Article

# Pricing Asian options under a Hyper-Exponential jump diffusion model

Operations Research (Impact Factor: 1.79). 07/2011; 60(1). DOI: 10.2307/41476338

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**ABSTRACT:**We develop approximate formulae expressed in terms of elementary functions for the density, the price and the Greeks of path dependent options of Asian style, in a general local volatility model. An algorithm for computing higher order approximations is provided. The proof is based on a heat kernel expansion method in the framework of hypoelliptic, not uniformly parabolic, partial differential equations.Journal of Computational and Applied Mathematics 01/2013; 237(1):442–459. · 0.99 Impact Factor -
##### Article: Fluctuations of stable processes and exponential functionals of hypergeometric Levy processes

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**ABSTRACT:**We study the distribution and various properties of exponential functionals of hypergeometric Levy processes. We derive an explicit formula for the Mellin transform of the exponential functional and give both convergent and asymptotic series expansions of its probability density function. As applications we present a new proof of some of the results on the density of the supremum of a stable process, which were recently obtained by Kuznetsov "On extrema of stable processes" (2010) and Hubalek and Kuznetsov "A convergent series representation for the density of the supremum of a stable process" (2010). We also derive some new results related to (i) the entrance law of the stable process conditioned to stay positive, (ii) the entrance law of the excursion measure of the stable process reflected at its past infimum and (iii) the entrance law and the last passage time of the radial part of n-dimensional symmetric stable process. Comment: 26 pagesActa Applicandae Mathematicae 12/2010; · 0.99 Impact Factor -
##### Article: CoCos, Bail-In, and Tail Risk

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**ABSTRACT:**We develop a capital structure model to analyze the incentives created by contingent convertibles (CoCos) and bail-in debt, two variants of debt that converts to equity as a bank nears or reaches financial distress. Our formulation includes firm-specific and market-wide tail risk in the form of two types of jumps and leads to a tractable jump-diffusion model of the firm's income and asset value. The firm's liabilities include insured deposits and senior and subordinated debt, as well as convertible debt. Our model combines endogenous default, debt rollover, and jumps; these features are essential in examining how changes in capital structure to include CoCos or bail-in debt change incentives for equity holders. We derive closed-form expressions to value the firm and its liabilities, and we use these to investigate how CoCos affect debt overhang, asset substitution, the firm's ability to absorb losses, the sensitivity of equity holders to various types of risk, and how these properties interact with the firm's debt maturity profile, the tax treatment of CoCo coupons, and the pricing of deposit insurance. We examine the effects of varying the two main design features of CoCos, the conversion trigger and the conversion ratio, and we compare the effects of CoCos with the effects of reduced bankruptcy costs through orderly resolution. Across a wide set of considerations, we find that CoCos generally have positive incentive effects when the conversion trigger is not set too low. The need to roll over debt, the debt tax shield, and tail risk in the firm's income and asset value have particular impact on the effects of CoCos. We also identify a phenomenon of debt-induced collapse that occurs when a firm issues CoCos and then takes on excessive additional debt: the added debt burden can induce equity holders to raise their default barrier above the conversion trigger, effectively changing CoCos to junior straight debt; equity value experiences a sudden drop at the point at which this occurs. Finally, we calibrate the model to past data on the largest U.S. bank holding companies to see what impact CoCos might have had on the financial crisis. We use the calibration to gauge the increase in loss absorbing capacity and the reduction in debt overhang costs resulting from CoCos. We also time approximate conversion dates for high and low conversion triggers.SSRN Electronic Journal 01/2013;

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