1 / 29

Jim Bodurtha Georgetown University

iden
Download Presentation

Jim Bodurtha Georgetown University

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Estimating a Local (Time- and State-Dependent) Volatility Surface(A Linearization-Based Solution to the Ill-Posed Local Volatility Estimation Problem,and Non-Parametric Estimation of an Implied Volatility Surface with Martin Jermakyanfromhttp://www.gsb.georgetown.edu/dept/facserv/faculty/bodurthj/research/research.html) • Jim Bodurtha • Georgetown University • Chicago Risk Management ConferenceMay 7, 1998 - Chicago

  2. Term Volatility Surfaces - • Shimko, Dumas, Fleming and Whaley ... • Ait-Sahalia-Lo, Longstaff, Elliot-Madan, Derman-Kani-Zhou… • Rubinstein, Rubinstein-Jackwerth ... Local Volatility Surfaces - • Avellanede • Bodurtha-Jermakyan • Dupire, Derman-Kani (interpolate artifical prices) • Lagnado-Oscher

  3. Table 2: Example European FX Call Options, Pricing and Vol “Smile” Implied Vol across options (s0) = 20%

  4. Binomial Tree Valuation Set upSee also Kamrad-Ritchken (1991)

  5. Trinomial Lattice Algebra

  6. Trinomial Lattice European Call Option Values and Volatilities

  7. Redefine Variance and European Call Option Values

  8. Estimation Procedure with Regularization

  9. Linear (Smoothed) Volatility Surface Estimator

  10. Risk Management - Valuing a European Option Book

  11. Augment discrepancy function for Gamma estimation error:

  12. Figure 2: PHLX DM European Options Local Volatility Surface - 11/25/91(2/9/95-4/14/97 average bid-ask spread 0.64% and standard deviation 0.52%)

  13. Other issues • Computation-estimation and benchmarking Restricted non-linear models vs. linearizations Higher-order regularizers (large GSVD problem) • Volatility surface dynamics • Exotics • American options • Interest rates • Convergence

  14. “Non-Parametric Estimation …” Problem statement:

  15. 5. A Finite Difference-Based Numerical Implementation - Change state variable (moving frame of coordinates), discretize in state and time, first-order forward difference for time derivatives, second-order central difference for state derivatives, and introduce artificial state boundary conditions for L,

More Related