A four-person group project for the Quantitative Methods II course, carried out entirely in R. The brief consisted of two independent cases — one in computational finance, one in applied statistics — each requiring reproducible R code, careful interpretation of the output, and a formal written report.

We estimated the fair value of a structured product whose payoff has no closed-form solution. Starting from 1,260 historical prices, we computed daily log-returns and estimated the drift and volatility of the underlying asset. We then simulated tens of thousands of possible year-end prices under a log-normal model, applied the certificate's payoff rule (a leveraged gain above the barrier, a fixed rebate below it), and approximated the value as the mean simulated payoff. We quantified the precision of that estimate through its variance and standard error, and showed empirically that the error decreases at a 1/n rate across sample sizes from 100 to 100,000 — connecting the result to the Central Limit Theorem. Finally, we computed investor risk metrics, including expected profit/loss and the 5% Value-at-Risk.

Using a dataset of 374 individuals, we produced a full descriptive analysis — distributions, frequency tables and visualisations — and then examined the relationships within the data. We compared sleep quality and stress across occupations and genders, built contingency tables of sleep disorders, and found a strong negative correlation (r ≈ −0.9) between stress and sleep quality. We formally tested two claims made by a sleep doctor using a one-sample proportion test and a one-sample t-test, rejecting both at the 5% level. Finally, we compared mean sleep duration and age across the three sleep-disorder categories using 99% confidence intervals to identify which group differences were statistically significant.