Economic Theory

Dynamic Asset Allocation with Forwards and Futures by Abraham Lioui

By Abraham Lioui

This can be a sophisticated textual content at the idea of ahead and futures markets which goals at offering readers with a complete wisdom of the way costs are proven and evolve through the years, what optimum suggestions you'll count on from the members, what characterizes such markets and what significant theoretical and useful changes distinguish futures from ahead contracts. it's going to be of curiosity to scholars (majoring in finance with quantitative abilities) lecturers (both theoreticians and empiricists), practitioners, and regulators.

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Extra info for Dynamic Asset Allocation with Forwards and Futures

Example text

Written on a discount bond of a given, arbitrary, maturity less than or equal to xE, say T2. For simplicity and without any loss of generality, its maturity T F (= TG = TH) is set at date Ti. Consider first the case where investors can hedge their positions using forward contracts. The forward price at date t < Tp is denoted by G(t,TF,T2) = G(t) for simplicity. Given that the market is free of frictions and arbitrage opportunities, it is equal to: Chapter 3: Pure Hedging 41 Equation (5) gives the no-arbitrage forward price of the forward contract, which is nothing but the cash-and-carry relationship.

Under Q, the price of a pure discount bond follows the dynamic process: ^ 5 ! ,n. (5) where Z(t) is a K-dimensional Brownian motion under Q. Using Girsanov's theorem, it is related to the Brownian motion Z by: Integrating (5) then yields: p(t,T j ) = p(0,Tj)exp - Consider any traded asset with payoff S(T) at time T and no intermediate cash flow. Its price today is S(t). T is assumed to be smaller than Tj so that all the discount bonds are "long-lived" assets. |FtJ denotes the conditional expectation under Q based upon all information available at time t.

In other words, there is no cash constraint imposed on the hedger's position. Applying Ito's lemma to the wealth (10) and to the price H(t) yields, respectively: Chapter 3: Pure Hedging 45 dw H (t) = ndP(t,T 2 )+dX(t) = ndP(t, T2) + r(t)X(t)dt + AH (t)dH(t) and dH(t) = H(t)jiH(t)dt + H(t)EH(t) 'dZ(t) (12) where JLLHCO is the instantaneous expected rate of price change of the futures contract and XH(0 is the (K-dimensional) volatility of the futures relative price changes. )dt need not be made explicit since it will play no role in the derivation of the solution.

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