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View article: Forward Start Volatility Swaps in Rough Volatility Models
Forward Start Volatility Swaps in Rough Volatility Models Open
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…
View article: On the implied volatility of Inverse options under stochastic volatility models
On the implied volatility of Inverse options under stochastic volatility models Open
In this paper, we study the short-time behavior of at-the-money implied volatility for inverse European options with a fixed strike price. The asset price is assumed to follow a general stochastic volatility process. Using techniques from …
View article: Short-time behavior of the At-The-Money implied volatility for the jump-diffusion stochastic volatility Bachelier model
Short-time behavior of the At-The-Money implied volatility for the jump-diffusion stochastic volatility Bachelier model Open
In this paper we use Malliavin Calculus techniques in order to obtain expressions for the short-time behavior of the at-the-money implied volatility (ATM-IV) level and skew for a jump-diffusion stock price. The diffusion part is assumed to…
View article: On the Curvature of the Bachelier Implied Volatility
On the Curvature of the Bachelier Implied Volatility Open
Our aim in this paper is to analytically compute the at-the-money second derivative of the Bachelier implied volatility curve as a function of the strike price for correlated stochastic volatility models. We also obtain an expression for t…
View article: On the Optimal Choice of Strike Conventions in Exchange Option Pricing
On the Optimal Choice of Strike Conventions in Exchange Option Pricing Open
An important but rarely-addressed option pricing question is how to choose appropriate strikes for implied volatility inputs when pricing more exotic multi-asset derivatives. By means of Malliavin calculus, we construct an asymptotically o…
View article: On the implied volatility of Inverse options under stochastic volatility models
On the implied volatility of Inverse options under stochastic volatility models Open
In this paper we study short-time behavior of the at-the-money implied volatility for Inverse European options with fixed strike price. The asset price is assumed to follow a general stochastic volatility process. Using techniques of the M…
View article: On the implied volatility of European and Asian call options under the stochastic volatility Bachelier model
On the implied volatility of European and Asian call options under the stochastic volatility Bachelier model Open
In this paper we study the short-time behavior of the at-the-money implied volatility for European and arithmetic Asian call options with fixed strike price. The asset price is assumed to follow the Bachelier model with a general stochasti…
View article: A Lower Bound for the Volatility Swap in the Lognormal SABR Model
A Lower Bound for the Volatility Swap in the Lognormal SABR Model Open
In the short time to maturity limit, it is proved that for the conditionally lognormal SABR model the zero vanna implied volatility is a lower bound for the volatility swap strike. The result is valid for all values of the correlation para…
View article: A lower bound for the volatility swap in the lognormal SABR model
A lower bound for the volatility swap in the lognormal SABR model Open
In the short time to maturity limit it is proved that for the conditionally lognormal SABR model the zero vanna implied volatility is a lower bound for the volatility swap strike. The result is valid for all values of the correlation param…
View article: On the implied volatility of Asian options under stochastic volatility models
On the implied volatility of Asian options under stochastic volatility models Open
In this paper we study the short-time behavior of the at-the-money implied volatility for arithmetic Asian options with fixed strike price. The asset price is assumed to follow the Black-Scholes model with a general stochastic volatility p…
View article: Forward start volatility swaps in rough volatility models
Forward start volatility swaps in rough volatility models Open
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…
View article: On the skew and curvature of implied and local volatilities
On the skew and curvature of implied and local volatilities Open
In this paper, we study the relationship between the short-end of the local and the implied volatility surfaces. Our results, based on Malliavin calculus techniques, recover the recent $\frac{1}{H+3/2}$ rule (where $H$ denotes the Hurst pa…
View article: CVA in fractional and rough volatility models
CVA in fractional and rough volatility models Open
In this work we present a general representation formula for the price of a vulnerable European option, and the related CVA in stochastic (either rough or not) volatility models for the underlying's price, when admitting correlation with t…
View article: Editorial: Long-Memory Models in Mathematical Finance
Editorial: Long-Memory Models in Mathematical Finance Open
EDITORIAL article Front. Appl. Math. Stat., 31 May 2021Sec. Mathematical Finance https://doi.org/10.3389/fams.2021.705429
View article: An Intuitive Introduction to Fractional and Rough Volatilities
An Intuitive Introduction to Fractional and Rough Volatilities Open
Here, we review some results of fractional volatility models, where the volatility is driven by fractional Brownian motion (fBm). In these models, the future average volatility is not a process adapted to the underlying filtration, and fBm…
View article: On the Difference Between the Volatility Swap Strike and the Zero Vanna Implied Volatility
On the Difference Between the Volatility Swap Strike and the Zero Vanna Implied Volatility Open
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,…
View article: A fractional model for the COVID-19 pandemic: Application to Italian data
A fractional model for the COVID-19 pandemic: Application to Italian data Open
We provide a probabilistic SIRD model for the COVID-19 pandemic in Italy, where we allow the infection, recovery and death rates to be random. In particular, the underlying random factor is driven by a fractional Brownian motion. Our model…
View article: The asymptotic expansion of the regular discretization error of Itô integrals
The asymptotic expansion of the regular discretization error of Itô integrals Open
We study an Edgeworth‐type refinement of the central limit theorem for the discretization error of Itô integrals. Toward this end, we introduce a new approach, based on the anticipating Itô formula. This alternative technique allows us to …
View article: A fractional model for the COVID-19 pandemic: Application to Italian\n data
A fractional model for the COVID-19 pandemic: Application to Italian\n data Open
We provide a probabilistic SIRD model for the COVID-19 pandemic in Italy,\nwhere we allow the infection, recovery and death rates to be random. In\nparticular, the underlying random factor is driven by a fractional Brownian\nmotion. Our mo…
View article: On smile properties of volatility derivatives and exotic products:\n understanding the VIX skew
On smile properties of volatility derivatives and exotic products:\n understanding the VIX skew Open
We develop a method to study the implied volatility for exotic options and\nvolatility derivatives with European payoffs such as VIX options. Our approach,\nbased on Malliavin calculus techniques, allows us to describe the properties of\nt…
View article: On smile properties of volatility derivatives and exotic products: understanding the VIX skew
On smile properties of volatility derivatives and exotic products: understanding the VIX skew Open
We develop a method to study the implied volatility for exotic options and volatility derivatives with European payoffs such as VIX options. Our approach, based on Malliavin calculus techniques, allows us to describe the properties of the …
View article: The asymptotic expansion of the regular discretization error of It\^o integrals
The asymptotic expansion of the regular discretization error of It\^o integrals Open
We study a Edgeworth-type refinement of the central limit theorem for the discretizacion error of It\^o integrals. Towards this end, we introduce a new approach, based on the anticipating It\^o formula. This alternative technique allows us…
View article: Target volatility option pricing in lognormal fractional SABR model
Target volatility option pricing in lognormal fractional SABR model Open
We examine in this article the pricing of target volatility options in the lognormal fractional SABR model. A decomposition formula by Ito's calculus yields a theoretical replicating strategy for the target volatility option, assuming the …
View article: On the Curvature of the Smile in Stochastic Volatility Models
On the Curvature of the Smile in Stochastic Volatility Models Open
In this paper we compute analytically the at-the-money second derivative of the implied volatility curve as a function of the strike price, for correlated stochastic volatility models. We also obtain an expression for the short-time limit …
View article: Pricing and hedging Margrabe options with stochastic volatilities
Pricing and hedging Margrabe options with stochastic volatilities Open
A Margrabe or exchange option is an option to exchange one asset for another. In a general stochastic volatility framework, by taking the second asset as a numeraire,we derive pricing as well as approximate pricing formulae for Margrabe op…