Aspiring Quant

Could you talk about what led you down into your career path? Also, why did you recommend Greek and politics instead of say, Physics?
 
tbh if your goal is to pursue a quant career in the industry, there really isn't much of a need to study all this material so early. Most buy side firms don't really care if you know about PDEs or stochastic calculus (this is more needed on the sell side). Even in top MFE programs, you don't even need that much in-depth knowledge of PDEs (just discretization of PDEs, solving HJB, Feynman-Kac) and I don't really see the usefulness of learning this extremely early (unless you're genuinely interested and just want to learn it for fun). You mentioned willmotts book and Hull and I agree they're useful to learn abt finance but I wouldn't rush to learn all of it early (hedge funds don't really care if you read these books already - they assume finance is easy and can be picked up fairly quickly by anyone smart enough, a Jane Street trader told our class this and said he just interviewed a lawyer). If your goal is to eventually land a quant career and make a crap ton of money, I think the best way is to learn more contest math/programming than theoretical math/programming. For example, the IMO contest doesn't even require any calculus but being a medalist is much much more impressive to hedge funds than just knowing abt Girsanov's theorem at a young age. My recommendation is to develop your probability intuition (i think probability is probably one of the most important subjects to land a new grad quant career), and develop your problem solving skills (for example, Putnam, IOI, IMO, USAMO, red in Codeforces).
 
tbh if your goal is to pursue a quant career in the industry, there really isn't much of a need to study all this material so early. Most buy side firms don't really care if you know about PDEs or stochastic calculus (this is more needed on the sell side). Even in top MFE programs, you don't even need that much in-depth knowledge of PDEs (just discretization of PDEs, solving HJB, Feynman-Kac) and I don't really see the usefulness of learning this extremely early (unless you're genuinely interested and just want to learn it for fun). You mentioned willmotts book and Hull and I agree they're useful to learn abt finance but I wouldn't rush to learn all of it early (hedge funds don't really care if you read these books already - they assume finance is easy and can be picked up fairly quickly by anyone smart enough, a Jane Street trader told our class this and said he just interviewed a lawyer). If your goal is to eventually land a quant career and make a crap ton of money, I think the best way is to learn more contest math/programming than theoretical math/programming. For example, the IMO contest doesn't even require any calculus but being a medalist is much much more impressive to hedge funds than just knowing abt Girsanov's theorem at a young age. My recommendation is to develop your probability intuition (i think probability is probably one of the most important subjects to land a new grad quant career), and develop your problem solving skills (for example, Putnam, IOI, IMO, USAMO, red in Codeforces).
I do genuinely enjoy these theories so I want to learn them for fun. My problem is the convoluted information regarding the mathematical requirements of these courses so I can truly understand them. That is the reason why I asked if real analysis is a perquisite to stochastic calculus was to understand how much more I need to do in order to be finally ready for these books.
 
if you want to know the requirements to learn stochastic calculus, I think they vary depending on if you just want an intuitive understanding or want to rigorously prove every theorem/detail presented. if you want to start learning stochastic calculus at an MFE level, the prerequisites are mainly just probability (martingales, moment generating functions, properties of normal distributions) and calculus ( a lot of Ito's is essentially just a taylor expansion but with quadratic variation). Filtrations and sigma algebras might be confusing at first but just having a general understanding of how it's used to model the flow of information is fine (no need to go too hard on measure theory). Girsanov's gets a bit confusing too but you can do a sketch proof just knowing the exponential martingale, moment generating functions and Ito's. Intuitevely, if you can understand how to make a Gaussian with different means the same as each other by just reweighing the probabilities of each outcome, then you understand enough of Girsanov's to get by.
 
Thanks for the answer. My interest in stochastic calculus is simply to be able to have a basic understanding without rigorously proving every theorem. I will take a course in Probability soon and I am very happy to see that it will not be wasted. Being honest I do not know what filtration and sigma algebras are but I am assuming they are part of real analysis. What book would you recommend for the subjects mentioned above around an MFE level?
I am looking forward to playing sims on the blockchain :>
 
sheldon ross introduction to probabiltiy models is pretty good to learn abt the probability prerequisites for stoch cal and is a fairly light read (ch 1, 2, 3, 4 can probably skip exponential and poisson unless you want to learn abt jump processes, skip queueing theory, ch.10 introduces brownian motions). shreves stochastic calculus books are the classic for MFE stoch cal (the first book is a relatively light read, the first few chapters of the second does get a bit challenging to read through at first but aren't too too important). tbh I learned it through mostly class lec notes and hwk sets though so there might be better recs for textbooks.
 
You're a lifesaver. I will definitely work though the first few chapters as I have found that a solid foundation is the most important of all when learning anything. Other than group theory mentioned by D.D what else high level maths courses would recommend (learning purely for enjoyment).
 
hmm I think you might find elements of statistical learning interesting (or start with introduction to statistical learning). it's not really directly finance related but it's pre useful imo and at least less dry than readin thru smthin like Hull
 
I can't give you much advice on what topics to study because I'm trying to figure out the same problem myself, but my two cents would be to "learn by doing" by doing coding projects. For example, I tried to learn about fat tailed probability distributions by going through some of the chapters in this book. I coded up the examples in a way to teach myself and then put them up online (here).

In my experience, there's four benefits to doing this:
  1. Learning by doing gives you a more solid grasp of ideas because you implement them practically instead of only consuming theoretical content
  2. You have motivation to learn how to code because you're using it solve a problem that interests you instead of because you have to learn
  3. You can talk about about your projects during interviews
  4. You end up with a portfolio of projects that you can show to people that want to hire you
Learning stuff by doing projects is really fun :))
 
Cool. What specifically do you mean by stochastic learning, stochastic calculus or processes?
Do you mean that I should write programs for theoretical probability ideas (or maths in general) in order to be able to actually implement the ideas rather than following theoretical content?
 
Is Sheldon Rosse's book a perquisite to Shreve's book or does Shreve introduce the necessary information through his books?
Would a course in statistics be necessary for both?
 
Should I work through both of Shreve's books or just the first?
Is there any other Stochastic Calculus books with more application/ exercises to finance problems.
 
Cool. What specifically do you mean by stochastic learning, stochastic calculus or processes?
Sorry, I don't think I said, was this directed at me?
Do you mean that I should write programs for theoretical probability ideas (or maths in general) in order to be able to actually implement the ideas rather than following theoretical content?
Yes basically. For example, if you're learning about normal distributions, maybe write some Python code that actually plots what a normal distribution looks.

EDIT: Or maybe something even simpler than that. Let's plot the equation of a line:

Plotting a line:
# code that somebody else has written that I want to use
import matplotlib.pyplot as plt
import numpy as np

# this function is the equation of a line (of the form y = mx + b)
# if I plug in the slope (m), the y-intercept (b) and value of x, this function gives me back y
def equation_of_a_line(
    x,
    slope,
    intercept
):
    return x * slope + intercept

# takes my x values and y values and plots them
def plot_line(
    x_list,
    y_list
):
    plt.plot(x_list, y_list)
    plt.xlabel("x")
    plt.ylabel("y")
    plt.show()
    plt.close()

# this function plugs in a bunch of x values into the "equation_of_a_line" function and gives me back a bunch of y values
def y_values_of_a_line(
    x_start,
    x_end,
    num_points,
    slope,
    intercept
):
    # I get a bunch of x values between the range x_start and x_end
    x_list = np.linspace(start=x_start, stop=x_end, num=num_points)
 
    # I get a bunch of y values for each x value in the list x_list
    y_list = [equation_of_a_line(x, slope, intercept) for x in x_list]
 
    plot_line(x_list, y_list)
 
 
def main():
    y_values_of_a_line(
        x_start=-1.5,
        x_end=2.3,
        num_points=50,
        slope=0.78,
        intercept=-4.6
    )

main()

Obviously understanding the equation of a line isn't that hard. But I hope I was able to explain the idea: code up the maths that you're learning to know, line-by-line, exactly what is going on. Not every single piece of maths, but the more interesting stuff
 
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Is Sheldon Rosse's book a perquisite to Shreve's book or does Shreve introduce the necessary information through his books?
Would a course in statistics be necessary for both?
Cool. What specifically do you mean by stochastic learning, stochastic calculus or processes?
Do you mean that I should write programs for theoretical probability ideas (or maths in general) in order to be able to actually implement the ideas rather than following theoretical content?

statistical learning: making inferences from data, hypothetisis testing, parameter estimation
stochastic processes: random processes - brownian motion, poisson processes etc.
stochastic calculus: calculus on stochastic processes

don't really need a course in stats for Shreve but its useful nonetheless. you don't necessarily need ross for shreve but I think shreve would be pretty tough without knowing abt stochastic processes or probability (MGFs, martingales, etc.). Shreve II is more in line with what'd you would expect from a MFE course on continous time models. Steve I is discrete and is a good introduction. For practice problems, Shreve has some.
 
Would you recommend skipping jump processes and skip queuing theory?
sheldon ross introduction to probabiltiy models is pretty good to learn abt the probability prerequisites for stoch cal and is a fairly light read (ch 1, 2, 3, 4 can probably skip exponential and poisson unless you want to learn abt jump processes, skip queueing theory, ch.10 introduces brownian motions).
 

Daniel Duffy

C++ author, trainer
I can't give you much advice on what topics to study because I'm trying to figure out the same problem myself, but my two cents would be to "learn by doing" by doing coding projects. For example, I tried to learn about fat tailed probability distributions by going through some of the chapters in this book. I coded up the examples in a way to teach myself and then put them up online (here).

In my experience, there's four benefits to doing this:
  1. Learning by doing gives you a more solid grasp of ideas because you implement them practically instead of only consuming theoretical content
  2. You have motivation to learn how to code because you're using it solve a problem that interests you instead of because you have to learn
  3. You can talk about about your projects during interviews
  4. You end up with a portfolio of projects that you can show to people that want to hire you
Learning stuff by doing projects is really fun :))
Nice.
 
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