Consider two options on the same stock and same time to maturity but with

different strike prices. For option A$,$ the strike price $($K$1)$ is equal to $10$ USD,

while for option B$,$ the strike price $($K$2)$ is equal to $9\mathrm{.}5$ USD. The current stock

price $($S$)$ is equal to$10$ USD. There are no dividends and the risk$-$free is $3\%$

p$.$a$.$ In calculating the arbitrage$-$free option prices an investor$$s volatility

estimate is $15\%$ p$.$a$.$ Yet option A trades for $0\mathrm{.}8$ USD and option B for $1$ USD.

i$.$ Compare the implied volatilities of both options A and B to the

investor$$s estimate of $15\%$

ii$.$ Identify the optimal strategy in the two options. Using the investor's

volatility estimate, derive the delta$-$neutral position of your call option

portfolio.