By Abraham Lioui
This can be a sophisticated textual content at the concept of ahead and futures markets which goals at offering readers with a entire wisdom of the way costs are demonstrated and evolve over the years, what optimum options you will count on from the contributors, what characterizes such markets and what significant theoretical and functional modifications distinguish futures from ahead contracts. it's going to be of curiosity to scholars (majoring in finance with quantitative abilities) teachers (both theoreticians and empiricists), practitioners, and regulators.
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Extra resources for Dynamic Asset Allocation with Forwards and Futures
Since these cumulative forward gains/losses are realized at date TF only, they must be discounted by the factor P(t,TF). Note that the hedger does not use the money market account at all in this problem. This is because the contribution of this asset, which is locally riskfree, to the instantaneous variance of the hedged portfolio is zero. In other words, the investor's position in this account is here indeterminate and irrelevant. That will not be the case later with futures contracts, because of the margins called on the hedger's position.
N. (4) where Ep(t,Tj) is the K-dimensional vector of the volatilities associated with the relative price changes of the discount bond maturing at Tj, P(t,Tj). ) of the forward rates volatilities. The drift |Lip(t,Tj) plays no particular role here, but could easily be computed as the sum of the riskless rate plus a risk premium that depends on the bond maturity date Tj. Note that, since the market is complete, we have n > K. - The absence of arbitrage implies the existence of a martingale measure Q, associated with the locally riskless asset (more precisely the money market account B(t)) as the numeraire, and such that its Radon-Nikodym derivative with respect to the historical probability is equal to: dQ dP where (|)(s) is the vector of market prices of risk.
For instance, if the underlying asset price and the forward price are positively correlated, as they are here, the forward price is larger than the futures price. However, because the forward and the futures price have different volatilities and covariances with their underlying bond price P(t,T2), one cannot infer which term is larger. c) The essential, and striking, difference between the two solutions, however, is the presence in equations (14) or (16) of an extra term when the hedger uses forwards.