THE MOMENT FORMULA FOR IMPLIED VOLATILITY AT EXTREME STRIKES

By Roger Lee. 2004

321 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/2ca527e4569ed111f82414a5a285949c0f893f65

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Economics and Econometrics

1. Peter Tankov
2. Martin Keller‐Ressel
3. Antoine Jacquier
4. Peter K. Friz
5. Aleksandar Mijatovic
6. Roger Lee
7. Jim Gatheral
8. Leif B. G. Andersen

In Finance

1. Peter Tankov
2. Antoine Jacquier
3. Martin Keller‐Ressel
4. Eberhard Mayerhofer
5. Peter K. Friz
6. Roger Lee
7. Aleksandar Mijatovic
8. Leif B. G. Andersen

Citations in the corpus

• Marginal Density Expansions for Diffusions and Stochastic Volatility I: Theoretical Foundations (2011, background): “We note that the square-root growth of implied volatility, in terms of log-strike, is actually a very general feature of models with moment explosions, [38, 7] which includes many stochastic volatility models [24, 39, 8].”
• Affine Diffusion Processes: Theory and Applications (2009, background): “We mention here explicitly just the few articles [2, 4, 8, 10, 13, 14, 17, 21, 26, 27, 29] and [12] for a broader overview.”
• REGULAR VARIATION AND SMILE ASYMPTOTICS (2006, methodology): “The purpose of this paper is to connect the tail behavior of X to the wing behavior of the Black–Scholes implied volatility, sharpening Roger Lee’s celebrated moment formula Lee (2004).”
• MOMENT EXPLOSIONS AND LONG‐TERM BEHAVIOR OF AFFINE STOCHASTIC VOLATILITY MODELS (2008, methodology): “We will show that many properties of such a model, including its longterm behavior and moment explosions, can be analyzed by studying differential equations of the generalized Riccati type. Our results on the long-term behavior are formulated as asymptotic results for the cumulant generating functio”
• Asymptotic Behavior of the Stock Price Distribution Density and Implied Volatility in Stochastic Volatility Models (2009, result): “Important results concerning the behavior of the implied volatility Î(k) in a general case were obtained by Lee (see [15]).”
• Asymptotics for Exponential Levy Processes and Their Volatility Smile: Survey and New Results (2012, background): “follow from the moment formulas of [69], [15], [16] and [55]; see [116] for a brief discussion.”
• Option Pricing by Transform Methods: Extensions, Unification, and Error Control (2004, methodology): “These extended payoff classes contain all of the derivative structures treated in Duffie, Pan and Singleton (2000), and in particular they allow payoffs dependent on multidimensional state variables.”
• Asymptotic formulae for implied volatility in the Heston model (2009, unknown): “Likewise, many papers have studied the behaviour of the implied volatility smile in the wings (see [4], [5], [16], [17], [26]).”
• PUT‐CALL SYMMETRY: EXTENSIONS AND APPLICATIONS (2009, background): “To establish (a) ⇔ (b), observe that Lee [15] Thm 4.”
• Convergence of Heston to SVI (2010, methodology): “This parameterization has two key properties that have led to its subsequent popularity with practitioners: • For a fixed time to expiry T , the implied Black-Scholes variance σ(2) BS(k, T ) is linear in the log-strike k as |k| → ∞ consistent with Roger Lee’s moment formula [4].”
• Optimal Fourier Inversion in Semi-Analytical Option Pricing (2007, unknown): “Lee [Lee04] intensively discussed Carr and Madan’s approach, and proposed an algorithm to arrive at an optimal α in the situation where the Fourier integral in (7) is approximated by the discrete Fourier transform (DFT).”
• SMILE ASYMPTOTICS II: MODELS WITH KNOWN MOMENT GENERATING FUNCTIONS (2006, background): “Such asymptotics are enough to make the tail-wing formula work and we so obtain a version of Lee’s moment formula with the novel guarantee that there is indeed a limiting slope when plotting implied variance against log-strike.”
• Arbitrage-free SVI volatility surfaces (2012, unknown): “• For a fixed time to expiry t , the implied Black–Scholes varianceσ 2 BS(k, t) is linear in the logstrike k as |k| → ∞ consistent with Roger Lee’s moment formula (Lee 2004).”
• EXPLICIT IMPLIED VOLATILITIES FOR MULTIFACTOR LOCAL‐STOCHASTIC VOLATILITY MODELS (2013, methodology): “Most notably, we mention the work of Lee (2004) and Gao and Lee (2014).”