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20. You calculate the Black-Scholes value of a call option as $3.50 for a stock

ID: 2807076 • Letter: 2

Question

20. You calculate the Black-Scholes value of a call option as $3.50 for a stock that does not pay dividends, but the actual call price is $3.75. The most likely explanation for the or the volatility you input into the discrepancy is that either the option is model is too B. undervalued and should be written; low: A. overvalued and should be written; low: C. overvalued and should be purchased; high: D. undervalued and should be purchased; high 21. In order for a binomial option price to approach the Black Scholes price, A. the number of subintervals must increase substantially B. the volatility must be low; C. the volatility must be high; D. the probability of each subinterval needs to be similar to the stock's standard deviation; E. the interest rate needs to increase 22. If the S&P; 500 Index futures contract is overpriced relative to the S&P; 500 Index, you should A. buy all the stocks in the S&P; 500 and write put options on the S&P; 500 Index B. sell all the stocks in the S&P; 500 and buy call options on S&P; 500 Index C. sell the S&P; 500 Index D. sell S&P; 500 Index futures and buy all the stocks in the S&P; 500. E. sell short all the stocks in the S&P; 500 and buy S&P; 500 Index futures

Explanation / Answer

20. Option- A

Overvalued- Because BSM calculated option price(intrinsic value) < the qouted call option price trading in the market

Written- The option call if is written will create to have an opportunity to get a premium and to get an arbitrage profit by selling high in one market and by purchasing low in the other market

Low- BSM calculation always does not reflect the right option price because it suffers from model error by factoring in the standard deviation as an input. So, if the model assumes less volatality then, the price would be less than the market price.

21. Option- A

BSM erradicts the short coming of Binomial by taking the continous compounding assumption

22. Option- D

Since futures is overvalued, we sell high and buy low, to get profit. Sell futures and buy stocks.