Exam 14: The Black-Scholes Model

The Black-Scholes price of a three-month 50-strike put option is $0.75.The stock is trading at $49.Given an interest rate of 2%,and no dividends,what is the implied volatility of the stock extracted from this option?

Consider a call option on a stock that pays dividends at the rate $q > 0$ .Which of the following statements is most valid for the Black-Scholes model?

Which of the following is not an assumption underlying the Black-Scholes model?

A put option can be replicated by holding a position in stock and bonds,i.e. , $P = B + \Delta S$ where $\Delta$ is the delta of the put option.Comparing the replication formula to the Black-Scholes formula,and assuming no dividends,what can you say about the delta of the option?

A stock is currently trading at $S _ { 0 } = 25.85$ .It is not expected to pay dividends over the next year.You price a six-month call option on the stock with a strike of $K = 15$ using the Black-Scholes model and find the following numbers: =2.115 =1.832 N =0.983 N =0.967 Given this information,the delta of the call is

The implied volatility of an option

A call option can be replicated by holding a position in stock and shorting bonds,i.e. , $C = \Delta S - B$ where $\Delta$ is the delta of the call option.Comparing the replication formula to the Black-Scholes formula (assume a non-dividend-paying stock),what can you say about the delta of the option?

Consider a Black-Scholes setting.When a call option is deep in-the-money,a decrease in interest rates results in,ceteris paribus,

The S&P 500 index is trading at a level of 1200.The rate of interest is 2%.The average rate of dividends for stocks in the index is 3%.Index volatility is 20%.What is the Black-Scholes price of a one-year at-the-money put option on the index?

A stock is currently trading at $S _ { 0 } = 25.85$ .It is not expected to pay dividends over the next year.You price a six-month put option on the stock with a strike of $K = 15$ using the Black-Scholes model and find the following numbers: =2.115 =1.832 N =0.983 N =0.967 Given this information,the risk-neutral probability of the put finishing in the money is

The current price of a stock is $100.What is the Black-Scholes model price of a six-month call option at strike $101,given an interest rate of 2% and a dividend rate of 1%? The volatility is 25%.

A stock is currently trading at $S _ { 0 } = 21.30$ .It is not expected to pay dividends over the next year.You price a one-month put option on the stock with a strike of $K = 22.50$ using the Black-Scholes model and find the following numbers: =-0.666 =-0.738 N =0.253 N =0.230 Given this information,the delta of the put is