Chapter 8: Binomial Lattices in Technical Detail. This chapter introduces the reader to some basics of options valuation and a step-by-step approach to analyzing them. | CH PTF 8 Binomial Lattices in Technical Detail This chapter introduces the reader to some basics of options valuation and a step-by-step approach to analyzing them. The methods introduced include closed-form models partial-differential equations and binomial lattices through the use of risk-neutral probabilities. The advantages and disadvantages of each method are discussed. But the focus is on the use of binomial lattices. In addition the theoretical underpinnings and black-box analytics surrounding the binomial equations are demystified here leading the reader through a set of simplified discussions on how certain binomial models are solved without the use of fancy mathematics. OPTIONS VALUATION BEHIND THE SCENES In options analysis there are multiple methodologies and approaches used to calculate an option s value. These range from using closed-form equations like the Black-Scholes model BSM or Generalized Black-Scholes model GBM and its modifications Monte Carlo path-dependent simulation methods lattices . binomial trinomial quadranomial and multinomial trees and variance reduction and other numerical techniques to using partial-differential equations and so forth. However the mainstream methods that are most widely used are the closed-form solutions partial-differential equations and the binomial lattices. Closed-form solutions are models like the BSM or GBM where there exist equations that can be solved given a set of input assumptions. For instance A B C is a closed-form equation where given any two of the three variables you obtain a unique answer to the third variable. Closedform solutions are exact quick and easy to implement with the assistance of some basic programming knowledge but are difficult to explain because 83 84 BACKGROUND OF THE BINOMIAL LATTICE AND BLACK-SCHOLES MODELS they tend to apply highly technical stochastic calculus mathematics when it comes to options valuation. They are also very specific in nature with very limited modeling .
