Pricing options is an important activity in quantitative finance for financial engineering purpose. Exotic options are class of options with nonstandard features serving market segments: specific hedging need, tax, accounting, legal, regulatory requirements or offer unique payoffs in particular market circumstances. While pricing options under the Wiener process is a well-established research topic, the introduction of Levy process into pricing procedure makes it become more challenging. However, the modification is a realistic reflection to the heavy tail property of returns of financial assets and it is a relevant research topic. In general, a close-form formula for pricing options does not exist, the objective of a potential dissertation thesis on this topic would be a design of a suitable numerical pricing model for a specified type of exotic options and then to verify its applicability for real-life conditions. The results will be submitted for publication in journals like Finance Research Letters, European Journal of Operational Research, SIAM Journal on Financial Mathematics.
References
- Jia, J., Lai, Y., Li, L., & Tan, V. (2020). Exotic options pricing under special Lévy process models: A biased control variate method approach. Finance Research Letters, 34, 101249.
- Lars Kirkby, J. (2018). American and exotic option pricing with jump diffusions and other Levy processes. Journal of Computational Finance, 22(3).
- Recchioni, M. C., Iori, G., Tedeschi, G., & Ouellette, M. S. (2021). The complete Gaussian kernel in the multi-factor Heston model: Option pricing and implied volatility applications. European Journal of Operational Research, 293(1), 336-360.
- Li, Y. (2022). A high-order numerical method for BSPDEs with applications to mathematical finance. SIAM Journal on Financial Mathematics, 13(1), 147-178.
