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A new well-posed algorithm to recover implied local volatility
Authors:
Lishang Jiang a;
Qihong Chen b;
Lijun Wang c;
Jin E. Zhang d
| Affiliations: | a Institute of Mathematics, Tongji University, Shanghai, People's Republic of China |
| b Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, People's Republic of China | |
| c Department of Applied Mathematics, Tongji University, Shanghai, People's Republic of China | |
| d Department of Finance, Hong Kong University of Science and Technology, Kowloon, Hong Kong, People's Republic of China |
DOI:
10.1088/1469-7688/3/6/304
Publication Frequency:
8 issues per year
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(English)
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Abstract
This paper presents a new algorithm to calibrate the option pricing model, i.e. the algorithm that recovers the implied local volatility function from market option prices in the optimal control framework. A unique optimal control is shown to exist. Our algorithm is well-posed. Our numerical experiments show that, with the help of the techniques developed in the field of optimal control, the local volatility function is recovered very well.
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