Journal
INVERSE PROBLEMS
Volume 32, Issue 11, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/0266-5611/32/11/115010
Keywords
inverse parabolic problem; inverse option pricing; numerical integral equations
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Funding
- Research Grant Council of the Hong Kong Special Administrative Region [CityU 101112]
- NNSF of China [11261029, 11461039]
- NSF [DMS 10-08902, 15-14886]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1514886] Funding Source: National Science Foundation
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In this paper we investigate an inverse problem of determining the time-dependent volatility from observed market prices of options with different strikes. Due to the non linearity and sparsity of observations, an analytical solution to the problem is generally not available. Numerical approximation is also difficult to obtain using most of the existing numerical algorithms. Based on our recent theoretical results, we apply the linearisation technique to convert the problem into an inverse source problem from which recovery of the unknown volatility function can be achieved. Two kinds of strategies, namely, the integral equation method and the Landweber iterations, are adopted to obtain the stable numerical solution to the inverse problem. Both theoretical analysis and numerical examples confirm that the proposed approaches are effective.
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