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.

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It is well-known that profitable options trading must be directional; either along with underlying security by the forecasting of its future move, or directionally by implied volatility via forecasting of its dynamics (to be more correct, by predicting the discrepancy between the implied and realized volatility). Theoretically, one factor can be isolated from another by either delta or vega hedging.

In the OptionSmile methodology of the options pricing, we use empirical distribution of underlying returns as a probability measure to find the Fair Value of a contract. Then, by comparing these values with the real market prices, we draw a conclusion about market mispricing. It is obvious that this difference between the two prices consists of both directional factors—underlying security move—and implied volatility of options.

In this post, we are going to present a method to eliminate the underlying price change factor (drift) to the Fair Value of options and to calculate the Driftless Fair Value of options.

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One of the interesting questions regarding the Fair Value calculation approach is how the put-call parity is sustained for these values. Remember that this rule stands for the equivalence of difference between put and call prices on the same strike and difference between the strike and underlying price. If it is not sustained, the arbitrage opportunity arises.

For example, buying a put and selling a call on the same, strictly at-the-money strike equals the short position in the underlying security. If a put-call parity did not hold, it would be possible to hedge this position by buying an underlying security and get some return without any risk. In a risk-neutral paradigm, on which the Black-Scholes model is based, with such a combination we must always earn a return equal to the risk-free interest rate.

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