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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.
Variance swaps for financial markets with underlying asset and stochastic volatilities with delay are modelled and priced in this paper. We found some analytical close forms for expectation and variance of the realized continuously sampled variance for stochastic volatility with delay both in stationary regime and in general case. The key features of the… (More)
The aim of this paper is to price European options for underlying assets with stochastic volatility (SV) in Heston model in 1993 using fuzzy set theory. The main idea is to transform the probability distribution of stochastic volatility to its possibility distribution (from ‘volatility smile to volatility frown’) and reduce the problem to a fuzzy stochastic… (More)
We consider a (B, S)-security market with standard riskless asset B(t) = B0ert and risky asset S(t) with stochastic volatility depending on time t and the history of stock price over the interval [t − τ, t]. The stock price process S(t) satisfies a stochastic delay differential equation (SDDE) with past-dependent diffusion coefficient. We state some results… (More)
The analogue of Black–Scholes formula for vanilla call option price in conditions of (B, S)-securities market with delayed response is derived. A special case of continuous-time version of GARCH is considered. The results are compared with the results of Black and Scholes. © 2006 IMACS. Published by Elsevier B.V. All rights reserved.
Variance swaps for financial markets with underlying asset and multi-factor stochastic volatilities with delay are modelled and priced in this paper. We obtain some analytical closed forms for the expectation and variance of the realized continuously sampled variances for multi-factor stochastic volatilities with delay. As applications, we provide numerical… (More)
We study the valuation of the variance swaps under stochastic volatility with delay and jumps. In our model, the volatility of the underlying stock price process not only incorporates jumps, which are found to be active empirically, but also exhibits past dependence: the behavior of a stock price right after a given time t depends not only on the situation… (More)
We consider a semi-Markov modulated security market consisting of a riskless asset or bond with constant interest rate and risky asset or stock, whose dynamics follow gemoetric Brownian motion with volatility that depends on semi-Markov process. Two cases for semi-Markov volatilities are studied: local current and local semi-Markov volatilities. Using the… (More)
We derive results similar to Bo et al. (2010), but in the case of dynamics of the FX rate driven by a general Merton jump-diffusion process. The main results of our paper are as follows: 1) formulas for the Esscher transform parameters which ensure that the martingale condition for the discounted foreign exchange rate is a martingale for a general Merton… (More)
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… (More)