How to Calculate the Derivative of a Call Option
A call option is where an investor has the option to buy a certain commodity or stock in the future, but is not committed to it. Pricing call options are often accomplished using derivatives, mostly through the Black Scholes method. The method requires a good grounding of both mathematical and statistical techniques, and often requires the use of spreadsheets, as well as statistical software. Learning the fundamentals of the Black Scholes method can, however, give you an understanding of how the pricing of call options works.
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Instructions
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Compile all of the data needed for your calculation and assign each variable an algebraic letter. You will need the price of the underlying asset (S), the exercise price of the option (X), the risk-free interest rate (r), the maturity date (T), the current date (t) and the standard deviation of the underlying asset (s.d.). You will need not only the data for a single call option, but also the data for the entire market.
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Divide "S" by "X" and take the natural log of the result. Name this result "A." Then, subtract "T" by "t," and multiply by "r." Name this result "B." Add "A" to "B." Name this result "C."
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Subtract "T" by "t" and take the square root of the result. Multiply by "s.d." to obtain "D." Divide "C" by "D" to obtain "E."
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Multiply the result you obtained for "D" by one half. Add this result to "E." This will give you the first derivative of your equation. Take the cumulative normal distribution of this result, and then multiply by "S." This will give you "F."
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Subtract "D" from "F," and take the cumulative normal distribution. This will give you "G," which is the second derivative of the equation.
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Subtract "t" from "T," multiply by "r," and again multiply by negative one. This gives you "H." Take the exponential of "H," and multiply by "X." Multiply "H" by "G." This gives "J."
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Subtract "J" from "F." This gives you the price of the call option.
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