Problem 316 of 333EasyCalculusP316

Bumping spot and rates on a forward

A two-year forward on a non-dividend stock is priced at $F(S, r) = S e^{2r}$ . Today $S = 100$ and $r = 5\%$ . Overnight, spot rises to $101$ and the rate rises to $5.25\%$ .
Use partial derivatives to estimate the change in $F$ , and say how much of it comes from each input. How close is the estimate to the exact change?
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