$-$ Choose your favorite stock that has traded calls

and puts on it$.$ Are the options on your

stock European or American?

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Choose two of your traded stock options, one call and one put, that have the same time

to expiration, and the same strike price.

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State each lower bound of the call and put in question $($E

uropean or American$).$ Test if the lower bound is satisfied for each option on your stock. Find relevant market prices for the options, e$.$g$.,$ traded prices, bid quotes, ask quotes, or the midpoint between the

bid and ask quotes.

$-$State the put$-$call parity for options on a non$-$dividend$-$paying stock. Try your best to

test if the put$-$call parity is satisfied for each of the two chosen options. What

assumptions do you need to make? Discuss any concerns or difficulties in your results

that you might encounter.

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What is a reasonable measure of the volatility of your favorite stock? If you, despite

being an expert in finance, cannot estimate the volatility of your favorite stock, assume

that it is $30\%$ per annum. Use the volatility to construct a binomial tree for the

stock.

You may use the DerivaGem software and as many time steps as you wish. Value the

two options, the call and the put, using the binomial model. Compare the theoretical

prices with the actual market prices. Which prices do you think are the most correct

ones? Why?