Volatility swaps and volatility options are financial products written on discretely sampled realized variance. Actively traded in over-the-counter markets, these products are often priced by continuously sampled approximations to simplify the computations. This paper presents an analytical...

In this paper, we price covariance and correlation swaps for financial markets with Markov-modulated volatilities. As an example, we consider stochastic volatility driven by a two-state continuous Markov chain. In this case, numerical examples are presented for VIX and VXN volatility indices...

In this article, we study stochastic orders over an interval. Mainly, we focus on orders related to the Laplace transform. The results are then applied to obtain a bound for heavy-tailed distributions and are illustrated by some examples. We also indicate how these ordering relationships can be...

We investigate the effect of discrete sampling and asset price jumps on fair variance and volatility swap strikes. Fair discrete volatility strikes and fair discrete variance strikes are derived in different models of the underlying evolution of the asset price: the Black-Scholes model, the...