An index option is a financial derivative that gives the holder the right to buy or to sell the value of the underlying index at the stated exercise price on or before the expiration date of the option. The holder has the right, but not the obligation to exercise the option. Since indices are actually more similar to physical goods than financial assets and at the same time, you can only trade with them indirectly, in this diploma thesis, I also mention options on physical goods and future options.
Because the cost of carry occurs in the case of index futures, the question arises whether the valuation of index options using the Black-Scholes formula is sufficiently precise. Fisher Black (1976) suggested that in the Black-Scholes formula, discounted forward prices should be used instead of spot prices. Empirical research has shown that Black's approach is better.
I compared the two approaches using real data on index options on the index S&P 500. Contrary to the findings of other authors, my study points to a slight advantage of the Black-Scholes model when pricing call options and slight advantage of Black's model when pricing put options.
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