Pricing Discretely Monitored Asian Options Under Regime-Switching and Stochastic Volatility Models with Jumps

This paper proposes a unified approach for pricing discretely monitored floating and fixed strike Asian options under a broad class of regime-switching and stochastic volatility models with jumps. The randomness in volatility can be either characterized by regime switching among discrete market stat...

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Vydáno v:Journal of scientific computing Ročník 98; číslo 2; s. 47
Hlavní autoři: Zhang, Weinan, Zeng, Pingping, Zhang, Gongqiu, Kwok, Yue Kuen
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.02.2024
Springer Nature B.V
Témata:
Algorithms
Approximation
Computational Mathematics and Numerical Analysis
Cosine series
Diffusion
Error analysis
Fourier series
Fourier transforms
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Partial differential equations
Pricing
Quadratures
Queuing theory
Randomness
Securities prices
Series expansion
Stochastic models
Switching
Theoretical
Valuation
Volatility
Discretely monitored Asian options
91G60
60E10
65T99
91G20
65D15
Floating and fixed strikes
Fourier-cosine series expansion
ISSN:0885-7474, 1573-7691
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Shrnutí:This paper proposes a unified approach for pricing discretely monitored floating and fixed strike Asian options under a broad class of regime-switching and stochastic volatility models with jumps. The randomness in volatility can be either characterized by regime switching among discrete market states, a diffusive stochastic variance process correlated with the underlying asset price, or a random time change applied to a background process. Our approach can be applied to price financial derivatives with exotic averaging type payoffs, which goes beyond most of the existing frameworks in terms of versatility. Our success relies on the adoption of the change-of-measure approach and a dimension reduction technique. Specifically, we construct new backward recursions for Asian options that include floating and fixed strike payoffs under a wide range of regime-switching and stochastic volatility models with jumps. The Fourier-cosine series expansion and Gauss quadrature rule are applied to solve the backward recursions. The exponential convergence rate of our approach is proven theoretically and verified numerically via comprehensive error analysis. Extensive numerical experiments demonstrate that our approach is reliable, accurate, and efficient.
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ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-023-02438-5