# Delta Hedging using another correlated asset

My question is about the following (from Maxime de Bellefroid, Ch. 5 The Greeks):

1. From my understanding $$\Delta_2$$ is the sensitive of the option (on the first instrument with underlying $$S_1$$) with respect to the price of the second instrument $$S_2$$, I guess this value can only be estimated and there are no closed formulas?

2. How is the value of $$\frac{\partial S_2}{\partial S_1}$$ calculated?

Look carefully. $$\frac{\partial S_2}{\partial S_1}$$ is explicitly given as $$\frac{\partial S_2}{\partial S_1} = \frac{\rho_{12}\sigma_2}{\sigma_1}\frac{S_2}{S_1}$$
Then the closed formula for finding $$\Delta_2$$ is $$\Delta_2 = \Delta / \frac{\partial S_2}{\partial S_1}$$, a simple division (let us hope the denominator is not zero).
• When you say '$\frac{\partial{S_2}}{\partial{S_1}}$ is explicitly given' you mean that it is defined that way? If so why? Feb 1 at 16:40
• It is a poor explanation if you ask me, very confusing. He was able to write $\Delta_2 \frac{\partial S_2}{\partial S_1} = \Delta_2 \rho_{12} \frac{\sigma_2}{\sigma_1}\frac{S_2}{S_1}$ because he calculated for you what $\frac{\partial S_2}{\partial S_1}$ is equal to, but he does not show the details. So it is implicit, not explicit, I suppose. Feb 1 at 16:53