Valutation risk in margin loan pricing

Margin loans have gained increasing attention as financial instruments tailored for newly listed firms such as startups or small emerging companies. These loans, provided by banks as financing instruments, utilize a specific number of company-owned shares as guarantee (aka “collateral”), valued higher than the loan amount at the beginning of the effective date. Like margin accounts, should the value of the company's shares decline, the borrower is required to provide additional shares to cover the shortfall and meet the stipulated collateral requirements. This thesis focuses on a comprehensive analysis of the financial risks associated with margin loans, with a particular emphasis on monitoring the performance of the company's shares following the loan agreement, whose price strongly depends on relevant market shocks. To achieve this, we delve into the study of renowned stochastic processes for simulating stock price movements in the stock market, specifically, Lévy processes. In this context, jump models become particularly relevant, proving invaluable for generating market scenarios to estimate the value of a shortfall event. We will conduct a comparative analysis of different pricing models: the Black-Scholes model, Merton's Jump Diffusion model, Kou's Double Exponential Jump Diffusion model, and the Variance Gamma process proposed by Madan and Seneta. As part of Margin Loan pricing, whether through Monte Carlo simulations or closed formulas, a crucial aspect involves the calibration of the model parameters to match market-priced option data This entails fine-tuning the model's internal settings to accurately replicate market prices, ensuring that the model is consistent with market forecasts. In detail, we will use both European plain vanilla options and a unique category of exotic options known as One-Touch Knock-Out Daily Cliquet Options, which are suitable for capturing significant fluctuations in stock prices. Calibrating these parameters will be treated as an optimization problem, and we will utilize the Non-Linear Least-Squares algorithm to find the optimal solutions. Tackling the subject of margin loan pricing using various models will enable us to assess the intricacies of pricing these instruments and the inherent valuation risk linked to model choices.