# On the implied volatility of Asian options under stochastic volatility models

@inproceedings{Als2022OnTI, title={On the implied volatility of Asian options under stochastic volatility models}, author={Elisa Al{\`o}s and Eulalia Nualart and Makar Pravosud}, year={2022} }

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 process. Using techniques of the Malliavin calculus such as the anticipating Itˆo’s formula we ﬁrst compute the level of the implied volatility of the option when the maturity converges to zero. Then, we ﬁnd and short maturity asymptotic formula for the skew of…

## References

SHOWING 1-10 OF 11 REFERENCES

### Short Maturity Asian Options in Local Volatility Models

- EconomicsSIAM J. Financial Math.
- 2016

An analytical approximation for Asian options prices is presented, and good numerical agreement of the asymptotic results with the results of Monte Carlo simulations and benchmark test cases in the Black-Scholes model for option parameters relevant in practical applications is demonstrated.

### On the Curvature of the Smile in Stochastic Volatility Models

- Economics, MathematicsSIAM J. Financial Math.
- 2017

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…

### On the short-time behavior of the implied volatility for jump-diffusion models with stochastic volatility

- Mathematics, EconomicsFinance Stochastics
- 2007

Abstract
In this paper we use Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model,…

### Estimating the Hurst parameter from short term volatility swaps: a Malliavin calculus approach

- MathematicsFinance Stochastics
- 2019

A Malliavin calculus approach is used to derive an exact expression for the difference between the fair strike of a volatility swap and the at-the-money implied volatility of a European call option, and develops a model-free approximation formula for the volatility swap in terms of the ATMI and its skew.

### A note on the implied volatility of floating strike Asian options

- MathematicsDecisions in Economics and Finance
- 2019

In this paper, we study the short-time behavior of the implied volatility for short-time floating strike Asian options. Our method is based on Malliavin calculus techniques and allows us to construct…

### A generalization of the Hull and White formula with applications to option pricing approximation

- MathematicsFinance Stochastics
- 2006

The classical Hull and White formula for option pricing can be extended to the case where the volatility and the noise driving the stock prices are correlated to describe the effect of correlation on option prices and derive approximate option pricing formulas.

### Malliavin Calculus in Finance

- Mathematics
- 2003

This article is an introduction to Malliavin Calculus for practitioners. We treat one specific application to the calculation of greeks in Finance. We consider also the kernel density method to…

### A note on the implied volatility for floating strike

- Asian options, Decisions in Economics and Finance
- 2019

### On Smile Properties of Volatility Derivatives: Understanding the VIX Skew

- Computer ScienceSIAM J. Financial Math.
- 2022