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# Assume that the initial stock price is So = $ 1 0 0 . You would like to hedge a long position of 2 0

Assume that the initial stock price is So$=$$$100.$ You would like to hedge a long position of $20$ call contracts $(100$ shares per contract$)$ with $250$ days to maturity anda strike price of $$120.$ The annualized risk$-$free rate is $2\%\text{}\backslash "">($continuously compounded. Suppose that, after $50$ days the stock price decreases to $$95.$ The volatility of the stock returns is constant at $50\%.$ How many shares of stock would you need to trade after those $50$ days to rebalance your hedge portfolio? $($Hint: Use the hedge ratio from the Black$-$Scholes formula in your calculations, and consider a year with $365$ days$)$Note: If you sell or take a short positich, please enter a negative number. If you buy back or take a long position, please enter a positive number. Enter your answer to thewhole number e$.$g$.$ if your answer is $98\mathrm{.}16$ enter as $99.$ If your answer is $-102\mathrm{.}3$ enteras $-103.$

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