Exercise II$.$A$\mathrm{.}5.$ You assumed the $1-$level tree model, priced and sold a put with strike E$,$

Sd $<$ E $<$ Su$,$ followed the hedging procedure but the market ended up at ST $,$

ST $<$ Sd$.$

Did you lose or make money? What if the market ended up at ST $>$ Su$?$ How do your answers

fit with the rule of thumb $$selling options is selling volatility$?$ Look up $$Volatility $($Finance$)$ on

Wikipedia, if necessary. You may assume r $=0$ for simplicity.