Heat Kernels, Solvable Lie Algebras, and the Mean Reverting Sabr Stochastic Volatility Model
نویسندگان
چکیده
We use commutator techniques and calculations in solvable Lie groups to investigate certain evolution Partial Differential Equations (PDEs for short) that arise in the study of stochastic volatility models, pricing contingent claims on risky assets. In particular we derive the exact kernel of the fundamental solution of a degenerate PDE, which corresponds to a singular small-diffusion limit of the full SABR model with mean reversion. Although our results are motivated by the SABR model with mean reversion, they often apply in a more general setting.
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