Financial engineering postgraduate personal statement example

Personal statement example

My mathematics degree taught me to be suspicious of tidy answers, and financial engineering is a field where the tidy answer is usually the beginning of the work rather than the end. My final-year project compared finite difference schemes for the one-dimensional heat equation, including explicit, implicit and Crank-Nicolson methods. I spent most of my time on stability: watching an explicit scheme dissolve into oscillation when I pushed the time step too far was more instructive than any proof I had read. Only afterwards, reading around the topic, did I properly understand that the same discretisation ideas underpin numerical option pricing, and that the Black-Scholes equation can be transformed into the heat equation. That connection is what redirected my plans from general applied mathematics towards this subject.

I did not have access to internships in trading or quantitative research, so I built something small instead. Using free end-of-day data on a handful of index options, I wrote a Python programme that prices European options by Monte Carlo simulation and by a binomial tree, then compares both against the closed-form Black-Scholes value. I extended it to back out implied volatilities from quoted prices and plot them against strike. Seeing a clear skew rather than a flat line was the point at which the limitations of constant-volatility assumptions stopped being a textbook sentence and became something I had produced myself. I then experimented with delta hedging a short call position through historical price paths, rebalancing daily and weekly, and recorded how the hedging error widened as rebalancing became less frequent and as transaction costs were introduced. The project is modest, but it forced me to confront data problems I had never met in coursework: stale quotes, missing days, dividends and the question of which interest rate to use.

Reading has filled some of the gaps. I worked through Hull's Options, Futures and Other Derivatives during my final year, mainly the chapters on binomial trees, the Greeks and interest rate products, and I have been slowly reading Shreve's first volume on the binomial asset pricing model because I want a firmer grasp of martingales and risk-neutral measure before starting a master's. My degree covered probability, stochastic processes and linear algebra, but measure-theoretic probability was not part of it, so I am working on that independently and would welcome the structure of formal teaching in stochastic calculus.

Since graduating I have worked part-time as a customer adviser at a building society, discussing mortgages, fixed-rate bonds and savings products with members. It is not quantitative work, but it has given me a practical sense of how interest rate changes reach ordinary households, and how differently people respond to the same product depending on how it is explained. Explaining an early repayment charge clearly to a worried customer requires the same discipline as explaining a model's assumptions to someone who will rely on its output. I also help at a Saturday maths club for GCSE pupils, where I mostly work with students who find algebra intimidating; breaking problems into small verifiable steps has improved my own habits of checking work.

What I want from postgraduate study is depth I cannot reach alone: continuous-time stochastic models, fixed income and credit, numerical methods applied at a scale beyond my laptop scripts, and proper training in programming for financial applications. My longer-term aim is a role in quantitative risk or model validation, where careful scepticism about a model's limits is the substance of the job. I am prepared for demanding mathematics and for the amount of independent reading a conversion into this field requires, and I have shown I will do that work without being prompted.

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