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  1. S

    Normal IV vs. Log-normal IV

    Hi All, Anyone has any idea/thoughts around how we can convert Log-normal Implied Volatility(Black Scholes) to Normal Implied Volatility?
  2. Nicole Seaman

    YouTube T4-07: Binomial option pricing model: up/down jumps based on volatility

    Instead of arbitrarily selecting the up (u) and down (d) jumps in the binomial, we can "match them to a volatility input assumption, σ. The correct values are given by u = exp[σ*sqrt(Δt)] and d = 1/u; notice that the exponent is just apply the Square Root Rule (SRR) of scaling the per annum...
  3. Nicole Seaman

    YouTube T4-01: Three approaches to value at risk (VaR) and volatility

    The three approaches are 1. Parametric; aka, analytical; 2. Historical simulation; and 3. Monte Carlo simulation (MCS). The parametric approach assumes a clean function, the other two work with messy data. Historical simulation is betrayed by a histogram, MCS is betrayed by a random number...
  4. Nicole Seaman

    YouTube T2-26: Maximum likelihood estimation of GARCH parameters

    GARCH(1,1) is the popular approach to estimating volatility, but its disadvantage (compared to STDDEV or EWMA) is that you need to fit three parameters. Maximum likelihood estimation, MLE, is an immensely useful statistical approach that can be used to find "best fit" parameters. In this video...
  5. Nicole Seaman

    YouTube T2-23: Volatility: GARCH 1,1

    The GARCH(1,1) volatility estimate shares a similarity to EWMA volatility: both assign greater (lesser) weight to recent (distant) returns. But the GARCH(1,1) has an additional feature: it models a long-run (aka, unconditional) variance toward which the volatility series is pulled. David's XLS...
  6. Nicole Seaman

    YouTube T2-22: Volatility: Exponentially weighted moving average, EWMA

    The exponentially weighted moving average (EWMA) cures the key weakness of the common historical standard deviation by assigning greater weight to more recent returns and lessor weights to more distant (in the past) returns. Its key parameter is lambda, λ, which specifies the ratio of...
  7. Nicole Seaman

    YouTube T2-21: Volatility: standard deviation

    The simple, common approach to estimating volatility is historical standard deviation. Here is a thread about the decision to include/exclude the mean return: https://trtl.bz/2kLRK7z David's XLS is here: https://trtl.bz/2kOmHb6
  8. G

    Convexity and Volatility

    Hi everyone, It's my first time posting but I've been reading the forums since I enrolled for the FRM part I more than a year ago and I wanted, before anything else, to thank you all, particularly David, for all the help I've gotten from such a knowledgeable and supportive community while...
  9. Nicole Seaman

    YouTube T1-3 How to translate volatility over time

    We typically scale volatility with the square root rule, but keep in mind the key assumption (i.i.d. returns). We APOLOGIZE that the bottom-right corner is obstructed by the web camera. It contains Expected return = +10.0% such that the Absolute VaR = -10%*10/250 + 2.326*20%*sqrt(10/250); i.e...
  10. Nicole Seaman

    P1.T4.811. Two-step binomial models (Hull Ch.13)

    Learning objectives: Calculate the value of an American and a European call or put option using a one-step and two-step binomial model. Describe how volatility is captured in the binomial model. Questions: 811.1 Consider a six-month at-the-money (ATM) European call option on a...
  11. R

    Tuckman Chapter 9 : Term Structure of Volatility

    In "The Art of Term Structure Models : Drift" Tuckman mentions regarding term structure of volatility that: "The term structure of volatility in Model 1 is constant at 113 basis points." He also mentions that the Model 2 and the Ho-Lee, both do not change the term structure of volatility...
  12. K

    What is the Heath Jarrow Morton (HJM) model in interest rates?

    Hello All, I am interested in knowing what is HJM model ? How are they computed ? What are they used for and how are volatility surface derived ? How are they useed for valuations? Want to know mainly in brief and simple/layman language. Thanks
  13. Nicole Seaman

    P1.T3.723. Swaps: valuation with OIS and LIBOR, comparative advantage, and currency swap valuation

    Learning objectives: Explain the mechanics of a currency swap and compute its cash flows. Explain how a currency swap can be used to transform an asset or liability and calculate the resulting cash flows. Calculate the value of a currency swap based on two simultaneous bond positions. Calculate...
  14. Nicole Seaman

    P2.T8.702. Macroeconomic risk factors including growth, inflation and volatility (Andrew Ang)

    Learning objectives: Describe the process of value investing, and explain reasons why a value premium may exist [BT note: this objective is somewhat out of sequence; the next practice question will review the value premium ]. Explain how different macroeconomic risk factors, including economic...
  15. Nicole Seaman

    P1.T2.703. EWMA versus GARCH volatility (Hull)

    Learning objectives: Apply the exponentially weighted moving average (EWMA) model to estimate volatility. Describe the generalized autoregressive conditional heteroskedasticity (GARCH(p,q)) model for estimating volatility and its properties. Calculate volatility using the GARCH(1,1) model...
  16. Nicole Seaman

    P1.T2.702. Simple (equally weighted) historical volatility (Hull)

    Learning objectives: Define and distinguish between volatility, variance rate, and implied volatility. Describe the power law. Explain how various weighting schemes can be used in estimating volatility. Questions 702.1. Consider the following series of closing stock prices over the tend most...
  17. U

    R16.P1.T2. Hull - expected value of u(n+t-1)^2

    In Hull - Risk Management and Financial Institutions, it is stated, in page 222 (10.10 using GARCH(1,1) to forecase future volatility), that: "the expected value of u(n+t−1)^2 is σ(n+t−1)^2". Is this something obvious? Can anybody explain why this should be the case? Thanks!
  18. V

    Implied Volatility

    Hello David, Can you please explain why the Implied volatility of calls is different from puts in real markets. As per Hull, the IV of call and puts have to be same. But when I look into actual markets, the data is otherwise. I tried to google around, but could not find a convincing answer...
  19. Nicole Seaman

    P1.T2.409 Volatility, GARCH(1,1) and EWMA

    Concept: These on-line quiz questions are not specifically linked to AIMs, but are instead based on recent sample questions. The difficulty level is a notch, or two notches, easier than bionicturtle.com's typical AIM-by-AIM question such that the intended difficulty level is nearer to an actual...
  20. T

    Square Root Rule with Mean Reversion & AutoCorrelation - VaR & Volatility

    David, I am now thoroughly confused by the Square Root Rule and scaling the VaR under the circumstance of Mean Reversion and Auto correlation. In search of an explanation, I found this thread http://www.bionicturtle.com/forum/newreply/1729/ , but your link is not attached anymore. The rules...