Suppose a stock is currently trading at $100.$ An at$-$the$-$money call with a maturity of

three months has the following price and greeks:

C $=5\mathrm{.}598$

$=0\mathrm{.}565$

$=0\mathrm{.}032$

$=12\mathrm{.}385$

V $=19\mathrm{.}685$

$\backslash$rho $=12\mathrm{.}71$

Chapter $17$ Sensitivity Analysis: The Option $$Greeks$431$

$($a$)$ If the stock price moves to S $=101,$ what is the predicted new option price $($using

the delta alone$)?$

$($b$)$ If the stock price moves to S $=101,$ what is the predicted new call delta?

$($c$)$ Repeat these questions assuming the stock price moves to $98$ instead.

$($d$)$ If the stock price registers a large jump increase to $120,$ what is the new call value

predicted by the delta alone? By the delta and gamma combined?

$($e$)$ Go back to the original parameters. If the time to maturity falls by $0\mathrm{.}01,$ what is the

new call value predicted by the theta?

$($f$)$ Repeat the last question if the time to maturity falls by $0\mathrm{.}05.$

$($g$)$ Go back to the original parameters. If the volatility increases by $1\%,$ what is the

predicted new value of the call? What if volatility fell by $2\%?$

$($h$)$ Go back to the original parameters. If interest rates should rise by $50$ basis points,

what is the new call value predicted by the rho?