Local Valuation of Options

Christine Juul Sørensen

Student thesis: Master thesis

Abstract

This paper examines the local valuation model proposed by (Carr og Wu 2020) and expands the model by assuming discontinuous dynamics of the price and volatility of the underlying. The local valuation model is based on the BlackScholes formula for option pricing, using the options own implied volatility. By examining the profit and loss attribution of an option investment, using riskneutral valuation and applying a no arbitrage condition, the fair price of the option can be expressed by its implied volatility and the first and second conditional moments of the change in the implied volatility. The pricing relation will hold at a specific time. The local valuation model is expanded to a discontinuous dynamic setup by formulating the price relation based on Mertons Jump-Diffusion Model. In the discontinuous model the fair price of an option, at a specific time, is given by the second order derivatives and moments of the implied volatility. Forecast of the conditional moments are used in investment strategies based on the difference between the observed and estimated implied volatility smile. The profit and loss of the investment strategies suggested that the local valuation model in continuous time is a better fit for forecasting the implied volatility smile, than the expanded model in discontinuous time.

EducationsMSc in Business Administration and Mathematical Business Economics, (Graduate Programme) Final Thesis
LanguageDanish
Publication date2021
Number of pages93
SupervisorsMads Stenbo Nielsen