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Volatility in options formulae for general stochastic dynamics
1. | School of Mathematical Sciences, Monash University, Victoria 3800, Australia, Australia |
2. | School of Mathematical Sciences, Monash University Vic 3800 |
References:
[1] |
D. Aldous, Stopping times and tightness, Annals of Probability, Volume 6 (1978), 335-340.
doi: 10.1214/aop/1176995579. |
[2] |
K. Hamza and F. C. Klebaner, On nonexistence of non-constant volatility in the Black-Scholes formula, Discrete and Continuous Dynamical Systems, Volume 6 (2006), 829-834.
doi: 10.3934/dcdsb.2006.6.829. |
[3] |
K. Hamza and F. C. Klebaner, On one inverse problem in financial mathematics, Journal of Uncertain Systems, Volume 1 (2007), 246-255. |
[4] |
K. Hamza and F. C. Klebaner, On the implicit Black-Scholes formula, Stochastics: An International Journal of Probability and Stochastic Processes, Volume 80 (2008), 97-102.
doi: 10.1080/17442500701607706. |
[5] |
K. Hamza and F. C. Klebaner, Martingales in the Itô-Tanaka formula with applications,, Submitted., ().
|
[6] |
K. Hamza, S. Jacka and F. C. Klebaner, The EMM conditions in a general model for interest rates, Advances in Applied Probability, Volume 37 (2005), 415-434.
doi: 10.1239/aap/1118858632. |
[7] |
F. C. Klebaner and R. Liptser, When a stochastic exponential is a true martingale. Extension of a method of Beneŝ, Teoriya Veroyatnostei i ee Primeneniya, Volume 58 (2013), 53-80. |
[8] |
I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Graduate Texts in Mathematics, Springer-Verlag, New York, second edition, 1991.
doi: 10.1007/978-1-4612-0949-2. |
[9] |
A. T. Wang, Generalized Ito's formula and additive functionals of Brownian motion,, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 41 (): 153.
doi: 10.1007/BF00538419. |
show all references
References:
[1] |
D. Aldous, Stopping times and tightness, Annals of Probability, Volume 6 (1978), 335-340.
doi: 10.1214/aop/1176995579. |
[2] |
K. Hamza and F. C. Klebaner, On nonexistence of non-constant volatility in the Black-Scholes formula, Discrete and Continuous Dynamical Systems, Volume 6 (2006), 829-834.
doi: 10.3934/dcdsb.2006.6.829. |
[3] |
K. Hamza and F. C. Klebaner, On one inverse problem in financial mathematics, Journal of Uncertain Systems, Volume 1 (2007), 246-255. |
[4] |
K. Hamza and F. C. Klebaner, On the implicit Black-Scholes formula, Stochastics: An International Journal of Probability and Stochastic Processes, Volume 80 (2008), 97-102.
doi: 10.1080/17442500701607706. |
[5] |
K. Hamza and F. C. Klebaner, Martingales in the Itô-Tanaka formula with applications,, Submitted., ().
|
[6] |
K. Hamza, S. Jacka and F. C. Klebaner, The EMM conditions in a general model for interest rates, Advances in Applied Probability, Volume 37 (2005), 415-434.
doi: 10.1239/aap/1118858632. |
[7] |
F. C. Klebaner and R. Liptser, When a stochastic exponential is a true martingale. Extension of a method of Beneŝ, Teoriya Veroyatnostei i ee Primeneniya, Volume 58 (2013), 53-80. |
[8] |
I. Karatzas and S. E. Shreve, Brownian Motion and Stochastic Calculus, Graduate Texts in Mathematics, Springer-Verlag, New York, second edition, 1991.
doi: 10.1007/978-1-4612-0949-2. |
[9] |
A. T. Wang, Generalized Ito's formula and additive functionals of Brownian motion,, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 41 (): 153.
doi: 10.1007/BF00538419. |
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