A Type Of Random Rate Of Exchange Model

Rate of exchange is two natural currencies ratio that exchange, is called the currency's "price" or "outward price" in the rate of exchange of western and economic theories inside. In the liberal currency economy, rate of exchange is a main lesson for very important economy changing, its fluctuation influencing economic realm had extensively, for this reason rate of exchange in times gone by is financial economics studying.Generally think, the process that decides rate of exchange is a complicated complicacy that can't use a factor or limit of a set change measure explain with the interaction of various factors. The rate of exchange is in practice be two native product currency with each from the commutation comparison for value of currency countries measure it than, constitute decision two native product currency the rate of exchange's foundation, this be two theories of currency country rate of exchange, generally come speaking, theory rate of exchange can't easy to do change, but foreign exchange relation for however hour having rising up or down, this is because foreign exchange supply and demand changing. The formation of the real rate of exchange with change to all relate to the decision from the foreign exchange market's supply and demand.In consideration of the influence of state varying toward rate of exchange, under the random economy environment this paper establishes a type of random rate of exchange model. This paper reflect the influence of the uncertainty which state varies toward the random changing of rate of exchange, then rate of exchange, demand and supply satisfy the following stochastic differential function:In this function, et,D(et) and S(et) are respectively rate of exchange, demand and supply at t time.When S(et) = -c + det,D(e,) = a-bet, this paper give out the resolve of this function and he pricing formula of option . They are theorem 1 and theorem 2: Theoreml: If the rate of exchange of 0 time is e0 , D(et) = a-bet ,S(et)=-c+det the rate of exchange variety satisfy the equation as before, thenAmong them A =Theorem! If the time is 0 now, the trade moment of foreign exchange's European type call option is T, the trade price is K, rate of exchange to satisfy the equation as before. Then the value of European type call option now is:Among them rf is no risk rate,Following these, this paper talk about the random disturbing of the demand and the supply. The following functions have been got:Then theorems is got:If the need, supply with the rate of exchange to satisfy above equations, thenAmong them, σ1, σ2,σ3, Wt(1), Wt(2), Wt(3) are as the supposed in paper and φ (t), φ(t), φ3(t), are of certain by the following equations:By deforming the function det =[ret +λ(D(et)-5(et))]dt + σetdWt, this paperapplies statistics analyst's method to analyze the foreign exchange market of dollar to yen.