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Frido Rolloos

Publications and source records attributed to Frido Rolloos.

6 recordsLinked to original sources
arXiv2025

Estimating the Hurst parameter from the zero vanna implied volatility and its dual

The covariance between the return of an asset and its realized volatility can be approximated as the difference between two specific implied volatilities. In this paper it is proved that in the small time-to-maturity limit the approximation error tends to zero. In addition a direct relation between the short time-to-maturity covariance and slope of the at-the-money implied volatility is established. The limit theorems are valid for stochastic volatility models with Hurst parameter $H \in(0, 1)$. An application of the results is to accurately approximate the Hurst parameter using only a discrete set of implied volatilities. Numerical examples under the rough Bergomi model are presented.

q-fin.MF↗
arXiv2022

Forward start volatility swaps in rough volatility models

This paper shows the relationship between the forward start volatility swap price and the forward start zero vanna implied volatility of forward start options in rough volatility models. It is shown that in the short time-to-maturity limit the approximation error in the leading term of the correlated case with $H\in(0,\frac12)$ does not depend on the time to forward start date, but only on the difference between the maturity date and forward start date and on the Hurst parameter $H$.

q-fin.MF↗
arXiv2022

Hull and White and Al\`os type formulas for barrier options in stochastic volatility models with nonzero correlation

Two novel closed-form formulas for the price of barrier options in stochastic volatility models with zero interest rate and dividend yield but nonzero correlation between the asset and its instantaneous volatility are derived. The first is a Hull and White type formula, and the second is a decomposition formula similar in form to the Al\`os decomposition for vanilla options. A model-free approximation is also given.

q-fin.PR↗
arXiv2020

Nonparametric Pricing and Hedging of Volatility Swaps in Stochastic Volatility Models

In this paper the zero vanna implied volatility approximation for the price of freshly minted volatility swaps is generalised to seasoned volatility swaps. We also derive how volatility swaps can be hedged using a strip of vanilla options with weights that are directly related to trading intuition. Additionally, we derive first and second order hedges for volatility swaps using only variance swaps. As dynamically trading variance swaps is in general cheaper and operationally less cumbersome compared to dynamically rebalancing a continuous strip of options, our result makes the hedging of volatility swaps both practically feasible and robust. Within the class of stochastic volatility models our pricing and hedging results are model-independent and can be implemented at almost no computational cost.

q-fin.PR↗
arXiv2019

On the difference between the volatility swap strike and the zero vanna implied volatility

In this paper, Malliavin calculus is applied to arrive at exact formulas for the difference between the volatility swap strike and the zero vanna implied volatility for volatilities driven by fractional noise. To the best of our knowledge, our estimate is the first to derive the rigorous relationship between the zero vanna implied volatility and the volatility swap strike. In particular, we will see that the zero vanna implied volatility is a better approximation for the volatility swap strike than the ATMI.

q-fin.MF↗