Abstract
The term arbitrage is used for making risk-free profit by buying and selling financial assets in one’s own account. Let π t be the value of a portfolio at times t ≥ 0, with π 0 = 0.
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Notes
- 1.
In particular, under the assumption of no-arbitrage, goods that produce the same cash flows over time will be required to have the same price (‘law of one price’).
- 2.
Modern means of communication and real-time price systems have significantly improved market transparency.
- 3.
This assumption will have to be reconsidered for certain markets, such as commodity markets. For example, shipping and insurance costs can be significant, so that prices between different market places can differ significantly without implying opportunities of arbitrage.
- 4.
For further details, check the current EU short sale regulations at ec.europa.eu/internal_market/securities/short_selling_en.htm
- 5.
In practice dividend payments are often modeled in such a way that the properties of the underlying model do not change much.
- 6.
In the presence of income from the underlying asset (e.g. dividends for a stock), storage costs or transportation costs, this formula will no longer hold (see Hull [41] for a discussion).
- 7.
Again under the assumption that the lending and borrowing rates are equal.
- 8.
For example, if a company has to report its assets and liabilities in between payment dates, it will also have to report the value of its swaps.
- 9.
Swap rates are quoted for a larger range of maturities than zero-coupon bonds (quoted in this context means that information providers, such as Reuters or Bloomberg, continuously publish current prices at which market makers, such as large banks, offer the respective product). Note, however, that swap rates will not be quoted for all maturities if one considers very long terms, e.g. there will be no liquid trading in 34-year swaps. In such a case one can interpolate the lacking rates from other data points.
- 10.
- 11.
Forward rates are interest rates for periods that start in the future, and they can be obtained from current interest curves.
References
F. Delbaen and W. Schachermayer. The Mathematics of Arbitrage. Springer Finance. Springer-Verlag, Berlin, 2006.
J. C. Hull. Options, Futures, and other Derivatives. 5th edition. Prentice Hall, Upper Saddle River, NJ, 2002.
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Albrecher, H., Binder, A., Lautscham, V., Mayer, P. (2013). The No-Arbitrage Principle. In: Introduction to Quantitative Methods for Financial Markets. Compact Textbooks in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0519-3_3
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