Exam 14: The Black-Scholes Model

A stock is currently trading at $S _ { 0 } = 26.15$ .It is not expected to pay dividends over the next year.You price a one-month call option on the stock with a strike of $K = 25$ using the Black-Scholes model and find the following numbers: =0.717 =0.645 N =0.763 N =0.740 Given this information,the risk-neutral probability of the call finishing in the money is

A stock is currently trading at $S _ { 0 } = 26.15$ .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 $K = 25$ using the Black-Scholes model and find the following numbers: =0.717 =0.645 N =0.763 N =0.740 Given this information,the delta of the put is

The current price of a stock is $100.What is the Black-Scholes model price of a six-month put option at strike $98,given an interest rate of 2% and a dividend rate of 1%? The volatility is 45%.

The current price of a stock is $100.Consider 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%.What is the real-world (physical)probability of the option ending up in the money if the growth rate of the stock is expected to be 5% per year?

The three-month S&P 500 futures contract is trading at a level of 1250.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 futures?

The current price of a stock is $100.Consider 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%.What is the risk-neutral probability of the option ending up in the money?

Let $E ^ { * } ( .)$ denote risk-neutral expectations in the Black-Scholes setting.Then,the Black-Scholes formula may calculated by taking the following expectation:

The implied volatility skew observed in stock indices cannot be attributed to which of the following reasons?

In the Black-Scholes setting,the prices of American options

If the Black-Scholes call delta (assume a non-dividend-paying stock)is equal to 1/2,then which of the following statements is most valid?

Which of the following quantities associated with equity option pricing is model dependent?

The Black-Scholes model differs from the binomial in that

The dollar-euro exchange rate is $1.30/€.The dollar interest rate is 2% and the euro interest rate is 3%.What is the price of a six-month call option to buy euros at a strike price of $1.25/€? The volatility of the $/€ exchange rate is 40%.

A variance swap is an option on the realized variance of a stock's return over a defined period of time.A variance swap may be replicated using

Most major stock indices,like the S&P 500,exhibit an implied volatility skew.This means if we consider three put options, $P \left( K _ { 1 } \right) , P \left( K _ { 2 } \right) , P \left( K _ { 3 } \right)$ at strikes $K _ { 1 } < K _ { 2 } < K _ { 3 } \leq S$ (where $S$ is the current index level)and the options have implied volatilities $\sigma _ { 1 } , \sigma _ { 2 } , \sigma _ { 3 }$ ,respectively,then the most likely pattern is

The Black-Scholes formula is based on

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 probability of the put finishing out-of-the-money is

A volatility swap is an option on the realized standard deviation of a stock's return over a defined period of time.A volatility swap may be replicated using

Consider a Black-Scholes setting.When a call option is deep in-the-money,an increase in volatility results in,ceteris paribus,

The VIX is an implied volatility index for roughly what maturity?