True False questions

$1.$ As a lender, you can hedge the interest rate risk by taking a short position in Eurodollar futures.

$2.$ The market value of swap is zero at initiation.

$3.$ In$-$the$-$money call has strike price lower than out$-$of$-$the$-$money put.

$4.$ The price of a call option cannot exceed the strike price, i$.$e$.$ C $=<$ K$.$

$5.$ An American call option will definitely not be early exercised when there are no dividends.

$6.$ An American call option is more likely to be early exercised when the underlying stock becomes more volatile and when there are dividends.

$7.$ The price of a European call option on a non$-$dividend$-$paying stock can never decline with an increase in time to expiration.

$8.$ The price of an American currency call option can never decline with an increase in time to expiration.

$9.$ The $1-$year standard deviation of a stock with uncorrelated monthly returns is the double of the $6-$month standard deviation of the same stock.

$10.$ Theta is always positive for deep$-$in$-$the$-$money calls with dividends.

$11.$ Magnitude of rho of a call option is larger as the underlying stock price increases.

$12.$ Gamma is always the same for both European call and an otherwise identical put.

$13.$ Assume premium$=$$$6,$ S $=$ $$100,$ r $=0\mathrm{.}03,$ the stock pays a $2\mathrm{.}0\%$ continuous dividend and the at$-$the$-$money put option expires in a year. What is the implied volatility?

$14.$ The Twentycent stock price is $630.$ If you believe the price will be $700$ next year with no doubt $(100\%),$ which of the following strategy is the best?