Abstract
We consider the inverse problem of finding the volatility σ∈L ρ(0, T) such that \(U_{BS}(X,K,r,t,{{\int }_{0}^{t}}\sigma ^{2}(\tau )d\tau )=u(t)\), 0≤t≤T, where U B S is the Black–Scholes formula and u(t) is the observable fair price of an European call option. The problem is ill-posed. Using the residual method, we shall regularize the problem. An explicit error estimate is given.
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The authors are grateful to three anonymous referees for their precious suggestions leading to the improvement version of our paper.
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Trong, D.D., Thanh, D.N. & Lan, N.N. Regularization for the Inverse Problem of Finding the Purely Time-Dependent Volatility. Vietnam J. Math. 44, 513–530 (2016). https://doi.org/10.1007/s10013-015-0164-9
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DOI: https://doi.org/10.1007/s10013-015-0164-9