The authors study the Wiener process and Itô integrals in some detail, with a focus on results needed for the Black–Scholes option pricing model. After developing the required martingale properties of this process, the construction of the integral and the Itô formula (proved in detail) become the centrepiece, both for theory and applications, and to provide concrete examples of stochastic differential equations used in finance.

It provides a clear treatment of the scope and limitations of mean-variance portfolio theory and introduces popular modern risk measures. Proofs are given in detail, assuming only modest mathematical background, but with attention to clarity and rigour.

Relatively elementary mathematics leads to powerful notions and techniques - such as viability, completeness, self-financing and replicating strategies, arbitrage and equivalent martingale measures - which are directly applicable in practice. The general methods are applied in detail to pricing and hedging European and American options within the Cox–Ross–Rubinstein (CRR) binomial tree model.

Students and instructors alike will benefit from this rigorous, unfussy text, which keeps a clear focus on the basic probabilistic concepts required for an understanding of financial market models, including independence and conditioning. Assuming only some calculus and linear algebra, the text develops key results of measure and integration, which are applied to probability spaces and random variables, culminating in central limit theory.

Driven by concrete computational problems in quantitative finance, this book provides aspiring quant developers with the numerical techniques and programming skills they need. The authors start from scratch, so the reader does not need any previous experience of C++.

The Black–Scholes option pricing model is the first and by far the best-known continuous-time mathematical model used in mathematical finance. Here, it provides a sufficiently complex, yet tractable, testbed for exploring the basic methodology of option pricing.

Stochastic Interest Rates covers practical topics such as calibration, numerical implementation and model limitations in detail. The authors provide numerous exercises and carefully chosen examples to help students acquire the necessary skills to deal with interest rate modelling in a real-world setting.

Maths plays a big part in our lives, and understanding how numbers work can have a hugely positive impact. The use of numbers and figures can be found everywhere, from finding a new job or getting a promotion, to managing debt and getting a better handle on family finances.

Whether it be in the sciences, business, sport or medicine we hope you will also enjoy studying mathematics for its own sake and come to appreciate its power and diversity. In order to solve problems in the real world, we often begin by translating the problem into mathematical equations to give us a clearer appreciation of the underlying aspects of the problem.

Forth Valley College offers a range of mathematics courses from National 5 through to Higher. This course is eligible for ITA funding.