You want to trade some options on Diskount Widgetz, the firm you used to work for....

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You want to trade some options on Diskount Widgetz, the firm you used to work for. Their stocks are currently trading at $35.00. You are considering options with a time to expiration of six months (half a year) and a strike price of $37.00. Zero rates, at all horizons, are r = 0.01 expressed per annum with continuous compounding. For this problem, use the 252 trading day per year convention. From historical daily stock returns, you compute a standard deviation of daily stock log- returns of s= 0.006. You also learn that Diskount Widgetz is expected to pay a $3.00 dividend in 3 months (one quarter of a year). (a) (10 points) Using your estimated volatility, price a European call option. Do not evaluate (), the standard normal cumulative distribution function. Instead, write your answer in the form ab(b) + co(d), where a, b, c, and d are numbers (given to three decimal places). Make sure to show your work, and don't forget the dividend. (b) (5 points) Suppose in part (a) you found a call option price of $0.50. (This is not the correct answer, but pretend it is.) Suppose the actual market price of the option is $1.00. What can you say about the Black-Scholes-Merton implied volatility? Express your answer as an (in)equality. (c) (5 points) Suppose the option was instead an American call option. What two European options would you price if you were to use Black's approximation? Write your answer as two sets of 5 numbers: the spot price, strike price, time to expiration, interest rate, and volatility. You want to trade some options on Diskount Widgetz, the firm you used to work for. Their stocks are currently trading at $35.00. You are considering options with a time to expiration of six months (half a year) and a strike price of $37.00. Zero rates, at all horizons, are r = 0.01 expressed per annum with continuous compounding. For this problem, use the 252 trading day per year convention. From historical daily stock returns, you compute a standard deviation of daily stock log- returns of s= 0.006. You also learn that Diskount Widgetz is expected to pay a $3.00 dividend in 3 months (one quarter of a year). (a) (10 points) Using your estimated volatility, price a European call option. Do not evaluate (), the standard normal cumulative distribution function. Instead, write your answer in the form ab(b) + co(d), where a, b, c, and d are numbers (given to three decimal places). Make sure to show your work, and don't forget the dividend. (b) (5 points) Suppose in part (a) you found a call option price of $0.50. (This is not the correct answer, but pretend it is.) Suppose the actual market price of the option is $1.00. What can you say about the Black-Scholes-Merton implied volatility? Express your answer as an (in)equality. (c) (5 points) Suppose the option was instead an American call option. What two European options would you price if you were to use Black's approximation? Write your answer as two sets of 5 numbers: the spot price, strike price, time to expiration, interest rate, and volatility.

Answer rating: 100% (QA)

a To price a European call option we can use the BlackScholesMerton formula C SeqtNd1 KertNd2 Where C Call option price S Current stock price 3500 q D... View the full answer