Valuation of piecewise linear barrier options |
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Institution: | School of Economic Mathematics, Southwestern University of Finance and Economics, 555 Liutai Boulevard, Wenjiang, Chengdu 611130, PR China;School of Marxism, School of Business, Key Laboratory of Large Data Processing and Analysis of Electronic Commerce in Henan, Luoyang Normal University, Luoyang 471934, China |
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Abstract: | This paper discusses the valuation of piecewise linear barrier options that generalize classical barrier options. We establish formulas for joint probabilities of the logarithmic returns of the underlying asset and its partial running maxima when the process has a piecewise constant drift. In particular, we show that our results embrace the famous reflection principle as a special case, and that our established proposition delivers useful scalability for computing desired probabilities related to various types of barriers. We derive the closed-form prices of piecewise linear barrier options under the Black–Scholes framework, which are obtainable with little effort by relying on the derived probabilities. In addition, we provide numerical examples and discuss how option prices respond to several types of piecewise linear barriers. |
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Keywords: | Brownian motion Piecewise linear barrier Esscher transform Refractive reflection principle Barrier option |
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