Abstract
In Chap. 10, we managed illiquidity in a Black and Scholes framework with an appropriate time change. Such an approach can be extended to jump-diffusions. Nevertheless, option pricing is a challenging task in this framework mainly because there is no analytical formula for options in the non-time-changed model. This chapter explores a new approach based on a fractional version of what is called Dupire’s equation (Dupire (Risk 7:18–20, 1994)), which is a forward partial differential equation (PDE) for option prices. This PDE is built on the assumption that the stock value is ruled by a geometric Brownian diffusion with a volatility that is a function of time and price.
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Hainaut, D. (2022). A Fractional Dupire Equation for Jump-Diffusions. In: Continuous Time Processes for Finance. Bocconi & Springer Series, vol 12. Springer, Cham. https://doi.org/10.1007/978-3-031-06361-9_11
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