Generalized trapezoidal formulas for the black-scholes equation of option pricing

• Published in: International journal of computer mathematics 2003-12, Vol.80 (12), p.1521-1526
• Main Authors: Chawla, M. M., Al-Zanaidi, M. A., Evans, D. J.
• Format: Article
• Language: English
• Subjects: Applied sciences; Black-Scholes equation; Crank-Nicolson scheme; European options; Exact sciences and technology; Generalized trapezoidal formula schemes; Mathematical analysis; Mathematics; Operational research and scientific management; Operational research. Management science; Option pricing; Partial differential equations; Portfolio theory; Sciences and techniques of general use; Unconditional stability
• ISSN: 0020-7160; 1029-0265
• DOI: 10.1080/00207160310001603299

For the celebrated Black-Scholes parabolic equation of option pricing, we present new time integration schemes based on the generalized trapezoidal formulas introduced by Chawla et al. [3]. The resulting GTF(α) schemes are unconditionally stable and second order in both space and time. Interestingly, since the Black-Scholes equation is linear, GTF (1/3) attains order three in time. The computational performance of the obtained schemes is compared with the Crank-Nicolson scheme for the case of European option valuation. Since the payoff is nondifferentiable having a "corner" on expiry at the exercise price, the classical trapezoidal formula used in the Crank-Nicolson scheme can experience oscillations at this corner. It is demonstrated that our present GTF (1/3) scheme can cope with this situation and performs consistently superior than the Crank-Nicolson scheme.