We obtain a closed-form solution for the double-Laplace transform of Asian options under the hyper-exponential jump diffusion model (HEM). Similar results are only available previously in the special case of the Black-Scholes model (BSM). Even in the case of the BSM, our approach is simpler as we essentially use only Itô’s formula and do not need more advanced results such as those of Bessel processes and Lamperti’s representation. As a by-product we also show that a well-known recursion relating to Asian options has a unique solution in a probabilistic sense. The double-Laplace transform can be inverted numerically via a two-sided Euler inversion algorithm. Numerical results indicate that our pricing method is fast, stable, and accurate, and performs well even in the case of low volatilities. Subject classifications: Finance: asset pricing. Probability: stochastic model applica-tions. Area of review: Financial engineering. 1

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Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. www.econstor.eu The Institute for the Study of Labor (IZA) in Bonn is a local and virtual international research center and a place of communication between science, politics and business. IZA is an independent nonprofit organization supported by Deutsche Post Foundation. The center is associated with the University of Bonn and offers a stimulating research environment through its international network, workshops and conferences, data service, project support, research visits and doctoral program. IZA engages in (i) original and internationally competitive research in all fields of labor economics, (ii) development of policy concepts, and (iii) dissemination of research results and concepts to the interested public. Terms of use: Documents in D I S C U S S I O N P A P E R S E R I E S IZA Discussion Papers often represent preliminary work and are circulated to encourage discussion. Citation of such a paper should account for its provisional character. A revised version may be available directly from the author. IZA Discussion Paper No. 7338 April 2013 ABSTRACT The Radical Innovation Investment Decision Refined We refine modelling of the radical innovation decision in this paper by extending real option theory to include non-marginal stochastic jump processes. From the model analytics we determine that the average magnitude and frequency of non-marginal stochastic jump processes are the most important parameters in this highly uncertain decision process. We show that these stochastic shocks imply that investment in radical innovation may very often be too time consuming and/or expensive to remain attractive for private entrepreneurs. JEL Classification: D92, D81, L26

We examine a Markov tree (MT) model for option pricing in which the dynamics of the underlying asset are modeled by a non-IID process. We show that the discrete probability mass function of log returns generated by the tree is closely approximated by a continuous mixture of two normal distributions. Using this normal mixture distribution and risk-neutral pricing, we derive a closed-form expression for European call option prices. We also suggest a regression tree-based method for estimating three volatility parameters σ, σ+, and σ − required to apply the MT model. We apply the MT model to price call options on 89 non-dividend paying stocks from the S&P 500 index. For each stock symbol on a given day, we use the same parameters to price options across all strikes and expiries. Comparing against the Black-Scholes model, we find that the MT model’s prices are closer to market prices. 1

Abstract Lévy processes with completely monotone jumps appear frequently in various applications of Probability. For example, all popular stock price models based on Lévy processes (such as the Variance Gamma, CGMY/KoBoL and Normal Inverse Gaussian) belong to this class. In this paper we continue the work started in

the unified form of pollaczek–khinchine formula for lévy processes with matrix-exponential negative jumps D. Gusak, Ie. Karnaukh For Lévy processes with matrix-exponential negative jumps, the unified form of the Pollaczek-Khinchine formula is established. 1

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