest rate derivatives than equity products, especially when it comes to models of the yield curve. The first lecture of the FIS course covered mostly basics, including definitions of simple interest rate instruments, such as LIBOR, forward rate agreements and interest rate swaps, but we also looked at interest rate derivatives (swaptions, caplets/floorlets) and Black's 1976 model. The second lecture was about one-factor term structure models, including Vasicek and Cox-Ingersoll-Roll (CIR), and, much like in AOT, we learned how to derive the pricing PDE and how to solve it (if possible). Lecture three, expectedly, continued with multi-factor models. We concentrated on the so-called exponential-affine class of models, such as the Gaussian Central Tendency (GCT) model, the Fong-Vasicek stochastic volatility model and the multi-factor CIR. From then on, the level of difficulty increased significantly as we proceeded to arbitrage-free models of the yield curve. Within this class of models there are basically two ways of perfectly fitting the initial yield curve. The first is to introduce time-dependent parameters, i.e. a time-varying drift or volatility, which then requires the calibration of the model parameters. The second possibility would be to use the 1992 Heath, Jarrow and Morton (HJM) framework, where the initial forward curve and volatility structure are given exogenously. Instead of calibrating the model parameters, you use a no-arbitrage argument to derive future movements of the forward curve. The lecture closed with the Markovian HJM model, an extension of the aforementioned HJM framework that gets rid of path-dependencies in the Brownian motion term by imposing a restriction on the volatility term. After this rather abstract topic, we went on to fixed income derivatives and the forward-risk adjusted measure. The remaining lectures covered market models (LIBOR and swap market models), different models for the pricing of defaultable bonds and convertible bonds.

There isn't much more to say about the final term of the MSc Finance programme. I am currently working on my research thesis, which I will hopefully be able to submit in a few weeks. Most of the other finance students are also putting the finishing touches on their projects. The term officially ends in August, but many students have already started to work for various banks and companies in the city either as an intern or analyst. I will refrain from writing a thorough review of the MSc Finance programme at this point, as I hope my posts about the individual terms provide enough information for aspiring students interested in Imperial's finance degree. Instead, I am going to occasionally publish complementing shorter posts that will answer specific questions I have received from undergraduate students and applicants via email over the past months.

For now, however, I'd like to conclude by thanking all readers for their interest and by wishing best of luck to those who are about to begin their studies in September 2013 and to those who are thinking about applying to Imperial College Business School for a future start date!