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Multilevel monte carlo for exponential L\’{e} vy models. arXiv preprint arXiv:1403.5309
, 2014
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Applying the WienerHopf Monte Carlo simulation technique for Lévy processes to path functionals such as first passage times, undershoots and overshoots
, 2013
"... In this note we apply the recently established WienerHopf Monte Carlo (WHMC) simulation technique for Lévy processes from Kuznetsov et al. [17] to path functionals, in particular first passage times, overshoots, undershoots and the last maximum before the passage time. Such functionals have many ap ..."
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In this note we apply the recently established WienerHopf Monte Carlo (WHMC) simulation technique for Lévy processes from Kuznetsov et al. [17] to path functionals, in particular first passage times, overshoots, undershoots and the last maximum before the passage time. Such functionals have many applications, for instance in finance (the pricing of exotic options in a Lévy model) and insurance (ruin time, debt at ruin and related quantities for a Lévy insurance risk process). The technique works for any Lévy process whose running infimum and supremum evaluated at an independent exponential time allows sampling from. This includes classic examples such as stable processes, subclasses of spectrally one sided Lévy processes and large new families such as meromorphic Lévy processes. Finally we present some examples. A particular aspect that is illustrated is that the WHMC simulation technique performs much better at approximating first passage times than a ‘plain ’ Monte Carlo simulation technique based on sampling increments of the Lévy process.
Acknowledgements
, 2014
"... First and foremost I wish to express my deepest gratitude to my supervisor, Prof. Mike Giles for being unfailingly supportive and for being an inspiration. Without his expertise, his dedication and outstanding guidance this thesis would never have been possible. I am extremely grateful to the Man Gr ..."
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First and foremost I wish to express my deepest gratitude to my supervisor, Prof. Mike Giles for being unfailingly supportive and for being an inspiration. Without his expertise, his dedication and outstanding guidance this thesis would never have been possible. I am extremely grateful to the Man Group plc for their financial backing and for providing me with such an amazing work environment at the OxfordMan Institute. Special thanks go to William Chesters for his understanding and stimulation in the final stages of my thesis. Thanks to the University of Oxford, Lady Margaret Hall, the common rooms and clubs for making these years so unique and enriching. Thanks to the many unsung heroes of free software without whom I wouldn’t have had the tools for writing this thesis. On a more personal level, I would also like to mention the very special people I have the privilege to know both in Oxford and across the globe. I am greatly indebted to all of them for their kindness, their joviality, their wisdom and for all the things I have learnt from them. Although not mentioned individually, they will recognise themselves. To all of them: “Thanks for being part of my life”. Finally I want to thank my family for their love and for always supporting me in times of doubt. All I have and will accomplish is only possible thanks to them, the importance of their sacrifices could never be overstated. This work is for them.
Journal of Credit Risk 9(3), 121–140 Pricing of contingent convertibles under smile conform models
"... We look at the problem of pricing contingent convertible bonds (CoCos) where the underlying risky asset dynamics are given by a smile conform model, more precisely, an exponential Lévy process incorporating jumps and heavy tails. A core mathematical quantity, needed in closed form in order to produc ..."
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We look at the problem of pricing contingent convertible bonds (CoCos) where the underlying risky asset dynamics are given by a smile conform model, more precisely, an exponential Lévy process incorporating jumps and heavy tails. A core mathematical quantity, needed in closed form in order to produce an exact analytical expression for the price of a CoCo, is the law of the infimum of the underlying equity price process at a fixed time. With the exception of Brownian motion with drift, no such closed analytical form is available within the class of Lévy processes that are suitable for financial modeling. Very recently, however, J. M. Corcuera is supported by the MCI grant MTM200908218. A. FerreiroCastilla was partially supported by the MCI grant MTM200908869 and FEDER and by a Royal Society Newton International Fellowship. 121 122 J. M. Corcuera et al there has been some remarkable progress made with the theory of a large family of Lévy processes, known as ˇprocesses. Indeed, for this class of Lévy processes,
RANDOMISATION AND RECURSION METHODS FOR MIXEDEXPONENTIAL LÉVY MODELS, WITH FINANCIAL APPLICATIONS
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Applying the WienerHopf Monte Carlo simulation
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