Solution X3.2 ii) from Assignment X3

Dont understand why the change in the option price is calculated this way with the changes in all the greeks in it as in [2]...

and also, why the volatility and the rate of interest and are plugged in as percentages, 5 and -0.5, and not as 0.05 and -0.005?

my intuition about this question is that i should use the B-S partial PDE on p.46 in the tables, because there's no ready formulae with greeks for the option price in the Core Reading?

thx in advance

 

The BS PDE expresses f in terms of delta, gamma and theta, but it doesn't tell you directly about changes in f due to changes in other variables or parameters. It also doesn't involve rho, so can't be any use in this question, where we have the risk-free rate changing.

When asked about df and given values for Greeks, your intuition should tell you to use Taylor in the relevant variable/parameters. Taylor/Ito is in the Core Reading, so this should seem reasonable.

So, for example, we have df = ... + vega. d(sigma) + ...

Vega is given to us as 0.91 pence per percent. Noting the units is very important. The volatility has changed from 30% to 35%, so the number of percentage points we have moved is 5.

Similarly, theta is given to us as a number of pence per day and so we want to express dt in days not years.