Consider the American corporation ACME INC
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Consider the American corporation ACME INC

Exercise 7.7

Consider the American corporation ACME INC. The price process S for ACME is of course denoted in US$ and has the P-dynamics


where a and σ are known constants. The currency ratio SEK/US$ is denoted by Y and Y has the dynamics


in SEK. Here Z(t) is the price at time t in SEK of the ACME stock.

Compute the arbitrage free price (in SEK) at time t of a T-Euler, given that the price (in SEK) of the ACME stock is z. The Swedish short rate is denoted by r.


Hint
Statistics"Euler's Method: this technique is used to analyze the Differential Equation that uses the idea of local linearity or even linear approximation, where there is use of small tangent lines over the short distance to approximate the solution to an initial-value problem.The formula to calculate is:  y = y (xi) + f (xi , y(xi)) (x−xi)"...

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