Exam 14: The Black-Scholes Model

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

A call option can be replicated by holding a position in stock and shorting bonds, i.e., $C = \Delta S - \bar { B }$ 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?

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

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

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

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?

The Black-Scholes formula is based on

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?

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

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

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

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