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A very efficient approach to compute the first-passage probability density function in a time-changed Brownian model: Applications in finance
- Publication Year :
- 2016
- Publisher :
- Elsevier B.V., 2016.
-
Abstract
- We propose a numerical method to compute the first-passage probability density function in a time-changed Brownian model. In particular, we derive an integral representation of such a density function in which the integrand functions must be obtained solving a system of Volterra equations of the first kind. In addition, we develop an ad-hoc numerical procedure to regularize and solve this system of integral equations. The proposed method is tested on three application problems of interest in mathematical finance, namely the calculation of the survival probability of an indebted firm, the pricing of a single-knock-out put option and the pricing of a double-knock-out put option. The results obtained reveal that the novel approach is extremely accurate and fast, and performs significantly better than the finite difference method.
- Subjects :
- Statistics and Probability
Mathematical optimization
System of integral equations
Option pricing
Probability density function
010103 numerical & computational mathematics
Default risk
First-passage probability
Numerical quadrature
Time-changed Brownian motion
01 natural sciences
010305 fluids & plasmas
System of integral equation
0103 physical sciences
Functional integration
0101 mathematics
Martingale representation theorem
Mathematics
Fractional Brownian motion
Numerical analysis
Mathematical finance
Probability and statistics
Condensed Matter Physics
Settore SECS-S/06 - METODI MATEMATICI DELL'ECONOMIA E DELLE SCIENZE ATTUARIALI E FINANZIARIE
Valuation of options
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....49f6929a96d595677b7a133b299494cb