# MathematicalModels

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Consider the Black-Scholes-Merton model for two stocks:

dS1(t)=0.1S1(t)dt+0.2S1(t)dW1(t)

dS2(t)=0.05S2(t)dt+0.1S2(t)dW2(t)

Suppose the correlation between W1 and W2 is 0.4. Consider the dynamics of the ratio S1/S2, where A,B,C,D,F,G,I,J,K,L are constants to be found:

d(S1(t)/S2(t))=(ASB1(t)+C)SD2(t)dt+FSG1(t)SI2(t)dW1(t)+JSK1(t)SL2(t)dW2(t)

Hint: it may help to write down first the explicit expression for the ratio.

Enter the value of A:

correct
0.05

Enter the value of B:

correct
1

Enter the value of C:

correct
0

Enter the value of D:

correct
−1

Enter the value of F:

correct
0.2

Enter the value of G:

correct
1

Enter the value of I:

correct
−1

Enter the value of J:

correct
−0.1

Enter the value of K:

correct
1

Enter the value of L:

correct
−1

• MathematicalModels -

Consider the Black-Scholes-Merton model for two stocks:

dS1(t)=0.1S1(t)dt+0.2S1(t)dW1(t)
dS2(t)=0.05S2(t)dt+0.1S2(t)dW2(t)

Suppose the correlation between W1 and W2 is 0.4. Consider the dynamics of the ratio S2/S1, where A,B,C,D,F,G,I,J,K,L are constants to be found:

d(S2(t)/S1(t))=(AS1B(t)+C)S2D(t)dt+FS1G(t)S2I(t)dW1(t)+JS1K(t)S2L(t)dW2(t)

Enter the value of A:

Enter the value of B:

Enter the value of C:

Enter the value of D:

Enter the value of F:

Enter the value of G:

Enter the value of I:

Enter the value of J:

Enter the value of K:

Enter the value of L:

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