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The most frequent nontrivial example of no-arbitrage bounds is put–call parity for option prices. In incomplete markets, the bounds are given by the subhedging and superhedging prices. [1] [2] The essence of no-arbitrage in mathematical finance is excluding the possibility of "making money out of nothing" in the financial market.
Interest rate parity is a no-arbitrage condition representing an equilibrium state under which investors compare interest rates available on bank deposits in two countries. [1] The fact that this condition does not always hold allows for potential opportunities to earn riskless profits from covered interest arbitrage.
Implementing No-Arbitrage Term Structure of Interest Rate Models in Discrete Time When Interest Rates Are Normally Distributed, Dwight M Grant and Gautam Vora. The Journal of Fixed Income March 1999, Vol. 8, No. 4: pp. 85–98; Heath–Jarrow–Morton model and its application, Vladimir I Pozdynyakov, University of Pennsylvania
No free lunch with vanishing risk (NFLVR) is a concept used in mathematical finance as a strengthening of the no-arbitrage condition. In continuous time finance the existence of an equivalent martingale measure (EMM) is no more equivalent to the no-arbitrage-condition (unlike in discrete time finance), but is instead equivalent to the NFLVR-condition.
The absence of arbitrage is crucial for the existence of a risk-neutral measure. In fact, by the fundamental theorem of asset pricing, the condition of no-arbitrage is equivalent to the existence of a risk-neutral measure. Completeness of the market is also important because in an incomplete market there are a multitude of possible prices for ...
The condition allows for no arbitrage opportunities because the return on domestic deposits, 1+i d, is equal to the return on foreign deposits, [F/S](1+i f). If these two returns weren't equalized by the use of a forward contract, there would be a potential arbitrage opportunity in which, for example, an investor could borrow currency in the ...
When stock price returns follow a single Brownian motion, there is a unique risk neutral measure.When the stock price process is assumed to follow a more general sigma-martingale or semimartingale, then the concept of arbitrage is too narrow, and a stronger concept such as no free lunch with vanishing risk (NFLVR) must be used to describe these opportunities in an infinite dimensional setting.
John Hull and Alan White, "One factor interest rate models and the valuation of interest rate derivative securities," Journal of Financial and Quantitative Analysis, Vol 28, No 2, (June 1993) pp. 235–254. John Hull and Alan White, "Pricing interest-rate derivative securities", The Review of Financial Studies, Vol 3, No. 4 (1990) pp. 573–592.