In the present paper we explore the problem for pricing discrete barrier options utilizing the Black Scholes model for the random movement of the asset price. We postulate the problem as a path integral calculation by choosing approach that is similar to the quadrature method. Thus, the problem is reduced to the estimation of a multi-dimensional integral whose dimension corresponds to the number of the monitoring dates. We propose a fast and accurate numerical algorithm for its valuation. Our results for pricing discretely monitored one and double barrier options are in agreement with those obtained by other numerical and analytical methods in Finance and literature. A desired level of accuracy is very fast achieved for values of the underlying asset close to the strike price or the barriers. The method has a simple computer implementation and it permits observing the entire life of the option.
Numerical valuation of discrete barrier options / M., Milev; Tagliani, Aldo. - In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - ISSN 0377-0427. - ELETTRONICO. - vol. 233:(2010), pp. 2468-2480.
Numerical valuation of discrete barrier options
Tagliani, Aldo
2010-01-01
Abstract
In the present paper we explore the problem for pricing discrete barrier options utilizing the Black Scholes model for the random movement of the asset price. We postulate the problem as a path integral calculation by choosing approach that is similar to the quadrature method. Thus, the problem is reduced to the estimation of a multi-dimensional integral whose dimension corresponds to the number of the monitoring dates. We propose a fast and accurate numerical algorithm for its valuation. Our results for pricing discretely monitored one and double barrier options are in agreement with those obtained by other numerical and analytical methods in Finance and literature. A desired level of accuracy is very fast achieved for values of the underlying asset close to the strike price or the barriers. The method has a simple computer implementation and it permits observing the entire life of the option.File | Dimensione | Formato | |
---|---|---|---|
Milev-M._2010_J.-Comput.-Appl.-Math.pdf
Solo gestori archivio
Tipologia:
Post-print referato (Refereed author’s manuscript)
Licenza:
Tutti i diritti riservati (All rights reserved)
Dimensione
670.2 kB
Formato
Adobe PDF
|
670.2 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione