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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&P 60 Canada Index to price swap on the volatility.
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)
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 version of GARCH is considered. The results are compared with the results of Black and Scholes.
We consider a (B, S)-security market with standard riskless asset B(t) = B 0 e rt 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… (More)
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 propose a stochastic model to develop a partial integro-differential equation (PIDE) for pricing and pricing expression for fixed type single Barrier options based on the Itô-Lévy calculus with the help of Mellin transform. The stock price is driven by a class of infinite activity Lévy processes leading to the market inherently incomplete, and dynamic… (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 th to Oct.… (More)
In this paper, we show how to calculate the price of zero-coupon bonds for many Gaussian and Lévy one-factor and multi-factor models of r(t) using change of time method. models and their various combinations. We also derive partial integro-differential equations (PIDEs) for the values of swaps, caps, floors and options on them, swaptions, captions and… (More)