$.$ The current price of a non$-$dividend paying stock is $40$ and the continuously compounded riskfree interest rate is $8\%.$ The following table shows call and put option premiums for threemonth European of various exercise prices:

Exercise Price Call Premium Put Premium

$356\mathrm{.}130\mathrm{.}44$

$402\mathrm{.}781\mathrm{.}99$

$450\mathrm{.}975\mathrm{.}08$

A trader interested in speculating on volatility in the stock price is considering two investment

strategies. The first is a $40-$strike straddle. The second is a strangle consisting of a $35-$strike put

and a $45-$strike call. Determine the range of stock prices in $3$ months for which the strangle

outperforms the straddle.