使用時變機率分配之歐式選擇權定價模型研究

Abstract

本篇論文採用市場真實報酬率並透過電腦技術以進行選擇權評價. 有別於傳統數學模型, 本模型並不需要對資產進行假設, 因而解決傳統選擇權評價時機率分配與現實世界不符的問題.

Most option pricing methods use mathematical distributions to approximate underlying asset behavior. However, pure mathematical distribution approaches have difficulty approximating the actual distribution. This study first introduces an innovative computational method for pricing European options based on time variant distributions of the underlying asset. The distribution can be either mathematically generated or simply apply real payoff distributions. Moreover, this computational approach can also be applied to applications related to expected value computation that require actual distributions rather than mathematical distributions. This study makes the following contributions: a) solving the risk neutral issue related to price options with none-mathematical distributions; b) proposing a simple method for adjusting standard deviation based on the need to apply short term volatility to real world applications; c) demonstrating option pricing algorithms that are easy to apply to cross field applications; d) helping traders to generate their own distributions to price new derivative instruments without the difficulty of deriving new closed form formulas.