There has been a lot of conflicting literature since the introduction of the Black and Scholes model. Such conflicts could be lessened if we accept, on a hypothetical basis, that market prices should correspond to the compound option pricing model. Chiras and Manaster have presented a to-be-tested profitable options trading strategy in which they would sell the option having a market price above the Black and Scholes model price and buy the option which has a market price lesser than that of Black Scholes model.
The difference in terms of weight of the implied variance values between the studies of Chiras and Manaster and that of Macbeth and Merville results in different outcomes of the Black and Scholes models of the two research groups. Though the differences are not significant, the price calculated by the model of Chiras and Manster comes out to be above than that of Macbeth and Merville. Apparently, the reason appears to be the deep selling of in the money option and deep out of money buying by Chiras and Manaster. Though the price is greater than that of Macbeth and Merville, it does not necessarily mean that the return would be greater as well when this strategy is employed. (Macbeth and Merville 1979)
Now that we have seen how the Black and Scholes model can give different result when elaborate studies use different assumptions and variables, let us go deeper into the pricing of options from the original perspective of Black and Scholes with their paper named ‘The Pricing of Options and Corporate Liabilities’. “We have done empirical tests of the valuation formula on a large body of call-option data. These tests indicate that the actual prices at which options are bought and sold deviate in certain systematic ways from the values predicted by the formula. Option buyers pay prices that are consistently higher than those predicted by the formula. Option writers, however, receive prices that are at about the level predicted by the formula. There are large transaction costs in the option market, all of which are effectively paid by option buyers.” (Black F. and Scholes M. 1973)
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