Advanced derivative pricing techniques

Derivatives, which are financial instruments for which the value is derived from underlying assets, play a crucial role in global finance, offering mechanisms for risk management, investment, and speculation. However, the pricing of complex derivatives, such as exotic options with intricate payoff structures or path-dependent features, demands sophisticated mathematical models and computational techniques to accurately capture their value and assess risk.

The evolution of derivatives pricing models has been marked by a continuous quest for greater accuracy and efficiency. From the foundational Black-Scholes model, which revolutionized the pricing of options, to the development of local volatility models and stochastic volatility frameworks, the field has expanded to address the limitations of earlier models and to better reflect the complexities of financial markets. In this context, numerical methods emerge as essential tools, enabling the...