Lognormal option pricing for arbitrary underlying assets: a synthesis |
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| Institution: | 1. Department of Radiology and Radiological Sciences, F. Edward Hébert School of Medicine, Uniformed Services University of the Health Sciences, 4301 Jones Bridge Road, Bethesda, MD 20814, USA;2. Pediatric Radiology Section, American Institute for Radiologic Pathology, 1100 Wayne Avenue, Silver Spring, MD 20910, USA;3. Department of Radiology, Walter Reed National Military Medical Center, 8901 Rockville Pike, Bethesda, MD 20889, USA;1. Department of Neurology, Henry Ford Health System, Detroit, MI 48202, USA;2. Department of Physics, Oakland University, Rochester, MI 48309, USA;1. International Institute of Earthquake Engineering and Seismology, Tehran, Iran;2. Faculty of Engineering, University of Mohaghegh Ardabili, Ardabil, Iran |
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| Abstract: | All European option pricing formulas sharing the assumption of a lognormally distributed terminal price for the underlying asset are formally similar. It is thus natural to seek a single explicit general formula for this class of options. This paper provides such a synthesis. The key insight is recognizing that all option pricing equations depend explicitly on the expected terminal price of the arbitrary underlying asset, which is often obtained through basic financial reasoning. To illustrate the power and pedagogical value of this framework, I obtain several classical option pricing formulas as special cases of the general equation. |
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