Pricing of vulnerable options based on an uncertain CIR interest rate model

Guiwen Lv; Ping Xu; Yanxue Zhang; Guiwen Lv; Ping Xu; Yanxue Zhang

doi:10.3934/math.2023563

AIMS Mathematics

2023, Volume 8, Issue 5: 11113-11130. doi: 10.3934/math.2023563

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Pricing of vulnerable options based on an uncertain CIR interest rate model

Guiwen Lv ¹,
Ping Xu ^{1
,
,},
Yanxue Zhang ^{2
,
,}

1.
Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043, China
2.
Department of Accounting, Shijiazhuang Vocational College of Economics, Shijiazhuang 050080, China

Received: 08 December 2022 Revised: 13 January 2023 Accepted: 21 February 2023 Published: 09 March 2023
MSC : 60H30, 62P05, 91B28

The traditional Cox-Ingersoll-Ross (CIR) interest rate model follows a stochastic differential equation that cannot obtain the closed solution while the uncertain CIR interest rate model is an uncertain differential equation. First, this paper gives the solution in terms of the distribution of the uncertain CIR interest rate model based on uncertainty theory. Second, the pricing formulas of vulnerable European call option and vulnerable European put option are obtained by using the uncertain CIR interest rate model. Finally, according to the proposed pricing formula, the corresponding numerical algorithms are designed and several numerical examples are given to verify the effectiveness of the algorithm. Our results not only enrich the option pricing theory, but they also have a certain guiding significance for the derivatives market.
- uncertain interest rate model,
- vulnerable options,
- option pricing,
- numerical algorithm
Citation: Guiwen Lv, Ping Xu, Yanxue Zhang. Pricing of vulnerable options based on an uncertain CIR interest rate model[J]. AIMS Mathematics, 2023, 8(5): 11113-11130. doi: 10.3934/math.2023563

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Abstract

The traditional Cox-Ingersoll-Ross (CIR) interest rate model follows a stochastic differential equation that cannot obtain the closed solution while the uncertain CIR interest rate model is an uncertain differential equation. First, this paper gives the solution in terms of the distribution of the uncertain CIR interest rate model based on uncertainty theory. Second, the pricing formulas of vulnerable European call option and vulnerable European put option are obtained by using the uncertain CIR interest rate model. Finally, according to the proposed pricing formula, the corresponding numerical algorithms are designed and several numerical examples are given to verify the effectiveness of the algorithm. Our results not only enrich the option pricing theory, but they also have a certain guiding significance for the derivatives market.

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