ON ROBUSTNESS OF THE BLACK–SCHOLES PARTIAL DIFFERENTIAL EQUATION MODEL

Miklavz Mastinsek ()
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Miklavz Mastinsek: EPF-University of Maribor, Razlagova 14, 2000 Maribor, Slovenia

International Journal of Theoretical and Applied Finance (IJTAF), 2016, vol. 19, issue 02, 1-11

Abstract: When the discretely adjusted option hedges are constructed by the continuous-time Black–Scholes delta, then the hedging errors appear. The first objective of the paper is to consider a discrete-time adjusted delta, such that the hedging error can be reduced. Consequently, a partial differential equation for option valuation associated with the problem is derived and solved.The second objective is to compare the obtained results with the results given by the Black–Scholes formula. The obtained option values may be higher than those given by the Black–Scholes formula, however, unless the option is near expiry, the difference is relatively small.

Keywords: Options; discrete and continuous hedging; partial delay differential equation (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1142/S0219024916500138

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