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In financial mathematics, no-arbitrage bounds are mathematical relationships specifying limits on financial portfolio prices. These price bounds are a specific example of good–deal bounds, and are in fact the greatest extremes for good–deal bounds. [1] The most frequent nontrivial example of no-arbitrage bounds is put–call parity for ...
In a futures contract, for no arbitrage to be possible, the price paid on delivery (the forward price) must be the same as the cost (including interest) of buying and storing the asset. In other words, the rational forward price represents the expected future value of the underlying discounted at the risk free rate (the " asset with a known ...
The forward exchange rate depends on three known variables: the spot exchange rate, the domestic interest rate, and the foreign interest rate. This effectively means that the forward rate is the price of a forward contract, which derives its value from the pricing of spot contracts and the addition of information on available interest rates. [4]
The forward price (or sometimes forward rate) is the agreed upon price of an asset in a forward contract. [ 1 ] [ 2 ] Using the rational pricing assumption, for a forward contract on an underlying asset that is tradeable, the forward price can be expressed in terms of the spot price and any dividends.
[1] [2] It is an adjustment to the cost of carry in the non-arbitrage pricing formula for forward prices in markets with trading constraints. Let F t , T {\displaystyle F_{t,T}} be the forward price of an asset with initial price S t {\displaystyle S_{t}} and maturity T {\displaystyle T} .
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.
As a result, the forward price for nonperishable commodities, securities or currency is no more a predictor of future price than the spot price is - the relationship between forward and spot prices is driven by interest rates. For perishable commodities, arbitrage does not have this The above forward pricing formula can also be written as:
Thus knowing how to price caps is also sufficient for pricing swaptions. In the event that the underlying is a compounded backward-looking rate rather than a (forward-looking) LIBOR term rate, Turfus (2020) shows how this formula can be straightforwardly modified to take into account the additional convexity.