Servicenavigation

Project A6: Calibration errors in Risk management

Project leader

Denis Belomestny

Abstract

With the dissemination of quantitative methods in risk management and introduction of complex derivative products, statistical methods have come to play an increasingly important role in financial derivatives making, especially in the context of calibration of derivative instruments. While the use of such methods has undeniably led to better managing of market risk, it has in turn given rise to a new type of risks linked to the unknown error bounds for the quantities delivered by these methods. When the pricing model is specified the aim of calibration is to estimate parameters of the model using the prices of liquidly traded options such as call and put options on major indices, exchange rates and major stocks. For such an option the price is determined by supply and demand on the market. Because of the bid-ask spread and small number of daily available options on the given stock (or interest rate) the calibration is an ill-posed problem and has to be treated carefully. For example, in the case of jump diffusion Merton model the bid-ask spread of order 1% and the number of vanilla call options as large as 50 can lead to a relative error in the parameters estimate of an order up to 20% if the calibration is not accompanied with a proper regularization. Moreover, the use of different calibration procedures (for example, based on different error measures) can lead to different calibration results and give rise to the so-called calibration uncertainty or calibration risk. The unknown error bounds can not only lead to the mispricing of derivative products but also make this mispricing sometimes unnoticeable for a long time. While this type of risk is acknowledged by most operators who make use of quantitative methods, most of the discussion on this subject has stayed at a qualitative level. The aim of this project is to quantify (construct error bounds, investigate worst-case scenarios) statistical and numerical errors arising during calibration and propose new computationally efficient algorithms for calibration which can reduce these errors.