Jumping from Volatility Surface to Exotic Option Price

2021 ◽  
Author(s):  
Roman Paolucci
Keyword(s):  
Option Price ◽  
Exotic Option ◽  
Volatility Surface

scholarly journals Option Price Decomposition in Spot-Dependent Volatility Models and Some Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-16
Author(s):  
Raúl Merino ◽  
Josep Vives
Keyword(s):  
Implied Volatility ◽  
Option Price ◽  
Model Parameters ◽  
Numerical Comparison ◽  
Cev Model ◽  
Volatility Models ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Volatility Surface ◽  
Price Decomposition

We obtain a Hull and White type option price decomposition for a general local volatility model. We apply the obtained formula to CEV model. As an application we give an approximated closed formula for the call option price under a CEV model and an approximated short term implied volatility surface. These approximated formulas are used to estimate model parameters. Numerical comparison is performed for our new method with exact and approximated formulas existing in the literature.

scholarly journals Online local volatility calibration by convex regularization

2014 ◽  
Vol 8 (2) ◽  
pp. 243-268 ◽  
Author(s):  
Vinicius Albani ◽  
Jorge Zubelli
Keyword(s):  
Inverse Problem ◽  
Stock Price ◽  
Convergence Rates ◽  
Regularization Parameter ◽  
Option Price ◽  
Local Volatility ◽  
Regularity Properties ◽  
Volatility Model ◽  
Volatility Surface ◽  
Online Methods

We address the inverse problem of local volatility surface calibration from market given option prices. We integrate the ever-increasing flow of option price information into the well-accepted local volatility model of Dupire. This leads to considering both the local volatility surfaces and their corresponding prices as indexed by the observed underlying stock price as time goes by in appropriate function spaces. The resulting parameter to data map is defined in appropriate Bochner-Sobolev spaces. Under this framework, we prove key regularity properties. This enable us to build a calibration technique that combines online methods with convex Tikhonov regularization tools. Such procedure is used to solve the inverse problem of local volatility identification. As a result, we prove convergence rates with respect to noise and a corresponding discrepancy-based choice for the regularization parameter. We conclude by illustrating the theoretical results by means of numerical tests.

scholarly journals An Analytic Approach for Pricing American Options with Regime Switching

2021 ◽  
Vol 14 (5) ◽  
pp. 188
Author(s):  
Leunglung Chan ◽  
Song-Ping Zhu
Keyword(s):  
Regime Switching ◽  
American Options ◽  
Option Price ◽  
Switching Model ◽  
Homotopy Analysis ◽  
State Regime ◽  
Markov Modulated ◽  
Appreciation Rate ◽  
The Interest Rate ◽  
Hidden States

This paper investigates the American option price in a two-state regime-switching model. The dynamics of underlying are driven by a Markov-modulated Geometric Wiener process. That means the interest rate, the appreciation rate, and the volatility of underlying rely on hidden states of the economy which can be interpreted in terms of Markov chains. By means of the homotopy analysis method, an explicit formula for pricing two-state regime-switching American options is presented.

scholarly journals An Intuitive Introduction to Fractional and Rough Volatilities

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 994
Author(s):  
Elisa Alòs ◽  
Jorge A. León
Keyword(s):  
Malliavin Calculus ◽  
Numerical Experiments ◽  
Implied Volatility ◽  
Natural Approach ◽  
Volatility Models ◽  
Implied Volatility Surface ◽  
Short Memory ◽  
White Type ◽  
Volatility Surface ◽  
Theoretical Results

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 is not a semimartingale in general. So, we cannot use the classical Itô’s calculus to explain how the memory properties of fBm allow us to describe some empirical findings of the implied volatility surface through Hull and White type formulas. Thus, Malliavin calculus provides a natural approach to deal with the implied volatility without assuming any particular structure of the volatility. The aim of this paper is to provides the basic tools of Malliavin calculus for the study of fractional volatility models. That is, we explain how the long and short memory of fBm improves the description of the implied volatility. In particular, we consider in detail a model that combines the long and short memory properties of fBm as an example of the approach introduced in this paper. The theoretical results are tested with numerical experiments.

Candidate point selection using a self-attention mechanism for generating a smooth volatility surface under the SABR model

2021 ◽  
Vol 173 ◽  
pp. 114640
Author(s):  
Hyeonuk Kim ◽  
Kyunghyun Park ◽  
Junkee Jeon ◽  
Changhoon Song ◽  
Jungwoo Bae ◽  
...  
Keyword(s):  
Attention Mechanism ◽  
Point Selection ◽  
Sabr Model ◽  
Volatility Surface ◽  
Candidate Point
Sign in / Sign up

Export Citation Format

Share Document