David's ProTip: This AIM should not include the "compute" verb: with the possible exception of delta (note delta has its own, different AIM), you will not be asked to compute option Greeks on the exam. For the vast majority of candidates, memorizing Greek formulas, aside from delta, is not a good spend of time. What do you need to know?
Questions:
8.1. Twelve days ago (T - 12 days), a European call option with a price of $4.80 had a theta of -6.30 per year. Between then and today (T), no stochastic option inputs have changed; i.e., stock price, volatility and riskfree rate are unchanged. What is the today's estimate of the option price, as reduced by only time decay, assuming 252 trading days per year?
a. $3.36
b. $4.50
c. $4.63
d. $4.77
8.2. An at-the-money call option has a (percentage) delta of 0.600 and gamma of 0.030. A market maker writes (sells) 100 call options, but only after the stock price unexpectedly jumps $2.00, so the written options are immediately in-the-money by $2.00. How many shares should the market maker buy to neutralize the delta of the option position?
a. Long 3.0 shares
b. Long 60.0 shares
c. Long 63.0 shares
d. Long 66.0 shares
8.3. Which is likely to have the highest gamma?
a. Deep in-the-money call option that is near to expiration
b. Deep out-of-the-money put option that is near to expiration
c. At-the-money put option that is very distant from expiration
d. At-the-money call option that is near to expiration
8.4. A call option with a price of $3.52 has a vega of 18.50. If the volatility increases from 20.0% to 26.0% per annum, what is the estimated price of the option under the higher volatility?
a. $3.69
b. $4.63
c. $8.33
d. $9.07
8.5. If at-the-money (ATM) options are otherwise identical, which of the following will have the LOWEST value of rho?
a. Put with distant time to expiration
b. Put near to expiration
c. Call near to expiration
d. Call with distant time to expiration
Answers:
- The conceptual profile of the Greeks; e.g., delta tends toward 1.0 for ITM calls (this is intuitive); gamma highest for ATM options (also intuitive!); theta is negative (why?) and uniquely non stochastic (why?); vega peaks ATM.
- If given the Greek, know how to apply (see my questions below) the Greek value to approximate the option price change. This is their whole reason for being: they are first partial derivatives. I think you are doing truly well if you grasp how the option Greeks are cousins to bond duration (~ delta) and convexity (~ gamma) as both are application of Taylor Series. Pretty much everything we do w.r.t. analytical VaR is Taylor Series.
Questions:
8.1. Twelve days ago (T - 12 days), a European call option with a price of $4.80 had a theta of -6.30 per year. Between then and today (T), no stochastic option inputs have changed; i.e., stock price, volatility and riskfree rate are unchanged. What is the today's estimate of the option price, as reduced by only time decay, assuming 252 trading days per year?
a. $3.36
b. $4.50
c. $4.63
d. $4.77
8.2. An at-the-money call option has a (percentage) delta of 0.600 and gamma of 0.030. A market maker writes (sells) 100 call options, but only after the stock price unexpectedly jumps $2.00, so the written options are immediately in-the-money by $2.00. How many shares should the market maker buy to neutralize the delta of the option position?
a. Long 3.0 shares
b. Long 60.0 shares
c. Long 63.0 shares
d. Long 66.0 shares
8.3. Which is likely to have the highest gamma?
a. Deep in-the-money call option that is near to expiration
b. Deep out-of-the-money put option that is near to expiration
c. At-the-money put option that is very distant from expiration
d. At-the-money call option that is near to expiration
8.4. A call option with a price of $3.52 has a vega of 18.50. If the volatility increases from 20.0% to 26.0% per annum, what is the estimated price of the option under the higher volatility?
a. $3.69
b. $4.63
c. $8.33
d. $9.07
8.5. If at-the-money (ATM) options are otherwise identical, which of the following will have the LOWEST value of rho?
a. Put with distant time to expiration
b. Put near to expiration
c. Call near to expiration
d. Call with distant time to expiration
Answers:
