5. Basic PDE in Finance

  1. Jacques Janssen,
  2. Oronzio Manca and
  3. Raimondo Manca
  1. Jacques Janssen,
  2. Oronzio Manca and
  3. Raimondo Manca

Published Online: 4 APR 2013

DOI: 10.1002/9781118578339.ch5

Applied Diffusion Processes from Engineering to Finance

Applied Diffusion Processes from Engineering to Finance

How to Cite

Janssen, J., Manca, O. and Manca, R. (2013) Basic PDE in Finance, in Applied Diffusion Processes from Engineering to Finance, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9781118578339.ch5

Publication History

  1. Published Online: 4 APR 2013
  2. Published Print: 4 MAR 2013

ISBN Information

Print ISBN: 9781848212497

Online ISBN: 9781118578339

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Keywords:

  • Black-Scholes-Samuelson model;
  • finance;
  • option theory;
  • partial differential equations (PDEs);
  • zero-coupon pricing

Summary

This chapter shows how some partial differential equations (PDEs) appear in finance in such a way that they are very similar to the PDEs found, a long time before, in engineering giving, in particular, to Black and Scholes the possibility to prove their famous formula in option theory. It develops two aspects; first, the case of option theory and second, the case of evaluating zero-coupons under the assumption of an absence of arbitrage (AOA). The first basic derivative instruments are called plain vanilla options. Pricing plain and no plain vanilla calls with the Black–Scholes–Samuelson model are considered in the chapter.