### My learning journey in Mathematical Methods for Quantitative Finance

My learning journey in Mathematical Methods for Quantitative Finance was an intensive and exciting experience. Over the course of the program, I gained a deep understanding of the mathematical concepts and techniques that underpin quantitative finance.

During the early weeks of the program, we focused on core topics such as calculus, linear algebra, and probability theory. These foundational topics were crucial for building a strong understanding of the more advanced concepts that we would encounter later on.

As the program progressed, we delved into more specialized topics such as stochastic calculus, Monte Carlo simulation, and partial differential equations. I found these topics challenging but incredibly rewarding, as they helped me to gain a deep understanding of the tools and techniques used in quantitative finance.

Throughout the program, we had the opportunity to work on real-world problems and case studies, which helped to cement our understanding of the concepts and techniques that we were learning. We also had access to industry experts who provided valuable insights into the practical applications of the mathematical techniques that we were studying.

**Week 1: Probability Distributions**

Week 1 focused on the important topics of random variables and probability distributions. Here are my main takeaways from the week:

- A random variable is a variable whose value is determined by chance.
- Probability distributions are mathematical functions that describe the likelihood of different outcomes for a random variable.
- We learned about important probability distributions, such as the normal distribution and the binomial distribution, and how to calculate probabilities using these distributions.

I found some problems quite interesting:

**Part 2**

Let R0 be tomorrow’s one-day return on the S&P 500. This question will walk through how long it will take, on average, to observe a return Rt>R0. We will not need a market data for this question. Assume each day’s return is independent and identically distributed.

**Week 2: Stochastic processes**

Week 2 focused on stochastic processes and linear time series models. Here are my main takeaways from the week

- Stochastic processes are mathematical models that describe the evolution of a random variable over time.
- We learned about different types of stochastic processes, such as random walks and Brownian motion, and how to simulate them using computer programs.
- Linear time series models are a type of stochastic process that describe how a variable changes over time based on its past values.

I found some problems quite interesting:

**Part C**

What is the lag-k auto-covariance, for three cases k=0, k=1 and k≥2.

**Week 3: Model Estimations**

Week 3 focused on the important topics of model estimation, forecasts, and binomial trees. Here are my main takeaways from the week:

- Model estimation is the process of using data to estimate the parameters of a mathematical model.
- We learned about different techniques for model estimation, such as maximum likelihood estimation and Bayesian estimation.
- Forecasting is the process of using a mathematical model to make predictions about future values of a variable.

I found some problems quite interesting:

Part A

Write a function MCpaths to generate a set of simulated price paths for a stock with lognormally distributed returns.

Overall, my learning journey in Mathematical Methods for Quantitative Finance was an enriching experience that provided me with a deep understanding of the mathematical foundations of finance. I feel confident that the knowledge and skills that I gained through the program will be valuable in my future career in the finance industry.

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