Computation of Greeks Using the Discrete Malliavin Calculus and Binomial Tree

This book presents new computation schemes for the sensitivity of options using the binomial tree and introduces readers to the discrete Malliavin calculus, which offers a simpler way to understand the complex mathematics of the Malliavin calculus. It also shows how the discrete Malliavin calculus approach can be used to compute Greeks for options, which are essential for understanding the sensitivities of derivative securities to changes in the underlying asset price or parameters.

Format: Paperback / softback
Length: 106 pages
Publication date: 18 April 2022
Publisher: Springer Verlag, Singapore

This book presents groundbreaking new computation schemes for the sensitivity of options using the binomial tree, while also introducing readers to the discrete Malliavin calculus. It demonstrates that applications of the discrete Malliavin calculus approach to the binomial tree model offer fundamental tools for computing Greeks, which are quantities that represent the sensitivities of the price of derivative securities with respect to changes in the underlying asset price or parameters.

The binomial tree approach, while being a fairly traditional model for option pricing, is still widely used in financial institutions due to its tractability and ease of understanding. However, the book reveals that the tree approach also provides a powerful tool for deriving the Greeks for options. Greeks are quantities that represent the sensitivities of the price of derivative securities with respect to changes in the underlying asset price or parameters.

The Malliavin calculus, a stochastic method of variations, is one of the most popular tools used to derive Greeks. However, it is also highly complex and difficult to understand for most students and practitioners, as it is based on advanced mathematics. To make the Malliavin calculus more accessible to a broader readership, the book introduces the discrete Malliavin calculus, a theory of the functional for the Bernoulli random walk.

The discrete Malliavin calculus is significantly easier to understand because the functional space of the Bernoulli random walk is realized in a finite dimensional space. As a result, this valuable tool becomes far more accessible to a wide range of readers, including those with limited mathematical backgrounds.

By presenting these new computation schemes and introducing the discrete Malliavin calculus, this book provides a valuable resource for anyone interested in option pricing and derivatives. It offers a comprehensive understanding of the binomial tree approach and its applications to computing Greeks, making it an essential tool for financial professionals and students alike.

Weight: 191g
Dimension: 235 x 155 (mm)
ISBN-13: 9789811910722
Edition number: 1st ed. 2022