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We propose an iterative method for pricing American options under jump-diffusion models. A finite difference discretization is performed on the partial integro-differential equation, and the American option pricing problem is formulated as a linear complementarity problem (LCP). Jump-diffusion...
Persistent link: https://www.econbiz.de/10014186631
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth order accurate in space and second order accurate in time. Under some restrictions, theoretical results like unconditional stability in the sense of von Neumann...
Persistent link: https://www.econbiz.de/10014193175
An exact closed-form pricing formula was derived for American options when stock returns follow a normal distribution or Lévy processes. It uses a new non-homogeneous partial differential equation for American options, the condition from optimal early exercise general solution, and hence a...
Persistent link: https://www.econbiz.de/10013250399
Closed-form pricing formulae and option Greeks are obtained for European-type options using an orthogonal polynomial series -- complex Fourier series. We assume that risky assets are driven by exponential Lévy processes and stochastic volatility models. We provide a succinct error analysis to...
Persistent link: https://www.econbiz.de/10012967806
This paper addresses several theoretical and practical issues in option pricing and implied volatility calibration in a fractional Black-Scholes market. In particular, we discuss how the fractional Black-Scholes model admits a non-constant implied volatility term structure when the Hurst...
Persistent link: https://www.econbiz.de/10012969066
In this paper we propose a Gaussian quadrature method to study American and exotic option pricing under the jump-diffusion model of Merton (1976). Our numerical experiments show that the Gaussian quadrature method, compared to several existing methods in the literature, including the fast Gauss...
Persistent link: https://www.econbiz.de/10012956280
This paper develops a closed-form model for options on commodities under the assumptions of mean-reversion in the commodity prices and regime-switching in the commodity returns volatility. After a closed-form solution for the option value in constant regimes has been developed, the model is...
Persistent link: https://www.econbiz.de/10013022750
American options are actively traded worldwide on exchanges, thus making their accurate and efficient pricing an important problem. As most financial markets exhibit randomly varying volatility, in this paper we introduce an approximation of American option price under stochastic volatility...
Persistent link: https://www.econbiz.de/10013031914
We propose a time-adaptive high-order compact finite difference scheme for option pricing in a family of stochastic volatility models. We employ a semi-discrete high-order compact finite difference method for the spatial discretisation, and combine this with an adaptive time discretisation,...
Persistent link: https://www.econbiz.de/10013218643
We build on of the work of Henry-Labordµere and Lewis on the small-time behaviour of the return distribution under a general local-stochastic volatility model with zero correlation. We do this using the Freidlin-Wentzell theory of large deviations for stochastic differential equations, and then...
Persistent link: https://www.econbiz.de/10013116586