This paper presents a valuation of vulnerable European options using a model with self‐exciting Hawkes processes that allow for clustered jumps rather than independent jumps. Many existing valuation models can be regarded as special cases of the model proposed here. Using numerical analyses, this study also performs sensitivity analyses and compares the results to those of existing models for European call options. The results show that jump clustering has a significant impact on the option value. © 2017 Wiley Periodicals, Inc. Jrl Fut Mark

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We investigate the valuation of volatility index (VIX) options by developing a model with a self-exciting Hawkes process that allows for clustering in the VIX. In the proposed framework, we find semianalytical expressions for the characteristic function and forward characteristic function, and then we solve the pricing problem of standard-start and forward-start options via the fast Fourier transform. The empirical results provide evidence to support the significance of accounting for volatility clustering when pricing VIX options. K E Y W O R D Sfast Fourier transform, self-exciting Hawkes process, VIX options, volatility clustering

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