Path integral approach to closed-form option pricing formulas with applications to stochastic volatility and interest rate models

被引：14

作者：

Lemmens, D. ^{[1
]}

Wouters, M. ^{[1
]}

Tempere, J. ^{[1
,3
]}

Foulon, S. ^{[2
]}

机构：

[1] Univ Antwerp, TFVS, B-2610 Antwerp, Belgium

[2] KBC Bank, B-1080 Brussels, Belgium

[3] Harvard Univ, Lyman Lab Phys, Cambridge, MA 02138 USA

来源：

PHYSICAL REVIEW E | 2008年 / 78卷 / 01期

关键词：

D O I：

10.1103/PhysRevE.78.016101

中图分类号：

O35 [流体力学]; O53 [等离子体物理学];

学科分类号：

070204 ; 080103 ; 080704 ;

摘要：

We present a path integral method to derive closed-form solutions for option prices in a stochastic volatility model. The method is explained in detail for the pricing of a plain vanilla option. The flexibility of our approach is demonstrated by extending the realm of closed-form option price formulas to the case where both the volatility and interest rates are stochastic. This flexibility is promising for the treatment of exotic options. Our analytical formulas are tested with numerical Monte Carlo simulations.

引用

页数：8

共 50 条

[1] The closed-form option pricing formulas under the sub-fractional Poisson volatility models
Wang, XiaoTian
Yang, ZiJian
Cao, PiYao
Wang, ShiLin
[J]. CHAOS SOLITONS & FRACTALS, 2021, 148
[2] The closed-form option pricing formulas under the sub-fractional Poisson volatility models
Wang, XiaoTian
Yang, ZiJian
Cao, PiYao
Wang, ShiLin
[J]. Chaos, Solitons and Fractals, 2021, 148
[3] Closed-form option pricing formulas with extreme events
Camara, Antonio
Heston, Steven L.
[J]. JOURNAL OF FUTURES MARKETS, 2008, 28 (03) : 213 - 230
[4] A Closed-Form Pricing Formula for Log-Return Variance Swaps under Stochastic Volatility and Stochastic Interest Rate
Mao, Chen
Liu, Guanqi
Wang, Yuwen
[J]. MATHEMATICS, 2022, 10 (01)
[5] Closed-form approximations with respect to the mixing solution for option pricing under stochastic volatility
Das, Kaustav
Langrene, Nicolas
[J]. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2022, 94 (05) : 745 - 788
[6] A path integral approach to option pricing with stochastic volatility: Some exact results
Baaquie, BE
[J]. JOURNAL DE PHYSIQUE I, 1997, 7 (12): : 1733 - 1753
[7] Closed-form option pricing for exponential Levy models: a residue approach
Aguilar, Jean-Philippe
Kirkby, Justin Lars
[J]. QUANTITATIVE FINANCE, 2023, 23 (02) : 251 - 278
[8] Erratum for 'Closed-form approximations with respect to the mixing solution for option pricing under stochastic volatility'
Das, Kaustav
Langrene, Nicolas
[J]. STOCHASTICS-AN INTERNATIONAL JOURNAL OF PROBABILITY AND STOCHASTIC PROCESSES, 2024,
[9] APPROXIMATING LOCAL VOLATILITY FUNCTIONS OF STOCHASTIC VOLATILITY MODELS: A CLOSED-FORM EXPANSION APPROACH
An, Yu
Li, Chenxu
[J]. PROBABILITY IN THE ENGINEERING AND INFORMATIONAL SCIENCES, 2015, 29 (04) : 547 - 563
[10] A fast numerical approach to option pricing with stochastic interest rate, stochastic volatility and double jumps
Zhang, Sumei
Wang, Lihe
[J]. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2013, 18 (07) : 1832 - 1839

← 1 2 3 4 5 →