JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2026, Vol. 61 ›› Issue (9): 84-95.doi: 10.6040/j.issn.1671-9352.0.2024.405

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Gap option pricing under the mixed sub-fractional Vasicek stochastic rate model

LI Li, SONG Ruili*   

  1. School of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210023, Jiangsu, China
  • Published:2026-09-30

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Abstract: A mixed sub-fractional Vasicek stochastic interest rate model is established based on the risky asset price process driven by mixed sub-fractional Brownian motion combined with the Vasicek stochastic interest rate model. With the help of Duffies idea of affine structure solution, the pricing formula of zero-coupon bond is derived. The partial differential equation satisfied by the option price is obtained using the Δ-hedging principle, and finally, the pricing formula for gap options is solved through variable substitution. Numerical simulations analyze the effects of Hurst index H, initial underlying asset price S, gap G, maturity date T, stock volatility σ2, and interest rate volatility σr2 on option prices. The results show that the increase in H, G, and σr2 will reduce the option price, while the increase in the S, T, and σ2 will increase the option price, which extends the existing research results on gap options.

Key words: mixed sub-fractional Brownian motion, gap option pricing, zero-coupon bond, Vasicek stochastic interest rate

CLC Number: 

  • O211.6
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[1] AN Xiang, GUO Jing-jun. Pricing and simulation of lookback options under the mixed sub-fractional jump-diffusion model [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(4): 100-110.
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