Exchange option pricing in jump-diffusion models based on esscher transform

被引：11

作者：

Li, Wenhan ^{[1
,2
]}

Liu, Lixia ^{[1
]}

Lv, Guiwen ^{[1
,3
]}

Li, Cuixiang ^{[1
]}

机构：

[1] Hebei Normal Univ, Coll Math & Informat Sci, Shijiazhuang 050024, Hebei, Peoples R China

[2] Hebei GEO Univ, Coll Math & Phys, Shijiazhuang, Hebei, Peoples R China

[3] Shijiazhuang Tiedao Univ, Dept Math & Phys, Shijiazhuang, Hebei, Peoples R China

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2018年 / 47卷 / 19期

关键词：

Change of numeraire; Esscher transform; Exchange option; jump-diffusion model;

D O I：

10.1080/03610926.2018.1444180

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In the real world, we introduce a dynamic model about the risky asset which is governed by Brownian motion, stationary compound Poisson process and its compensation process. By choosing Esscher transform parameters, we obtain a risk-neural measure Q under which the discounted value of the risky underlying asset is a martingale. Then, we give the pricing formulas of Exchange option by change of numeraire. At last, we analyze the option pricing formula and provide numerical illustrations by introducing BBY stock and SBUX stock.

引用

页码：4661 / 4672

页数：12

共 20 条

[11] On option pricing under a completely random measure via a generalized Esscher transform [J].

Lau, John W. ;

Siu, Tak Kuen .

INSURANCE MATHEMATICS & ECONOMICS, 2008, 43 (01) :99-107

[12]

Lewis A. L., 2001, SSRN ELECT J, V6, P1

[13] THEORY OF RATIONAL OPTION PRICING [J].

MERTON, RC .

BELL JOURNAL OF ECONOMICS, 1973, 4 (01) :141-183

[14] OPTION PRICING WHEN UNDERLYING STOCK RETURNS ARE DISCONTINUOUS [J].

MERTON, RC .

JOURNAL OF FINANCIAL ECONOMICS, 1976, 3 (1-2) :125-144

[15] An approximation of American option prices in a jump-diffusion model [J].

Mulinacci, S .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 1996, 62 (01) :1-17

[16] Valuing variable annuity guarantees with the multivariate Esscher transform [J].

Ng, Andrew Cheuk-Yin ;

Li, Johnny Siu-Hang .

INSURANCE MATHEMATICS & ECONOMICS, 2011, 49 (03) :393-400

[17]

Pham H., 1998, Journal of Mathematical Systems, estimations, and Control, V8, P1

[18]

Shreve S.E., 2004, Stochastic Calculus for Finance II: Continuous-Time Models, V11

[19] Pricing currency derivatives with Markov-modulated Levy dynamics [J].

Swishchuk, Anatoliy ;

Tertychnyi, Maksym ;

Elliott, Robert .

INSURANCE MATHEMATICS & ECONOMICS, 2014, 57 :67-76

[20]

Yue K. K., 2011, MATH MODELS FINANCIA

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