Price Dynamics in Finance, a Essay

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It was first proposed in 1979 and uses a "discrete time" or lattice-based model of the way price varies over time -- without using closed form solutions (Cox, et al., 1979). In actual usage, the BOPM is quite widely used because it handles a wide variety of conditions that other models do not account for -- largely because it is based on the description of an underlying instrument over a longer period of time, as opposed to a single point without a large number of variables. Scholars say that it is computationally slower than the Black-Scholes formula, but more accurate, specifically for longer-dated options on securities that have dividend payments, trade in multiple securities, or have a number of complicated features within their variables. The BOPM model works by tracing the options key underlying variables through a lattice tree, which identifies steps between variables over time. For example, each node in the tree represents a hypothetical (or possible) price at a given point in time, then solves based on a combination of those nodes (Conroy, 2003).

Both the BOPM and the BS are based on the same assumptions of stock price and behavior, as well as risk-neutral valuation. BS implies volatility, and while one of the most critical parameters within option pricing, volatility cannot be directly observed and must be estimated, which is done more reliably by the BOPM. BS cannot be used to accurately price options with an American-style exercise since it only calculates the option price at one point in time -- the expiration.

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Because of the lattice structure, the BOPM makes it possible to check price at every point in an options life. Many scholars believe the BOPM to be superior, but without a huge leap in calculation power, it is not a practical solution to calculate thousands of variables within a few seconds (Hoadley, 2013).

REFERENCES

Black, F. And Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy. 81 (3): 637-54, Retrieved May 2013 from: http://www.cs.princeton.edu/courses/archive/fall09/cos323/papers/black_scholes73.pdf

Conroy, R. (2003). Binomial Option Pricing. Darden Graduate School -- University of Virginia. Retrieved May 2013 from: http://faculty.darden.virginia.edu/conroyb/derivatives/Binomial%20Option%20Pricing%20_f-0943_.pdf

Cox, J., et al. (1979). Option Pricing: A Simplified Approach. Journal of Financial Economics. 7 (2): 229-63. Retrieved May 2013 from: http://fisher.osu.edu/~fellingham_1/seminar/CRR79.pdf

Friedman, D. (1990). Price Theory. Retrieved May 2013 from: http://www.daviddfriedman.com/Academic/Price_Theory/PThy_ToC.html

Hoadley, P. (2013). Option Pricing Models and the "Greeks." Hoadley Trading and Investment Tools. Retrieved May 2013 from: http://www.hoadley.net/options/bs.htm

Investopedia. (2013). Options Pricing: An Introduction. Retrieved May 2013 from: http://www.investopedia.com/university/options-pricing/

Nobel Foundation. (1997). Bank of Sweden Prize in Economics. Nobelprize.org. Retrieved May 2013 from: http://www.nobelprize.org/nobel_prizes/economics/laureates/1997/press.html

Wilmott, P. (2008). Science in Finance IX. Wilmott Foundation. Retrieved from: http://www.wilmott.com/blogs/paul/index.cfm/2008/4/29/Science-in-Finance-IX-in-defence-of-Black-Scholes-and-Merton.....

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