Abstract
There is a close connection between the value of an option and the volatility process of the financial underlying. Assuming that the price process follows a geometric Brownian motion, we have derived the Black-Scholes formula (BS) for pricing European options. With this formula and when the following values are given, the option price is, at a given time point, a function of the volatility parameters: \(\tau \) (time to maturity in years), K (strike price), r (risk free, long-run interest rate) and S (the spot price of the underlying).
Put all your eggs in one basket – and watch that basket. Mark Twain, The Tragedy of Pudd’nhead Wilson.
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Borak, S., Härdle, W.K., López-Cabrera, B. (2013). Volatility Risk of Option Portfolios. In: Statistics of Financial Markets. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33929-5_17
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DOI: https://doi.org/10.1007/978-3-642-33929-5_17
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