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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.
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:
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.
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 ...
In a discrete (i.e. finite state) market, the following hold: [2] The First Fundamental Theorem of Asset Pricing: A discrete market on a discrete probability space (,,) is arbitrage-free if, and only if, there exists at least one risk neutral probability measure that is equivalent to the original probability measure, P.
The lack of arbitrage opportunities implies that the price of P and C must be the same now, as any difference in price means we can, without any risk, (short) sell the more expensive, buy the cheaper, and pocket the difference. In the future we will need to return the short-sold asset but we can fund that exactly by selling our bought asset ...
Good–deal bounds are price bounds for a financial portfolio which depends on an individual trader's preferences. Mathematically, if A {\displaystyle A} is a set of portfolios with future outcomes which are "acceptable" to the trader, then define the function ρ : L p → R {\displaystyle \rho :{\mathcal {L}}^{p}\to \mathbb {R} } by
We define the forward price to be the strike K such that the contract has 0 value at the present time. Assuming interest rates are constant the forward price of the futures is equal to the forward price of the forward contract with the same strike and maturity. It is also the same if the underlying asset is uncorrelated with interest rates.