Uniform bounds for Black--Scholes implied volatility

Article, Preprint English OPEN
Tehranchi, Michael;
(2016)

In this note, Black--Scholes implied volatility is expressed in terms of various optimization problems. From these representations, upper and lower bounds are derived which hold uniformly across moneyness and call price. Various symmetries of the Black--Scholes formula ... View more
  • References (27)
    27 references, page 1 of 3

    [1] L. Andersen and A. Lipton. Asymptotics for exponential Levy processes and their volatility smile: survey and new results. International Journal of Theoretical and Applied Finance 16(01): 1350001. (2013)

    [2] S. Benaim and P. Friz. Regular variation and smile asymptotics. Mathematical Finance 19(1): 1{12. (2009)

    [3] S. Benaim and P. Friz. Smile asymptotics. II. Models with known moment generating functions. Journal of Applied Probability 45(1) 16{23. (2008)

    [4] F. Black and M. Scholes. The pricing of options and corporate liabilities. Journal of Political Economy 81:637{654. (1973)

    [5] M. Brenner and M.G. Subrahmanyam. A simple formula to compute the implied standard deviation. Financial Analysts Journal 44(5): 80{83. (1988)

    [6] F. Caravenna and J. Corbetta. General smile asymptotics with bounded maturity. arXiv:1411.1624 [q- n.PR]. (2015)

    [7] C.J. Corrado and Th.W. Miller, Jr. A note on a simple, accurate formula to compute implied standard deviations. Journal of Banking & Finance 20: 595{603. (1996)

    [8] A. Cox and D. Hobson. Local martingales, bubbles and option prices. Finance and Stochastics 9(4): 477{492. (2005)

    [9] S. De Marco, C. Hillairet and A. Jacquier. Shapes of implied volatility with positive mass at zero. arXiv:1310.1020 [q- n.PR]. (2013)

    [10] F. Delbaen and W. Schachermayer. The fundamental theorem of asset pricing for unbounded stochastic processes. Mathematische Annalen 312: 215{250. (1998)

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