Abstract
The empirical characteristics of the underlying asset prices should be taken into account for the pricing and hedging of options. In this paper, we show how to price basket options when assets follow the “shifted asymmetric jump-diffusion” process. The methodology is based on the Hermite polynomial expansion that can match exactly the first m moments of the model implied-probability distribution. The resultant pricing and hedging formulae are in closed-form and similar to the Black and Scholes ones.
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Notes
- 1.
The content and notation in this subsection benefit from [6, Chap. 11.5].
- 2.
The proofs of this and all other results are provided by the authors upon request.
- 3.
For a review on selection of pricing measures, see [2] and references within.
- 4.
Henceforth, \({\tilde {E}}\) is used to indicate the expectation operator under the risk-neutral measure \(\tilde {P}\).
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Paletta, T., Leccadito, A., Tunaru, R. (2014). Pricing and Hedging Basket Options Under Shifted Asymmetric Jump-Diffusion Processes. In: Perna, C., Sibillo, M. (eds) Mathematical and Statistical Methods for Actuarial Sciences and Finance. Springer, Cham. https://doi.org/10.1007/978-3-319-05014-0_38
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DOI: https://doi.org/10.1007/978-3-319-05014-0_38
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-05013-3
Online ISBN: 978-3-319-05014-0
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