無套利市場、完全市場與風險中立機率的唯一存在 (An Arbitrage-Free and Complete Market and the Unique Existence of Risk-Neutral Probabilities)

15 Pages Posted: 17 Oct 2019

See all articles by Jen-Chang Liu

Jen-Chang Liu

Takming University of Science and Technology - Department of Banking and Finance

Mark Yeats

Takming University of Science and Technology - Department of Applied Foreign Languages

Date Written: October 8, 2019

Abstract

Chinese Abstract: 衍生性金融商品的基本訂價理論,是根植於不存在套利機會與完全市場假設,它的對等命題是存在唯一的風險中立測度。闡述以上定理的直覺、精簡模型是單期、二資產且二狀態的二項樹模型;因此,原文的衍生性金融商品教科書,都將二項樹模型安排在布雷克修斯連續時間模型之前。然而,大部分的中文教科書卻將二項樹模型安排在連續模型之後,而且普遍忽略風險中立訂價的必要條件:無套利機會假設,以及忽略風險中立機率唯一存在的必要條件:完全市場。本文利用單期、三狀態與三獨立基礎資產假設,呈現三維度報酬率的圖形表達、闡述不存在套利機會市場、完全市場與平賭測度機率的直覺意涵。最後,本文列表比較十數冊教科書對於本文討論議題的表達方式,並且提出評論。本文作者相信,也試圖為期貨與選擇權教科書貢獻清楚、嚴謹的學理意涵,也啟發對無套利市場、完全市場與平賭測度的解讀。

English Abstract: The fundamental pricing theory of derivatives is based on the assumptions of arbitrage-free and complete markets, which is equivalent to the unique existence of a risk-neutral measure. A single-period binomial-tree model with two assets and two states provides an intuitive and concise way to interpret this theory. As a result, English textbooks on derivatives present binomial-tree models before the Black-Scholes continuous-time model. However, most Chinese textbooks on derivatives present them in reverse order. In particular, they tend to neglect that the assumption of arbitrage-free markets is a necessary condition for the legitimacy of risk-neutral pricing, and that a condition of complete markets is for the uniqueness of a risk-neutral measure. The objective of this paper is to provide an intuitive interpretation of arbitrage-free and complete markets, as well as martingale measures, in three-dimensional figures. It is done by presenting discrete single-period models with three states, accompanied by three underlying assets. Finally, this paper compares and critiques the contents of more than ten textbooks. This paper intends to contribute to a clearer theoretical illustration of arbitrage-free, complete markets, and martingale measures.

Note: Downloadable document is in Chinese.

Keywords: Risk-neutral pricing, Futures and Options, complete market, arbitrage-free pricing, equivalent measure

JEL Classification: G12, G13

Suggested Citation

Liu, Jen-Chang and Yeats, Mark, 無套利市場、完全市場與風險中立機率的唯一存在 (An Arbitrage-Free and Complete Market and the Unique Existence of Risk-Neutral Probabilities) (October 8, 2019). Available at SSRN: https://ssrn.com/abstract=3465983 or http://dx.doi.org/10.2139/ssrn.3465983

Jen-Chang Liu (Contact Author)

Takming University of Science and Technology - Department of Banking and Finance ( email )

56, Sec 1, Huan Shan Rd.
Nei Hu Dist.
Taipei City
Taiwan
886226585801 (Phone)

HOME PAGE: http://nas.takming.edu.tw/robertliu/

Mark Yeats

Takming University of Science and Technology - Department of Applied Foreign Languages ( email )

56, Sec 1, Huan Shan Rd.
Nei Hu Dist.
Taipei City
Taiwan

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