Valuation of options subject to default risk under a mixed fractional and multiscale stochastic volatility model

• Published in: Advances in continuous and discrete models Vol. 2025; no. 1; p. 93
• Main Authors: Lee, Min-Ku, Kim, Jeong-Hoon
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 12.05.2025; Springer Nature B.V
• Subjects: Accuracy; Analysis; Approximation; Arbitrage; Brownian motion; Default; Difference and Functional Equations; Functional Analysis; Mathematics; Mathematics and Statistics; Monte Carlo simulation; Ordinary Differential Equations; Parameter sensitivity; Partial Differential Equations; Securities prices; Stochastic models; Volatility; Stochastic volatility; Option pricing; Fractional Brownian motion; Multiscale; Default risk

Based on the recent trend in developing stochastic volatility models in terms of a fractional Brownian motion, we introduce a volatility model for option’s underlying asset and option issuer’s total assets by incorporating the short and long memory properties into the fast and slow scale variations...