Smiling for the Delayed Volatility Swaps
نویسندگان
چکیده
We present a variance drift adjusted version of the Heston model which leads to a significant improvement of the market volatility surface fitting (compared to Heston). The numerical example we performed with recent market data shows a significant reduction of the average absolute calibration error 1 (calibration on 12 dates ranging from Sep. 19 to Oct. 17 2011 for the FOREX underlying EURUSD). Our model has two additional parameters compared to the Heston model, can be implemented very easily and was initially introduced for volatility derivatives pricing purpose. The main idea behind our model is to take into account some past history of the variance process in its (risk-neutral) diffusion. Using a change of time method for continuous local martingales, we derive a closed formula for the Brockhaus&Long approximation of the volatility swap price in this model. We also consider dynamic hedging of volatility swaps using a portfolio of variance swaps.
منابع مشابه
Modeling of Variance and Volatility Swaps for Financial Markets with Stochastic Volatilities
A new probabilistic approach is proposed to study variance and volatility swaps for financial markets with underlying asset and variance that follow the Heston (1993) model. We also study covariance and correlation swaps for the financial markets. As an application, we provide a numerical example using S&P60 Canada Index to price swap on the volatility.
متن کاملA Cautious Note on the Design of Volatility Derivatives
This cautious note aims to point at the potential risks for the financial system caused by various increasingly popular volatility derivatives including variance swaps on futures of equity indices. It investigates the pricing of variance swaps under the 3/2 volatility model. Carr with Itkin and Sun have discussed the pricing of variance swaps under this type of model. This paper studies a speci...
متن کاملVolatility Derivatives
Volatility derivatives are a class of derivative securities where the payoff explicitly depends on some measure of the volatility of an underlying asset. Prominent examples of these derivatives include variance swaps and VIX futures and options. We provide an overview of the current market for these derivatives. We also survey the early literature on the subject. Finally, we provide relatively ...
متن کاملPricing Exotic Variance Swaps under 3/2-Stochastic Volatility Models
We consider pricing of various types of exotic discrete variance swaps, like the gamma swaps and corridor swaps, under the 3/2-stochastic volatility models with jumps. The class of stochastic volatility models (SVM) that use a constant-elasticity-of-variance (CEV) process for the instantaneous variance exhibit nice analytical tractability when the CEV parameter takes just a few special values (...
متن کاملPricing Volatility Swaps Under Heston’s Stochastic Volatility Model with Regime Switching
We develop a model for pricing volatility derivatives, such as variance swaps and volatility swaps under a continuous-time Markov-modulated version of the stochastic ∗The Corresponding Author: RBC Financial Group Professor of Finance, Haskayne School of Business, University of Calgary, Calgary, Alberta, Canada, T2N 1N4; Email: [email protected]; Fax: 403-770-8104; Tel: 403-220-5540 †Lecturer...
متن کامل