The use of Markov discontinuous processes in the pricing of derivative securities: the application of APL

ABSTRACT

The paper deals with one of the most important fields of research in modern financial theory: the valuation of derivatives. The aim of the work is the use of a discontinuous Markov process to model the dynamics of stock prices and, consequently to discover the right price of the derivative instruments, in place of the traditional binomial multiplicative process used frequently in many discrete models. At the end of the work various applications are presented. In them the stochastic process of the stock prices is modelled with the use of a simple and powerful APL program. In the applications APL shows all its capacity of calculation and matrix manipulation for mathematical uses.

REFERENCES

• 1: APL PLUS Iti for Windows (1994); Manugistics
• 2: ODX D. - MILLER H. (1965) 7he Oheory of uodmstic pro0m~; Chapman & Hall
• 3: DE F}NETTI B. (1970) Tmr/a de//e ~/t~ Einaudi; pag. 321-335
• 4: ~ J. (1988) ~ fua~~ arm o~ s~ Prentice Hall Int.
• 5: MIC~XX}I M. (1993) Note sul con'Cvnwne~ di alomi ti~i ~#a del mor,~ t~s~ italia~: la pm~sta di m ~ di w/umz~rw, Institute of Economical Studies; University of Rome LUISS; Working Paper n. 78

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing

Additional Classification:
  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY

General Terms:
Experimentation, Languages

Keywords:
APL applications in finance, discrete Markov processes, option pricing