Absolutely. In fact, a good fraction of quantitative analysts, traders and developers make the change to finance only in their late twenties or early-to-mid thirties. In this article I'm going to talk about how you can achieve the same thing.
Age really isn't a barrier in financial markets. What matters the most is competence, drive and initiative. It is a very meritocratic industry (for better or worse!) in that good performers of all ages are well-rewarded. It is quite common to enter the industry after a stint elsewhere in some other technical field, particularly within the asset management (hedge fund) sector, so don't be put off applying, even if you think you're too senior for the roles.
If you're considering a switch to quantitative finance then the first task you must carry out is to make a frank assessment of your background, experience and skill set. Most forms of quantitative finance are highly mathematical and require solid undergraduate experience in linear algebra, calculus (real analysis in the UK!), probability and statistics. If you have gained, or built upon, these skills in subsequent qualifications such as a MSc (science masters program) or quantitative PhD then so much the better. Prospective employers will also prefer you to have made use of such skills in previous roles.
Programming is the second area that is highly important within quantitative finance. Quants nowadays are spending more and more of their time programming. This includes financial engineers, quant traders, quant researchers, quant developers and risk managers. Not being fluent in a computer language will put you at a severe disadvantage compared to other candidates applying for quant roles. If you haven't done any programming before then you will need to start brushing up on a language such as Python or C++. Take a look at my quantitative finance reading list for a good list of beginner programming books.
One thing that doesn't matter as much in comparison to the first two areas is that of knowing financial concepts inside and out. Since you will be applying for junior level quant roles (unless you can demonstrate significant seniority with mathematics and programming), you won't be expected to know much about financial derivatives, options pricing or algorithmic trading. A lot of this knowledge can be gained by general reading or by picking up one or two textbooks. The remainder will be picked up "on the job". Once again, take a look at the reading list.
Another common route in to quantitative finance is to head back to school and carry out a Masters in Financial Engineering (MFE) or take a part-time financial engineering certificate, of which Paul Wilmott's Certificate of Quantitative Finance is the most prominent. These courses are a good way to get up to speed quickly with the necessary mathematical material, which would otherwise need to be obtained studying in your spare time. They are expensive, however. Course fees range from 20,000 dollars to upwards of 50,000 dollars per year. These courses are all designed to help you become a financial engineer, which involves pricing options and other derivatives. The market has moved on somewhat since the 2008 crisis and now there is less demand for such roles and more supply (due to the prevalence of the courses!). Thus it is worth considering whether you really want to be a financial engineer in a bank, or whether quantitative trading in a fund is of more interest.
Given that you will likely be making a significant career move, you should be prepared for the fact that you will be studying a lot! You will have to find the time to fit it in around your personal life. You will need to honestly ask yourself whether you are really keen for the career move, because there is a lot of work involved simply to get up to the required standard. You will need to become a proficient programmer and carry out some extra mathematical study. For financial engineering, this article will help you determine which books are appropriate.
Quantitative finance is a great place to spend a career, as it is challenging, intellectually stimulating and provides above-average compensation compared to other industries. Switching into it is not a decision to take lightly, but the financial markets can be extremely rewarding as a career, so make sure you give it a good deal of thought!
If you'd like any more information or guidance about how to make the switch, then please email me at email@example.com. I get multiple emails a week from individuals who wonder whether their background or age is suitable for finance. Nearly always the answer is yes - assuming they're prepared for a lot of study.