Analytic approximations for European-style Asian spread options

Boling Chen; Guohe Deng; Boling Chen; Guohe Deng

doi:10.3934/math.2024573

AIMS Mathematics

2024, Volume 9, Issue 5: 11696-11717. doi: 10.3934/math.2024573

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Research article

Analytic approximations for European-style Asian spread options

Boling Chen ¹,
Guohe Deng ^{2
,
,}

1.
College of Mathematics and Statistics, Yulin Normal University, Yulin 537000, China
2.
College of Mathematics and Statistics, Guangxi Normal University, Guilin 541006, China

Received: 14 January 2024 Revised: 01 March 2024 Accepted: 07 March 2024 Published: 26 March 2024
MSC : 90A09, 91B24, 91B28, 93E20

Spread option is a exotic option, which allows investors to simultaneously take positions in two correlated underlying assets and profit from their price difference over some spread. This option provides stable investment opportunities for practitioners in unpredictable and complex financial markets. However, investors of the spread option may face problems caused by manipulating the two underlying assets' prices near the expiry, compared to plain vanilla options. To overcome such disadvantages, we propose Asian-spread options, which are linked to the price difference between two average prices of two underlying assets over the life of the option, and exhibit the original properties of standard spread options. In this paper, using distribution-approximating and moment-matching approaches, lower bounds of prices for the European spread option on the geometric average Asian option and arithmetic average Asian option are obtained in the classical Black-Scholes model. We verified the pricing accuracy of the proposed Asian-spread options by comparing our solutions with those obtained by Monte Carlo simulations. Finally, we analyzed the influence of stock price, maturity date, and some model parameters on option price and delta value through numerical examples. Numerical results showed that the lower bounds had a very high precision.
- spread options,
- Asian option,
- closed-from approximation,
- distribution-approximating method,
- moment-matching approach
Citation: Boling Chen, Guohe Deng. Analytic approximations for European-style Asian spread options[J]. AIMS Mathematics, 2024, 9(5): 11696-11717. doi: 10.3934/math.2024573

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Abstract

Spread option is a exotic option, which allows investors to simultaneously take positions in two correlated underlying assets and profit from their price difference over some spread. This option provides stable investment opportunities for practitioners in unpredictable and complex financial markets. However, investors of the spread option may face problems caused by manipulating the two underlying assets' prices near the expiry, compared to plain vanilla options. To overcome such disadvantages, we propose Asian-spread options, which are linked to the price difference between two average prices of two underlying assets over the life of the option, and exhibit the original properties of standard spread options. In this paper, using distribution-approximating and moment-matching approaches, lower bounds of prices for the European spread option on the geometric average Asian option and arithmetic average Asian option are obtained in the classical Black-Scholes model. We verified the pricing accuracy of the proposed Asian-spread options by comparing our solutions with those obtained by Monte Carlo simulations. Finally, we analyzed the influence of stock price, maturity date, and some model parameters on option price and delta value through numerical examples. Numerical results showed that the lower bounds had a very high precision.

References

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