AIM: Define and describe ... vega for option positions
Questions:
402.1. Consider an option with a vega of 38.20 while the underlying stock's volatility is 20.0% per annum with continuous compounding. Which of the following is the best interpretation?
a. If the volatility increases by 10 basis points from 20.00% to 20.10%, then the price of the option will increase by approximately $3.82
b. If the volatility increases by 100 basis points from 20.0% to 21.0%, then the price of the option will increase by approximately $0.3820
c. If the volatility increases by 100 basis points from 20.0% to 21.0%, then the price of the option will increase by approximately $38.20
d. If the volatility increases by 1,000 basis points from 20.0% to 30.0%, then the price of the option will increase by approximately $0.03820
402.2. Consider a the following call option which is re-priced after a mild + 3.0% shock to its volatility. In both cases, the stock = strike = $50 (i.e., at an-the-money call option), the riskfree rate is 2.0% and the maturity is one year:
a. 0.19
b. 0.580
c. 19.33
c. 58.40
402.3. Recall that option vega is given by S(0)*sqrt(T)*N'(d1). Each of the following is true about vega EXCEPT which is false?
a. Vega tends to increase with option maturity
b. Vega is highest for at-the-money options (compared to ITM and OTM options)
c. If the stock price doubles, vega approximately doubles
d. Per put-call parity, the vega above is the same for both a call and a put with an identical strike price and maturity
Answers here:
Questions:
402.1. Consider an option with a vega of 38.20 while the underlying stock's volatility is 20.0% per annum with continuous compounding. Which of the following is the best interpretation?
a. If the volatility increases by 10 basis points from 20.00% to 20.10%, then the price of the option will increase by approximately $3.82
b. If the volatility increases by 100 basis points from 20.0% to 21.0%, then the price of the option will increase by approximately $0.3820
c. If the volatility increases by 100 basis points from 20.0% to 21.0%, then the price of the option will increase by approximately $38.20
d. If the volatility increases by 1,000 basis points from 20.0% to 30.0%, then the price of the option will increase by approximately $0.03820
402.2. Consider a the following call option which is re-priced after a mild + 3.0% shock to its volatility. In both cases, the stock = strike = $50 (i.e., at an-the-money call option), the riskfree rate is 2.0% and the maturity is one year:
- When volatility is 30.0%, the option price is $6.41
- When volatility increases to 33.0%, the option price is $6.99
a. 0.19
b. 0.580
c. 19.33
c. 58.40
402.3. Recall that option vega is given by S(0)*sqrt(T)*N'(d1). Each of the following is true about vega EXCEPT which is false?
a. Vega tends to increase with option maturity
b. Vega is highest for at-the-money options (compared to ITM and OTM options)
c. If the stock price doubles, vega approximately doubles
d. Per put-call parity, the vega above is the same for both a call and a put with an identical strike price and maturity
Answers here:
Last edited by a moderator:
