Studies of Barrier Options and their Sensitivities

Abstract

Barrier options are cheaper than the respective standard European options, because a zero payoff may occur before expiry time T. Lower premiums are usually offered for more exotic barrier options, which make them particularly attractive to hedgers in the financial market. Under the Black-Scholes framework, we explicitly derive and present pricing formulae for a range of different European barrier options depending the options barrier variety, direction, activation time and whether it will be a call or put. A new pricing formulae is also presented, which to the best of our knowledge has not yet appeared in the literature. We compare numerical results of analytical formulae for option prices with Monte Carlo simulation where efficiency is improved via the variance reduction technique of antithetic variables. We also present numerical results for sensitivity estimation. We used finite differences to estimate the values of two Greeks, the Delta and the Eta, that characterise the changes in the specified options prices in response to small changes in the initial asset price S0 and barrier height H. Politics is for the present, but an equation is for eternity... Albert Einstein

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Cite this paper

@inproceedings{Stoklosa2007StudiesOB, title={Studies of Barrier Options and their Sensitivities}, author={Jakub Stoklosa and Aihua Xia}, year={2007} }