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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 ...
When the volatility and drift of the instantaneous forward rate are assumed to be deterministic, this is known as the Gaussian Heath–Jarrow–Morton (HJM) model of forward rates. [ 1 ] : 394 For direct modeling of simple forward rates the Brace–Gatarek–Musiela model represents an example.
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 ...
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:
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 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.
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]
A trader has observed that the price of six-month gold futures price (F) is $1,300 per troy ounce, whereas the spot price (S) is $1,371 per troy ounce. The (not compounded) borrowing rate for a six-month loan ( r {\displaystyle r} ) is 3.5% per annum, and storage cost for gold is negligible (0%).