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A numerical analysis of the extended Black-Scholes model. (English) Zbl 1131.91025

Summary: Some numerical results regarding the multidimensional extension of the Black-Scholes model introduced by S. Albeverio and V. Steblovskaya [Finance Stoch. 6, 383–396 (2002; Zbl 1025.91007)] (a multidimensional model with stochastic volatilities and correlations) are presented. The focus lies on aspects concerning the use of this model for the practice of financial derivatives. Two parameter estimation methods for the model using historical data from the market and an analysis of the corresponding numerical results are given. Practical advantages of pricing derivatives using this model compared to the original multidimensional Black-Scholes model are pointed out. In particular the prices of vanilla options and of implied volatility surfaces computed in the model are close to those observed on the market.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)

Citations:

Zbl 1025.91007
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References:

[1] DOI: 10.1007/s007800100066 · Zbl 1025.91007 · doi:10.1007/s007800100066
[2] Albeverio S., Proc. of the Steklov Inst. of Math. 237 pp 164–
[3] DOI: 10.1111/j.1540-6261.1997.tb02749.x · doi:10.1111/j.1540-6261.1997.tb02749.x
[4] DOI: 10.1086/260062 · Zbl 1092.91524 · doi:10.1086/260062
[5] DOI: 10.1086/338705 · doi:10.1086/338705
[6] Dupire B., Risk 7 pp 18– · Zbl 0997.90515
[7] DOI: 10.1086/294743 · doi:10.1086/294743
[8] Frey R., CWI Quaterly 10 pp 1–
[9] Genon-Catalot V., Ann. Inst. Poincaré 29 pp 119–
[10] DOI: 10.1016/0304-4149(81)90026-0 · Zbl 0482.60097 · doi:10.1016/0304-4149(81)90026-0
[11] DOI: 10.1093/rfs/6.2.327 · Zbl 1384.35131 · doi:10.1093/rfs/6.2.327
[12] DOI: 10.1111/j.1540-6261.1987.tb02568.x · doi:10.1111/j.1540-6261.1987.tb02568.x
[13] Karatzas I., CRM Monograph Series 8, in: Lectures on the Mathematics of Finance (1996)
[14] DOI: 10.1007/978-3-662-12616-5 · doi:10.1007/978-3-662-12616-5
[15] DOI: 10.1023/A:1009703431535 · Zbl 0937.91052 · doi:10.1023/A:1009703431535
[16] DOI: 10.1086/294632 · doi:10.1086/294632
[17] DOI: 10.1016/0304-405X(76)90022-2 · Zbl 1131.91344 · doi:10.1016/0304-405X(76)90022-2
[18] DOI: 10.1111/1467-9965.00039 · Zbl 1020.91030 · doi:10.1111/1467-9965.00039
[19] DOI: 10.1093/rfs/4.4.727 · Zbl 1458.62253 · doi:10.1093/rfs/4.4.727
[20] DOI: 10.1016/0304-405X(87)90009-2 · doi:10.1016/0304-405X(87)90009-2
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