Pricing Formulae of Power Binary and Normal Distribution Standard Options and Applications

TL;DR

This paper extends existing binary option pricing formulas to power binary and normal distribution standard options, deriving new formulas and demonstrating their applications in pricing savings plans and Asian options, including convergence properties.

Contribution

It introduces new pricing formulas for power binary and normal distribution standard options based on Buchen's formulas, and applies them to various financial derivatives.

Findings

Derived pricing formulas for power binary options.

Established convergence of discrete to continuous Asian option prices.

Applied formulas to savings plans and Asian options.

Abstract

In this paper the Buchen's pricing formulae of (higher order) asset and bond binary options are incorporated into the pricing formula of power binary options and a pricing formula of "the normal distribution standard options" with the maturity payoff related to a power function and the density function of normal distribution is derived. And as their applications, pricing formulae of savings plans that provide a choice of indexing and discrete geometric average Asian options are derived and the fact that the price of discrete geometric average Asian option converges to the price of continuous geometric average Asian option when the largest distance between neighboring monitoring times goes to zero is proved.