Applied and Computational Mathematics
Volume 4, Issue 3, June 2015, Pages: 214-219
Received: May 8, 2015;
Accepted: May 20, 2015;
Published: Jun. 16, 2015
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Mihai Grigore Bunea Domsa, Department of Mathematics and Computer Science, Babes-Bolyai University, Cluj-Napoca, Romania
The aim of this paper is to present the price and replicating strategy for an European option on spot (or cash) underlier with continuous dividend yield, when the instrument used in the dynamic hedging of the option is a futures contract on the respective underlier. It formalizes the heuristic practice among option traders to replicate options on a stock index using futures on the respective stock index and investigates weather the obtained results differ significantly from what they would get using the actual stock index, as required by Black-Scholes pricing. Heuristically, the substitution is supported by index and futures prices being close, at least for small dividends and time to maturity. Our method is to express this practice in accounting terms, derive the self-financing portfolio dynamics and then the closed form option price and delta. Finally, run numerical simulations and compare results obtained by Black-Scholes versus our approach. Results show both the price and delta formulas differ from Black-Scholes, however numeric simulation doesn’t yield high enough differences to warrant obvious arbitrage, meaning that while not rigorously exact, the approximation is good enough for most practical use cases.
Mihai Grigore Bunea Domsa,
Hedging Stock Options Using Futures Contracts on the Stock, Applied and Computational Mathematics.
Vol. 4, No. 3,
2015, pp. 214-219.
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