View Full Document

Local Volatility Calibration using the Most Likely Path



View the full content.
View Full Document
View Full Document

579 views

Unformatted text preview:

Local Volatility Calibration using the Most Likely Path 19 December 2006 Computational Methods in Finance Professor Ali Hirsa Paris Pender Submitted by Kwasi Danquah Saurav Kasera Brian Lee Sonky Ung TABLE OF CONTENTS 1 Introduction 2 Our method 3 Key Concepts a Implied volatility proxy b Most likely path 4 Option Data Extraction 5 Results Our Method applied to SPX 6 Monte Carlo Validation 7 Conclusion 8 References INTRODUCTION Why are we interested in calibrating a local volatility surface It is mostly to price dependent exotic options which are not very liquid and the proper market quotes are not available Local volatility also gives rise to some interesting relative value trading strategies There are a number of local volatility calibration methods available but no one agrees on the perfect calibration method There is no single correct answer Perhaps that is the reason why calibration is not only a science but also an art The problem of calibration requires creativity and that is the reason why there is no perfect calibration model There is always room for improvement in these kinds of problems Below we discuss a robust local volatility calibration method that appeared in a 2 page Risk Magazine article in April 2006 1 The method is based a fixed point iteration and on the concept of the most likely path first observed by Jim Gatheral 2 He calls it the most probable path We start with a market implied volatility surface and then by an iterative process construct our local volatility surface We have taken special care in making sure that our market option prices have been interpolated using liquid options as it can be very tempting to neglect the quality of data in these kinds of projects Filtering data is again a mixture or art and sciences The process then entails forming a most likely path and then taking the time average of the volatility along that path We then price options using this surface and compare it with the Monte Carlo prices generated by our Monte



Access the best Study Guides, Lecture Notes and Practice Exams

Loading Unlocking...
Login

Join to view Local Volatility Calibration using the Most Likely Path and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Local Volatility Calibration using the Most Likely Path and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?