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Option prices as probabilities
Finance Research Letters, 2008Four distribution functions are associated with call and put prices seen as functions of their strike and maturity. The random variables associated with these distributions are identified when the process for moneyness defined as the stock price relative to the forward price is a positive local martingale with no positive jumps that tends to zero at ...
Madan, Dilip +2 more
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A Mellin transform approach to barrier option pricing
IMA Journal of Management Mathematics, 2018A barrier option is an exotic path-dependent option contract that, depending on terms, automatically expires or can be exercised only if the underlying asset ever reaches a predetermined barrier price. Using a partial differential equation approach, we
C. Guardasoni, M. Rodrigo, S. Sanfelici
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Pricing Vulnerable Options with Copulas [PDF]
SSRN Electronic Journal, 2002 Counterparty risk is usually defined as the risk which stems from the fact that the counterparty of a derivative contract is not solvent before or at expiration. As most of the derivative trading activity has been moving from standardized products quoted on futures‐style markets, towards customized products traded on over‐the‐counter markets, the issue
CHERUBINI, U, LUCIANO, Elisa, E.
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CONVERGENCE SPEED OF GARCH OPTION PRICE TO DIFFUSION OPTION PRICE [PDF]
International Journal of Theoretical and Applied Finance, 2009 It is well known that as the time interval between two consecutive observations shrinks to zero, a properly constructed GARCH model will weakly converge to a bivariate diffusion. Naturally the European option price under the GARCH model will also converge to its bivariate diffusion counterpart.
Duan, J.-C., Wang, Y., Zou, J.
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Theory of Probability & Its Applications, 1995
We describe various models, which can be approximated by binomial models of a market of securities [\textit{J. C. Cox}, \textit{S. A. Ross} and \textit{M. Rubinstein}, J. Financ. Econ. 7, No. 3, 229--263 (1979; Zbl 1131.91333)] and introduce the corresponding approximation formulas for the value of options.
Svetlozar T. Rachev, Ludger Rüschendorf
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We describe various models, which can be approximated by binomial models of a market of securities [\textit{J. C. Cox}, \textit{S. A. Ross} and \textit{M. Rubinstein}, J. Financ. Econ. 7, No. 3, 229--263 (1979; Zbl 1131.91333)] and introduce the corresponding approximation formulas for the value of options.
Svetlozar T. Rachev, Ludger Rüschendorf
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2004
Publisher Summary This chapter discusses how the seminal Black-Scholes model, which relies on constant volatility and a normal distribution, has problems capturing the pricing properties of particularly close-to-maturity and deep in and out-of-the-money options..
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Publisher Summary This chapter discusses how the seminal Black-Scholes model, which relies on constant volatility and a normal distribution, has problems capturing the pricing properties of particularly close-to-maturity and deep in and out-of-the-money options..
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The Journal of Finance, 1985
ABSTRACTThe purpose of this article is to compare the Perrakis and Ryan bounds of option prices in a single‐period model with option bounds derived using linear programming. It is shown that the upper bounds are identical but that the lower bounds are different. A comparison of these bounds, together with Merton's bounds and the Black‐Scholes prices in
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ABSTRACTThe purpose of this article is to compare the Perrakis and Ryan bounds of option prices in a single‐period model with option bounds derived using linear programming. It is shown that the upper bounds are identical but that the lower bounds are different. A comparison of these bounds, together with Merton's bounds and the Black‐Scholes prices in
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2002
This chapter is devoted to exotic options, which include multifactor options and Asian options. Non-constant coefficients require numerical methods for more general PDEs than those discussed in Chapter 4. Upwind schemes, stability issues and total variation diminishing are discussed.
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This chapter is devoted to exotic options, which include multifactor options and Asian options. Non-constant coefficients require numerical methods for more general PDEs than those discussed in Chapter 4. Upwind schemes, stability issues and total variation diminishing are discussed.
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Dark wave, rogue wave and perturbation solutions of Ivancevic option pricing model
Nonlinear dynamics, 2021Yu-Qiong Chen +4 more
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On the theory of option pricing
Acta Applicandae Mathematicae, 1984The study of speculative prices led the French mathematician L. Bachelier already in 1900 to the discovery of the mathematical theory of Brownian motion, five years before Einstein's classic paper. Since then, several prominent economists and mathematicians, i.e. P. Samuelson, H. P. McKean, R. Merton, H. Fölmer and C. Stricker,...
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