Uncertain volatility models

Many introductory texts on mathematical finance touch on computer algorithms, but this work delves deeper into the algorithmic challenges posed by complex pricing models, particularly in uncertain volatility models, an extension of Black-Scholes theory. It explores applications related to exotic option portfolios featuring barriers and early exercise options. An object-oriented C++ solution is provided, with source code included on the accompanying CD, making it beneficial for practitioners and students aiming to develop analytic software libraries. The book emphasizes a specific family of mathematical models, acknowledging the broader variety of instrument properties encountered in practice. To achieve optimal systems, a blend of mathematical and financial knowledge with strong programming skills is essential. The design of analytic software is a central theme in the later chapters. This work is derived from my Ph.D. thesis, and I extend my gratitude to my academic advisor, Marco Avellaneda, for his guidance in mathematical finance and uncertain volatility. His encouragement of an algorithmic approach made computational finance exciting for me. I also appreciate the valuable feedback from Afshin Bayrooti, Vladimir Finkelstein, and Antonio Paras, the co-inventor of the original uncertain volatility model, A-UVM. Richard Holmes identified a crucial bug in an early software implementation.