Pricing variance and volatility swaps in a stochastic volatility model with regime switching: discrete observations case

This study presents a set of closed-form exact solutions for pricing discretely sampled variance swaps and volatility swaps, based on the Heston stochastic volatility model with regime switching. In comparison with all the previous studies in the literature, this research, which obtains closed-form exact solutions for variance and volatility swaps with discrete sampling times, serves several purposes. (1) It verifies the degree of validity of Elliott et al.'s [Appl. Math. Finance, 2007, 14(1), 41–62] continuous-sampling-time approximation for variance and volatility swaps of relatively short sampling periods. (2) It examines the effect of ignoring regime switching on pricing variance and volatility swaps. (3) It contributes to bridging the gap between Zhu and Lian's [Math. Finance, 2011, 21(2), 233–256] approach and Elliott et al.'s framework. (4) Finally, it presents a semi-Monte-Carlo simulation for the pricing of other important realized variance based derivatives.     

Jump-diffusion volatility models for variance swaps: An empirical performance analysis

This paper studies a class of tractable jump-diffusion models, including stochastic volatility models with various specifications of jump intensity for stock returns and variance processes. We employ the Markov chain Monte Carlo (MCMC) method to implement model estimation, and investigate the performance of all models in capturing the term structure of variance swap rates and fitting the dynamics of stock returns. It is evident that the stochastic volatility models, equipped with self-exciting jumps in the spot variance and linearly-dependent jumps in the central-tendency variance, can produce consistent model estimates, aptly explain the stylized facts in variance swaps, and boost pricing performance. Moreover, our empirical results show that large self-exciting jumps in the spot variance, as an independent risk source, facilitate term structure modeling for variance swaps, whilst the central-tendency variance may jump with small sizes, but signaling substantial regime changes in the long run. Both types of jumps occur infrequently, and are more related to market turmoils over the period from 2008 to 2021.     

Pricing options on illiquid assets with liquid proxies using utility indifference and dynamic-static hedging

This work addresses the problem of optimal pricing and hedging of a European option on an illiquid asset Z using two proxies: a liquid asset S and a liquid European option on another liquid asset Y. We assume that the S-hedge is dynamic while the Y-hedge is static. Using the indifference pricing approach, we derive a Hamilton–Jacobi–Bellman equation for the value function. We solve this equation analytically (in quadrature) using an asymptotic expansion around the limit of perfect correlation between assets Y and Z. While in this paper we apply our framework to an incomplete market version of Merton’s credit-equity model, the same approach can be used for other asset classes (equity, commodity, FX, etc.), e.g. for pricing and hedging options with illiquid strikes or illiquid exotic options.