Local volatility calibration with optimal control in a Hamiltonian framework

• We formulate the calibration of a local volatility function that makes a solution to Dupie's equation match market data as an optimal control problem for which optimality conditions are given by a Hamiltonian system. Regularization is added by mollifying the Hamiltonian functional in this system. We have direct access to the Jacobian matrix of the Hamiltonian system, and can therefore employ a Newton based method in the solving phase, whereas other studies tend to use gradient based methods or quasi Newton algorithms. We illustrate our method by calibrating a volatility function to market data on the Euro Stoxx 50 index and find that our algorithm is both accurate and robust.

Ämnesord

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Nyckelord

Finance

local volatility

calibration

optimal control

inverse problems

Matematik

Mathematics

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