 |
|
|
| | | | | |
|
|
|
|
|
Option Price When the Stock is a Semimartingale
|
Fima Klebaner, University Melbourne
|
Abstract
The purpose of this note is to give a PDE
satisfied by a call
option when the price process is a semimartingale. The main
result generalizes the PDE
in the case when the stock price is a diffusion. Its proof uses
Meyer-Tanaka and occupation density formulae. Presented approach
also gives a new insight into the classical Black-Scholes formula.
Rigorous proofs of some known results are also given.
|
Full text: PDF
Pages: 79-83
Published on: January 31, 2002
|
Bibliography
- Bartels, H-J. (2000), On martingale diffusions describing the
'smile-effect' from implied volatilities. Appl. Stochastic models Bus.
Ind. 16, 1-9. Math. Review
2001d:91089
- Breeden, D. and Litzenberger, R. (1978), Prices of contingent claims
implied in option prices. Journal of Business, 51, 621-651. Math. Review number not
available.
- Dupire, B. (1994)), Pricing with a smile. Risk 7, 18-20.
Math. Review number not available.
- Dupire, B. (1997) Pricing and hedging with smiles. in Mathematics
of derivative securities. Dempster and Pliska eds., Cambridge Uni. Press,
103-112. Math.
Review 98k:90014
- Klebaner, F.C. (1998), Introduction to Stochastic Calculus with
Applications, Imperial College Press, London. Math. Review
1832481
- Protter, P. (1992), Stochastic Integration and Differential
Equations, Springer-Verlag, Berlin. Math. Review
91i:60148
- Shiryaev, A.N. (1999), Essentials of Stochastic Finance World
Scientific, Singapore. Math. Review
2000e:91085
|
|
|
|
|
|
|
|
| | | | |
Electronic Communications in Probability. ISSN: 1083-589X |
|
Context