Variance and Volatility Swaps Under a Two-Factor Stochastic Volatility Model With Regime Switching

Abstract

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.

Volatility Swaps Valuation Under a Modified Risk-Neutralized Heston Model With a Stochastic Long-Run Variance Level

“…By now, we have derived the closed-form pricing formula for volatility swaps under the modified Heston model. In the next section, the accuracy of our newly derived formula will be verified by comparing numerical results obtained from our formula and those through Monte Carlo simulation [17]. Also, we will show the difference caused by the introduction of the stochastic long-run variance level through the comparison of our results and those under the Heston model [29].…”

“…For the completeness of this paper, we first sketch the derivation of a general formula for the delivery price in a volatility swap contract, while the full details can be found in the existing literature [17].…”

“…A double exponential Ornstein–Uhlenbeck stochastic volatility was adopted by Kim and Kim [22]. Both variance and volatility swaps were valued under a two-factor Heston model with an additional regime switching factor [17] and a multi- factor Heston stochastic volatility model [21]. Being quite similar to these multi-factor stochastic volatility models, another trend for introducing additional stochastic factors is to make the parameters of stochastic volatility models as random variables to increase the flexibility of the model.…”