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Transform analysis and asset pricing for affine jump-diffusions. (English) Zbl 1055.91524
Summary: In the setting of ‘affine’ jump-diffusion state processes, this paper provides an analytical treatment of a class of transforms, including various Laplace and Fourier transforms as special cases, that allow an analytical treatment of a range of valuation and econometric problems. Example applications include fixed-income pricing models, with a role for intensity-based models of default, as well as a wide range of option-pricing applications. An illustrative example examines the implications of stochastic volatility and jumps for option valuation. This example highlights the impact on option ‘smirks’ of the joint distribution of jumps in volatility and jumps in the underlying asset price, through both jump amplitude and jump timing.

MSC:
91G60 Numerical methods (including Monte Carlo methods)
60J60 Diffusion processes
91G20 Derivative securities (option pricing, hedging, etc.)
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