Efficient Pricing and Calibration of High-Dimensional Basket Options
| Autor: | Grzelak, Lech A., Jablecki, Juliusz, Gatarek, Dariusz |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | This paper studies equity basket options -- i.e., multi-dimensional derivatives whose payoffs depend on the value of a weighted sum of the underlying stocks -- and develops a new and innovative approach to ensure consistency between options on individual stocks and on the index comprising them. Specifically, we show how to resolve a well-known problem that when individual constituent distributions of an equity index are inferred from the single-stock option markets and combined in a multi-dimensional local/stochastic volatility model, the resulting basket option prices will not generate a skew matching that of the options on the equity index corresponding to the basket. To address this ``insufficient skewness'', we proceed in two steps. First, we propose an ``effective'' local volatility model by mapping the general multi-dimensional basket onto a collection of marginal distributions. Second, we build a multivariate dependence structure between all the marginal distributions assuming a jump-diffusion model for the effective projection parameters, and show how to calibrate the basket to the index smile. Numerical tests and calibration exercises demonstrate an excellent fit for a basket of as many as 30 stocks with fast calculation time. Comment: 23 pages, 21 figures |
| Databáze: | arXiv |
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