Question $12\mathrm{.}23$ :

A trader sells a strangle by selling a $7-$month European call option with a strike price of $$60$ for $$4$ and selling a $7-$month European put option with a strike price of $$50$ for $$5.$ For what range of prices of the underlying asset in $7$ months does the trader make a profit?

Question $12\mathrm{.}24$ :

Three put options on a stock have the same expiration date and strike prices of $$60,$ $$65,$ and $$70.$ The market prices are $$5,$ $$8,$ and $$10,$ respectively. Explain how a butterfly spread can be created. Construct a table showing the profit from the strategy. For what range of stock prices would the butterfly spread lead to a loss?