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We construct a stochastic volatility model considering stochastic liquidity risks when valuing variance and volatility swaps with discrete sampling. We base our model on Heston stochastic volatility, which is adopted for the modeling of stock prices when the market is perfectly liquid. Stock dynamics are further revised by discounting their prices through the employment of mean reverting market liquidity. We convert the stock dynamics under the physical measure into the one under a risk‐neutral measure via measure transform, with which the analytical valuation of variance and volatility swaps is realized. By taking the limit of sampling frequency, we further consider how both swaps with continuous sampling can be priced. Numerical implementation is finally carried out, with which the capability of the constructed model in capturing the influence of the two common types of financial risks can be clear. [ABSTRACT FROM AUTHOR]

In this paper, the pricing problem of variance and volatility swaps is discussed under a two-factor stochastic volatility model. This model can be treated as a two-factor Heston model with one factor following the CIR process and another characterized by a Markov chain, with the motivation originating from the popularity of the Heston model and the strong evidence of the existence of regime switching in real markets. Based on the derived forward characteristic function of the underlying price, analytical pricing formulae for variance and volatility swaps are presented, and numerical experiments are also conducted to compare swap prices calculated through our formulae and those obtained under the Heston model to show whether the introduction of the regime switching factor would lead to any significant difference. [ABSTRACT FROM AUTHOR]

This paper proposes a new model with a two-factor stochastic equilibrium volatility level that can be used to price variance and volatility swaps with nonlinear payoff. The adopted model uses the CIR process as the volatility process with the constant equilibrium level replaced with a stochastic one, and at the same time incorporates the regime switching mechanics in order to better describe the underlying price. To better understand how the introduced regime switching impacts both swap prices, we also conduct numerical experiments to compare our results with those obtained without regime switching. • We propose a new stochastic volatility model with two-factor equilibrium volatility level. • We introduce economic cycles by incorporating regime switching. • We analytically evaluate variance and volatility swaps. [ABSTRACT FROM AUTHOR]

We establish a new nonlinear stochastic volatility model by modeling the volatility long-run mean with a particular stochastic process, whose parameters can jump between different regimes according to a Markov chain. Introducing the regime switching factor is consistent with the empirical evidence of the economic cycle and nonlinear volatility mean-reversion observed from market data. A closed-form solution that can be used to value European options has been successfully obtained based on the characteristic function approach, followed by some numerical examples comparing the models with and without regime switching. • We propose a new nonlinear three-factor stochastic volatility model. • We capture economic cycles and nonlinear volatility mean-reversion. • We present a closed-form solution for European option pricing. [ABSTRACT FROM AUTHOR]

• European option pricing is studied under a FMLS model with stochastic volatility. • We have successfully solved a fractional partial differential equation system. • The derived pricing formula is truly explicit, involving no Fourier inversion. In this paper, we introduce the stochastic volatility into the FMLS (finite moment log-stable) model to capture the effect of both jumps and stochastic volatility. However, this additional stochastic source adds another degree of complexity in seeking for analytical formula when pricing European options, as the involved FPDE (fractional partial differential equation) system governing option prices is now of three dimensions. Albeit difficult, we have still managed to present an analytical solution expressed in terms of Fourier cosine series, after a two-step solution procedure is developed for the target FPDE system. This solution is different from the most literature as it is truly explicit, involving no Fourier inversion. It is also shown through the numerical experiments that it converges very rapidly and has potential to be applied in practice. [ABSTRACT FROM AUTHOR]