- Date: 14 Apr. (Thu.)
- Place: On the Web
- Time: 17:00-18:30
- Speaker: Umut Cetin (London School of Economics)
- Title: Speeding up the Euler scheme for killed diffusions
- Abstract:
Let X be a linear diffusion taking values in (l,r) and consider the standard Euler discretisation to compute the fair price of a Barrier option written on X that becomes worthless if X hits one of the barriers before the maturity date T. It is well-known since Gobet’s work that the presence of killing introduces a loss of accuracy and reduces the weak convergence rate to N^{-1/2} with N being the number of discretisatons. We introduce a drift-implicit Euler method to bring the convergence rate back to 1/N, i.e. the optimal rate in the absence of killing, using the theory of recurrent transformations. Although the current setup assumes a one-dimensional setting, multidimensional extension is within reach as soon as a systematic treatment of recurrent transformations is available in higher dimensions.
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