You want to stay away from this as a student for a project, even if you are a doctoral student. If you want to tackle this a doctoral student, then I would love to completely consume every moment of your time working on this because I do have a problem that I want to reduce to deterministic polynomial time. Trust me, you don't want to talk to me because there will never be an end to your headaches.
The Black-Scholes option pricing model has never had a successful validation study. Indeed, there are 3800 articles on just one anomaly that I have looked at. Part of a paper I am submitting for publication contains an argument that if the assumptions of Black-Scholes were strictly true, then there cannot exist an estimator that can converge to the population parameter, even with an infinitely large data set. No one ever actually formally looked at the properties of Black-Scholes as an estimator. Everyone just assumed the formula, if valid under the assumptions, would also be a valid estimator of the parameter. That turns out not to be the case, hence all of the anomalies.
If you want to stay in computational finance, go to bankruptcy estimation. It is a large and rich area with a nearly infinite tool set. The toolset is overly vast because of the combined pressures of publish or perish and the need to show that "I am smart, hire me, I could do something crazy fancy."
I tested 78 models of bankruptcy over a period of nearly 90 years. Using Bayesian methods, one model had approximately a 46% chance of being the true model, one model had a roughly 54% chance of being the true model and the remaining 76 models had a combined posterior probability that one of them was true of 1/10000th of one percent. All were statistically significant. Of the two, fortunately, neither shared the same variables so I was able to do a weighted average and that was far better than either separately.
It is easy to verify the qualities of a model, after it is built and you run it through the data. That is a linear problem. Testing multiple models is a combinatoric problem. This is even more so if no one knows the form of the function such as "even though the assumptions are violated, can you use logistic regression?" You will find random forests, logistic regression, Hopfield nets, and just about any technique that could classify or estimate failure. It is so difficult because firms across industries are not alike and the nature of those industries change as technology and preferences change. No model could be strictly stationary.
You will want to go back until at least the 1960's as paths started diverging then and the most recent stuff isn't really better than the foundational work. Much of the foundational work isn't really that good either.
If you think about bankruptcy as being akin to dying, then you are getting it wrong unless you read the children's books "Animorphs." Berkshire Hathaway was, for most of its history, a textiles firm. Now it sells ice cream through its Dairy Queen subsidiary, insurance through its Geico subsidiary and dozens of other things from carpeting to shoes. Firms change from turtles to cows to half-bears, quarter-dogs and quarter-fish. They survive by becoming something else. If you are writing software and assuming stability, then you are solving the wrong problem. That is complicated and that is complex. Look at bankruptcy.
