Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/telegraph-processes-and-option-pricing-financial-modelling-and-option-D0I9Q1QhBn
References (38)
-
E. Nicolato, E. Venardos (2003)
Option Pricing in Stochastic Volatility Models of the Ornstein‐Uhlenbeck typeMathematical Finance, 13
-
L. Bachelier (2006)
Louis Bachelier's Theory of Speculation: The Origins of Modern Finance -
V. Anh, A. Inoue (2005)
Financial Markets with Memory I: Dynamic ModelsStochastic Analysis and Applications, 23
-
J. Masoliver, M. Montero, J. Perelló, George Weiss (2003)
The Ctrw in Finance: Direct and Inverse ProblemsCapital Markets: Market Efficiency
-
R. Elliott, Carlton Osakwe (2006)
Option Pricing for Pure Jump Processes with Markov Switching CompensatorsFinance and Stochastics, 10
-
F. Delbaen, W. Schachermayer (1994)
A general version of the fundamental theorem of asset pricingMathematische Annalen, 300
-
A. Crescenzo, F. Pellerey (2002)
On prices' evolutions based on geometric telegrapher's processApplied Stochastic Models in Business and Industry, 18
-
S. Shreve (2010)
Stochastic Calculus for Finance II: Continuous-Time Models -
J. Masoliver, M. Montero, J. Perelló, G. Weiss (2006)
The continuous time random walk formalism in financial marketsJournal of Economic Behavior and Organization, 61
-
A. Pogorui, R. Rodríguez-Dagnino (2009)
Evolution process as an alternative to diffusion process and Black–Scholes Formula, 17
-
Kwai Leung, Y. Kwok (2007)
Distribution of occupation times for constant elasticity of variance diffusion and the pricing of α-quantile optionsQuantitative Finance, 7
-
D. Lamberton, B. Lapeyre (2007)
Introduction to Stochastic Calculus Applied to Finance -
Y. Kwok, K. Leung (2006)
Distribution of Occupation Times for Cev Diffusions and Pricing of Alpha-Quantile OptionsS&P Global Market Intelligence Research Paper Series
-
F. Black, Myron Scholes (1973)
The Pricing of Options and Corporate LiabilitiesJournal of Political Economy, 81
-
G. Masi, Y. Kabanov, W. Runggaldier (1995)
Mean-variance hedging of options on stocks with Markov volatilitiesTheory of Probability and Its Applications, 39
-
N. Ratanov, A. Melnikov (2007)
On financial markets based on telegraph processesStochastics, 80
-
A. Etheridge (2002)
A course in financial calculus -
N. Ratanov (2008)
Jump telegraph processes and a volatility smile -
Oscar López, N. Ratanov (2012)
Option Pricing Driven by a Telegraph Process with Random JumpsJournal of Applied Probability, 49
-
M. Musiela, M. Rutkowski (2002)
Martingale Methods in Financial Modelling -
J. Harrison, S. Pliska (1981)
Martingales and stochastic integrals in the theory of continuous tradingStochastic Processes and their Applications, 11
-
B. Øksendal (1985)
Stochastic Differential EquationsThe Mathematical Gazette, 77
-
A. Inoue, Yumiharu Nakano, V. Anh (2006)
Linear filtering of systems with memory and application to financeJournal of Applied Mathematics and Stochastic Analysis, 2006
-
N. Ratanov (2004)
A jump telegraph model for option pricingQuantitative Finance, 7
-
Leif Andersen, J. Andreasen (1999)
Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for PricingDerivatives eJournal
-
J. Harrison, S. Pliska (1983)
A stochastic calculus model of continuous trading: Complete marketsStochastic Processes and their Applications, 15
-
P. Malliavin, Anton Thalmaier (2005)
Stochastic Calculus of Variations in Mathematical Finance -
Patrick Billingsley (1970)
Convergence of Probability MeasuresThe Mathematical Gazette, 54
-
A. Whitehead (1949)
An Introduction to MathematicsNature, 163
-
L. Bachelier (1964)
Theory of Speculation -
S. Shreve (2004)
Stochastic calculus for finance -
S. Garrett (2013)
An Introduction to Derivative Pricing -
N. Ratanov (2008)
Option Pricing Model Based on a Markov-modulated Diffusion with JumpsarXiv: Pricing of Securities
-
J. Steele (2000)
Stochastic Calculus and Financial Applications -
M. Abramowitz, I. Stegun, David Miller (1965)
Handbook of Mathematical Functions With Formulas, Graphs and Mathematical Tables (National Bureau of Standards Applied Mathematics Series No. 55)Journal of Applied Mechanics, 32
-
J. Cardoso, Edward Lee, Jie Liu, Haiyang Zheng (2013)
Continuous-Time Models -
M. Baxter (1996)
Financial Calculus: An Introduction to Derivative Pricing -
I. Karatzas, S. Shreve (2010)
Methods of Mathematical Finance
- Publisher
- Springer Berlin Heidelberg
- Copyright
- © The Author(s) 2013
- ISBN
- 978-3-642-40525-9
- Pages
- 89 –125
- DOI
- 10.1007/978-3-642-40526-6_5
- Publisher site
- See Chapter on Publisher Site
Abstract
[In Chapter 5 we apply the results of previous chapters for option pricing. The fundamental building block of all financial modelling is the concept of arbitrage-free and complete market. For the time- and space-continuous stochastic models the unique underlying process satisfying this concept is the geometric Brownian motion. In contrast, we suggest another approach to the continuous-time stochastic modelling of financial markets based on the telegraph processes. We construct a simple model, which is free of arbitrage and complete.]
Published: Oct 18, 2013
Keywords: Option pricing; Hedging strategies; Martingales; Jump-telegraph processes; Rescaling; Implied volatility