Download Volatility Core Concepts Practice Exam: Questions and Answers and more Exams Technology in PDF only on Docsity!
Question 1. Which of the following best defines financial volatility? A) The average price of an asset over a year B) The degree of variation of a trading price series over time C) The total return earned by an investment D) The correlation between two assets Answer: B Explanation: Volatility measures how much the price of an asset fluctuates around its mean over a given period. Question 2. In finance, volatility is most commonly used as a proxy for: A) Liquidity B) Credit risk C) Market risk (uncertainty) D) Dividend yield Answer: C Explanation: Higher volatility implies greater uncertainty about future price movements, reflecting market risk. Question 3. The relationship between volatility and expected return is best described by: A) Higher volatility always leads to lower returns B) Higher volatility generally offers higher potential returns, but also higher risk C) Volatility and return are unrelated D) Lower volatility guarantees higher returns Answer: B
Explanation: Risk‑return trade‑off states that investors demand higher expected returns for taking on greater volatility. Question 4. Volatility clustering refers to the empirical observation that: A) Volatility is constant over time B) Large price changes tend to be followed by large changes, and small changes by small changes C) Volatility is highest at market open and close D) Volatility is only observed in emerging markets Answer: B Explanation: Clustering means periods of high (or low) volatility tend to persist, a hallmark of financial time series. Question 5. The standard deviation of logarithmic returns is used to estimate: A) Expected dividend payout B) Historical volatility C) Net present value D) Sharpe ratio Answer: B Explanation: Taking log returns stabilizes variance; their standard deviation is the conventional measure of historical volatility. Question 6. If the variance of a return series is 0.0004, what is the corresponding volatility (σ)? A) 0.
Answer: C Explanation: Real‑world returns exhibit heavier tails than the normal distribution, leading to underestimation of extreme moves. Question 9. Historical volatility is typically calculated using which type of price data? A) Forward rates B) Closing prices or high/low ranges over a past window C) Dividend yields D) Credit spreads Answer: B Explanation: HV relies on past price observations, often daily closes or intraday high/low ranges. Question 10. To annualize a daily volatility estimate, you multiply by the square root of: A) 365 B) 12 C) 252 (trading days) D) 30 Answer: C Explanation: There are roughly 252 trading days in a year; annualized σ = σ_daily × √252. Question 11. Which factor does NOT affect the calculation of historical volatility? A) Length of the look‑back period B) Sampling frequency (daily vs. hourly) C) The risk‑free rate
D) Choice of price (close vs. high/low) Answer: C Explanation: The risk‑free rate is irrelevant for pure historical volatility, which is purely statistical. Question 12. Implied volatility is derived from: A) Past price movements B) Option market prices using an option‑pricing model C) Company earnings forecasts E) Bond yields Answer: B Explanation: IV is the volatility input that, when placed into a model (e.g., Black‑Scholes), reproduces the observed option price. Question 13. In the Black‑Scholes‑Merton model, a higher implied volatility will have what effect on a call option’s premium, all else equal? A) Decrease it B) Increase it C) Have no effect D) Turn the call into a put Answer: B Explanation: Higher σ raises the expected future dispersion of the underlying, increasing the option’s time value.
Explanation: VIX is a forward‑looking measure derived from S&P 500 option prices, representing 30 ‑day expected volatility. Question 17. Which of the following is a technical volatility indicator that uses price range rather than standard deviation? A) Bollinger Bands B) Average True Range (ATR) C) MACD D) RSI Answer: B Explanation: ATR calculates the average of true ranges (high‑low, high‑previous close, low‑previous close) to gauge volatility. Question 18. Bollinger Bands are constructed by plotting a moving average plus/minus how many standard deviations? A) 1 B) 1. C) 2 D) 3 Answer: C Explanation: Standard Bollinger Bands use a 20‑period SMA with ± 2 σ bands. Question 19. A volatility smile occurs when implied volatility: A) Is constant across strikes B) Increases for deep‑in‑the‑money and deep‑out‑of‑the‑money options, forming a U‑shape
C) Decreases linearly with strike price D) Is highest at the ATM strike only Answer: B Explanation: The “smile” describes higher IV for far OTM and ITM strikes relative to ATM, forming a convex curve. Question 20. The primary economic reason for a volatility skew (higher IV for low strikes) in equity markets is: A) Higher demand for upside leverage B) Greater demand for downside protection (puts) C) Regulatory constraints on call options D) Tax advantages of OTM calls Answer: B Explanation: Investors often buy protective puts, pushing up demand and IV for low‑strike options, creating a skew. Question 21. In a Delta‑neutral skew trade, the trader aims to profit from: A) Changes in the underlying price only B) Movements in implied volatility across strikes while keeping net Delta zero C) Time decay of options D) Interest‑rate differentials Answer: B Explanation: A delta‑neutral skew position isolates volatility‑skew risk while neutralizing directional exposure.
Answer: B Explanation: GARCH captures volatility clustering by allowing variance to depend on past squared shocks and past variance. Question 25. In a GARCH(1,1) specification, the term “α” (alpha) represents: A) The long‑run average volatility B) The impact of the most recent squared return shock on current variance C) The risk‑free rate D) The speed of mean reversion Answer: B Explanation: α measures the reaction of conditional variance to the latest innovation (ε²_{t‑1}). Question 26. Local volatility models differ from stochastic volatility models mainly because they assume: A) Volatility is a deterministic function of spot and time, matching the observed implied volatility surface B) Volatility follows a jump‑diffusion process C) Volatility is constant D) Volatility depends on macro‑economic variables Answer: A Explanation: Local volatility is a deterministic surface calibrated to match market‑observed option prices. Question 27. The SABR model is primarily used to model which market feature? A) Credit default probabilities
B) Interest‑rate volatility smiles C) Currency carry trades D) Equity dividend yields Answer: B Explanation: SABR (Stochastic Alpha Beta Rho) is popular for modeling the volatility smile in interest‑rate derivatives. Question 28. Which Greek measures the sensitivity of an option’s price to a change in the underlying price? A) Delta (Δ) B) Gamma (Γ) C) Vega (ν) D) Theta (Θ) Answer: A Explanation: Delta is the first‑order derivative of the option price with respect to the underlying price. Question 29. Gamma is best described as: A) The rate of decay of an option’s time value B) The curvature of the option’s price relative to the underlying (second‑order Delta) C) Sensitivity to changes in implied volatility D) Sensitivity to changes in interest rates Answer: B
D) Undefined Answer: A Explanation: An increase in IV raises the value of a long call, giving it positive Vega. Question 33. Vanna is a second‑order Greek that captures the sensitivity of: A) Delta to changes in volatility, or Vega to changes in underlying price B) Theta to changes in dividend yield C) Rho to changes in time D) Gamma to changes in interest rates Answer: A Explanation: Vanna measures the cross‑effect between underlying price and volatility on the option’s value. Question 34. Charm (or Delta decay) measures: A) The rate at which Delta changes as time passes, holding price constant B) The sensitivity of Vega to changes in interest rates C) The effect of dividend changes on Gamma D) The impact of volatility on Theta Answer: A Explanation: Charm reflects how Delta evolves over time, important for dynamic hedging. Question 35. In a delta‑hedged portfolio, the primary source of residual risk is: A) Vega (volatility) risk, because Delta is neutralized but volatility can change
B) Interest‑rate risk C) Dividend risk D) Currency risk Answer: A Explanation: After delta hedging, the portfolio’s exposure to volatility (Vega) remains, especially when σ moves. Question 36. A trader who is long Vega is exposed to: A) Increases in implied volatility B) Decreases in implied volatility C) Changes in the underlying price only D) Time decay only Answer: A Explanation: Positive Vega positions profit when IV rises. Question 37. Which of the following is a static hedging technique for volatility exposure? A) Continuously rebalancing delta B) Using a calendar spread that offsets Vega across expirations C) Buying the underlying asset D) Holding cash Answer: B Explanation: A calendar spread can be structured to have near‑zero net Vega, providing a static hedge.
Explanation: Variance swaps settle on the realized variance of the underlying over the contract period versus the fixed strike. Question 41. Compared to a variance swap, a volatility swap provides a payoff based on: A) The square root of realized variance (i.e., realized volatility) B) The realized variance itself C) The underlying’s price level D) The risk‑free rate Answer: A Explanation: Volatility swaps settle on realized volatility (σ), which is the square root of variance, making the payoff linear in σ. Question 42. Which strategy profits when implied volatility is higher than realized (historical) volatility? A) Long straddle B) Short straddle C) Long butterfly D) Calendar spread Answer: B Explanation: Selling options (short straddle) collects premium when IV is high; if realized volatility is lower, the position gains. Question 43. A long straddle consists of: A) Buying a call and a put at the same strike and expiration B) Selling a call and a put at different strikes
C) Buying a call spread D) Selling a put spread Answer: A Explanation: A straddle captures pure volatility; profit occurs if the underlying moves significantly in either direction. Question 44. An iron condor is best described as: A) A delta‑neutral, volatility‑selling strategy using two vertical spreads (call and put) out‑of‑the‑money B) A long‑gamma, long‑vega position C) A calendar spread on futures D) A synthetic long stock Answer: A Explanation: Iron condors collect premium from both sides while limiting risk, profiting when volatility stays low. Question 45. In a calendar spread, the trader typically: A) Buys a short‑dated option and sells a longer‑dated option of the same strike B) Buys a longer‑dated option and sells a shorter‑dated option of the same strike C) Trades options on different underlying assets D) Trades only futures contracts Answer: B Explanation: The classic calendar spread is long the far‑dated option and short the near‑dated one, expressing a view on volatility term structure.
Answer: B Explanation: Unanticipated news, such as an earnings surprise, can trigger rapid re‑pricing of options, raising IV. Question 49. The “square‑root‑of‑time” rule is used to: A) Convert daily volatility to annual volatility B) Estimate option delta C) Compute the price of a variance swap D) Determine the breakeven point of a straddle Answer: A Explanation: Because variance scales linearly with time, volatility scales with the square root of time. Question 50. Which of the following best describes the relationship between gamma and vega for an at‑the‑money (ATM) option? A) Both are highest for ATM options and decline as the option moves away from ATM B) Gamma is highest for deep‑in‑the‑money options, while vega peaks for OTM options C) Gamma and vega are unrelated D) Vega is highest for deep‑in‑the‑money options, while gamma peaks for OTM options Answer: A Explanation: ATM options have the greatest curvature (gamma) and are most sensitive to volatility changes (vega).
Question 51. If a trader is long a 30‑day variance swap with a strike of 0.04 (i.e., 20% annualized variance) and the realized variance over the period is 0.09, the trader’s payoff will be: A) +0.05 (positive) B) – 0.05 (negative) C) +0.03 (positive) D) – 0.03 (negative) Answer: A Explanation: Payoff = Realized variance – Strike = 0.09 – 0.04 = +0.05. Question 52. The “sticky‑strike” assumption in option pricing implies that: A) Implied volatility remains constant for a given strike regardless of spot moves B) Implied volatility moves one‑for‑one with the underlying price C) Volatility surface is flat across maturities D) The risk‑free rate is constant Answer: A Explanation: Sticky‑strike assumes IV is a function of strike, not of moneyness; it does not shift with spot. Question 53. Under a “sticky‑delta” assumption, implied volatility is assumed to be constant for: A) A given strike price B) A given delta (moneyness) level as the underlying moves C) A given time to expiration D) A given dividend yield
