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Deelstra, Griselda; Rayée, Grégory; Vanduffel, Steven; Yao, Jing

Using model-independent lower bounds to improve pricing of Asian style options in Lévy markets. (English) Zbl 1290.91159

Astin Bull. 44, No. 2, 237-276 (2014).
Summary: H. Albrecher et al. [Appl. Math. Finance 15, No. 2, 123–149 (2008; Zbl 1134.91394)] have proposed model-independent lower bounds for arithmetic Asian options. In this paper we provide an alternative and more elementary derivation of their results. We use the bounds as control variates to develop a simple Monte Carlo method for pricing contracts with Asian-style features. The conditioning idea that is inherent in our approach also inspires us to propose a new semi-analytic pricing approach. We compare both approaches and conclude that these both have their merits and are useful in practice. In particular, we point out that our newly proposed Monte Carlo method allows to deal with Asian-style products that appear in insurance (e.g., unit-linked contracts) in a very efficient way, and outperforms other known Monte Carlo methods that are based on control variates.

Cited in 3 Documents

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)

Keywords:

Asian-style options; conditional expectation; control variates; stochastic clock

Citations:

Zbl 1134.91394
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\textit{G. Deelstra} et al., ASTIN Bull. 44, No. 2, 237--276 (2014; Zbl 1290.91159)
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References:

[1] DOI: 10.1214/aop/1176995609 · Zbl 0392.60057
[2] DOI: 10.2307/3318481 · Zbl 0836.62107
[3] DOI: 10.1080/13527260701356633 · Zbl 1134.91394
[4] DOI: 10.1016/j.cam.2004.01.037 · Zbl 1107.91042
[5] Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (1964) · Zbl 0171.38503
[6] DOI: 10.1086/294632
[7] Quantitative Finance 13 pp 125– (2011)
[8] DOI: 10.1023/A:1009703431535 · Zbl 0937.91052
[9] DOI: 10.1086/296519
[10] DOI: 10.1080/10920277.2003.10596119 · Zbl 1084.60530
[11] Lévy Processes and Infinitely Divisible Distributions (1999) · Zbl 0973.60001
[12] DOI: 10.1140/epjb/e2003-00131-6 · Zbl 01908731
[13] Risk 10 pp 139– (1997)
[14] Numerical Recipes in C (1992)
[15] DOI: 10.1111/1539-6975.t01-1-00062
[16] Insurance: Mathematics and Economics 42 pp 189– (2008)
[17] Finance and Stochastics 2 pp 41– (1998)
[18] Comparison Methods for Stochastic Models and Risks (2002) · Zbl 0999.60002
[19] DOI: 10.1080/10920277.2010.10597639 · Zbl 1219.91136
[20] DOI: 10.1016/0378-4266(90)90039-5
[21] Modern Actuarial Risk Theory (2008) · Zbl 1148.91027
[22] Insurance: Mathematics and Economics 27 pp 151– (2000)
[23] Monte Carlo Methods in Financial Engineering (2003)
[24] Shiu, Transactions of the Society of Actuaries 46 pp 99– (1994)
[25] Lévy Base Correlation (2007)
[26] DOI: 10.1016/j.jbankfin.2007.12.027
[27] Journal of Computational Finance 2 pp 49– (1999)
[28] DOI: 10.1109/TCOM.1960.1097606
[29] DOI: 10.1086/209749
[30] DOI: 10.1016/j.cam.2007.10.050 · Zbl 1154.91021
[31] DOI: 10.1016/j.ejor.2012.03.046 · Zbl 1253.91177
[32] Insurance: Mathematics and Economics 44 pp 385– (2009)
[33] Financial Modeling with Jump Processes (2004)
[34] Gaussian Quadrature Formulas (1966) · Zbl 0156.17002
[35] DOI: 10.1086/338705
[36] Stochastic Orders and Their Applications (1994) · Zbl 0806.62009
[37] DOI: 10.21314/JCF.1998.020
[38] Insurance: Mathematics and Economics 35 pp 369– (2004)
[39] Lévy Processes in Finance: Pricing Financial Derivatives (2003)
[40] Valdez, Insurance: Mathematics and Economics 42 pp 1109– (2008)
[41] Journal of Risk and Insurance 68 pp 93– (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.