The Fair Value of an option is actually the current value of expected payoff of a contract at its expiration. Mathematically speaking, an expected value is always calculated by weighting of all possible outcomes by their probabilities.
The key property of such a formula, using the arithmetic average, is that it does not take into account the compounding effect of the previous returns. In other words, the Fair Value of options assumes that the profit/losses of all the hypothetical “trades” are not capitalized, and one particular outcome does not influence the “magnitude” on the next trade. The basis of each trade is the initial portfolio value and does not change during the whole experiment.
That is not exactly what happens in real trading, of course. Usually, the result of a trade is accrued on the portfolio and the size of the next trade is calculated on the new basis – including the previous results. That requires a new dimension of the strategy development, which is usually called Money management or Position sizing.
In this post, we discuss the influence of the returns compounding on the final results and observe all the instruments provided by the OptionSmile platform to deal with the volatility impact.