Journal of Applied Probability · 2011 · 22 citations · 6 references
EngineeringEconomicsFinanceFinancial EconomicsMathematical EconomicsStochastic ProcessesBrownian MotionMarkov ProcessesOption PricingOption Pricing ModelsSemi-markov ProcessesStochastic CalculusBarrier Option ValuationBrownian ExcursionLaplace TransformLaplace Transform AnalysisOption Pricing TheoryOption Pricing ValuationSemi-markov ModellingSemi-markov Multi-state Models
In this paper we study the excursion time of a Brownian motion with drift outside a corridor by using a four-state semi-Markov model. In mathematical finance, these results have an important application in the valuation of double-barrier Parisian options. We subsequently obtain an explicit expression for the Laplace transform of its price.
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Richard J. Haber, Philipp Schönbucher, Paul Wilmott · 1999 · 74 citations
Business, Finance, Mathematics +17
A Guided Tour through Excursions
L. C. G. Rogers · Bulletin of the London Mathematical Society · 1989 · 68 citations