Suppose the stochastic state variables S 1 and S 2 follow the Geometric Brownian processes where Let

Question:

Suppose the stochastic state variables S₁ and S₂ follow the Geometric Brownian processes where

d Si Si Mi dt + oi dzi, i = 1, 2.

Let ρ₁₂denote the correlation coefficient between the Brownian processes dZ₁ and dZ₂. Let f = S₁S₂, show that f also follows the Geometric Brownian process of the form

= dt + o dZf, where = + + P120102 and o = 0 +03+20120102. Similarly, let M2 S show that 8 == S df = (1 +

Note that

() 1 S2 -=-urdt + o dt ordZ2. Treat S₁/S₂ as the product of S₁ and 1/S₂ and use the result obtained for the product of Geometric Brownian processes.

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Mathematical Models Of Financial Derivative

ISBN: 9783642447938

2nd Edition

Authors: Yue-Kuen Kwok

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Question Posted: Dec 02, 2023 03:16 AM

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Suppose the stochastic state variables S 1 and S 2 follow the Geometric Brownian processes where Let

Question:

d Si Si Mi dt + oi dzi, i = 1, 2.

Step by Step Answer:

To derive the stochastic differential equations SDES for f SS and g you can use the rules for the pr...View the full answer

Mathematical Models Of Financial Derivative

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