Exact Barrier Option Valuation with Arbitrary Functions for the Volatility
| Autor: | Allan Jonathan da Silva, Jack Baczynski, Dorival Leão, Estevão Rosalino |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | TEMA (São Carlos). 16:61 |
| ISSN: | 2179-8451 1677-1966 |
| DOI: | 10.5540/tema.2015.016.01.0061 |
| Popis: | Focus, in the past four decades, has been obtaining closed-form expressions for the no-arbitrage prices and hedges of modified versions of the Europeanoptions, allowing the dynamic of the underlying assets to have non-constant pa-rameters.In this paper, we obtain a closed-form expression for the price and hedge of an up-and-out European barrier option, assuming that the volatility in the dynamicof the risky asset is an arbitrary deterministic function of time. Setting a con-stant volatility, the formulas recover the Black and Scholes results, which suggestsminimum computational effort.We introduce a novel concept of relative standard deviation for measuring the ex-posure of the practitioner to risk (enforced by a strategy). The notion that is found in the literature is different and looses the correct physical interpreta-tion. The measure serves aiding the practitioner to adjust the number of rebalancesduring the option’s lifetime. |
| Databáze: | OpenAIRE |
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