Valuation of lookback option under uncertain volatility model

2021 ◽  
Vol 153 ◽  
pp. 111566
Author(s):  
Weiwei Wang ◽  
Dan A. Ralescu
Keyword(s):  
Lookback Option ◽  
Volatility Model ◽  
Uncertain Volatility

Double barrier American put option pricing under uncertain volatility model

2021 ◽  
pp. 2150038
Author(s):  
El Kharrazi Zaineb ◽  
Saoud Sahar ◽  
Mahani Zouhir
Keyword(s):  
Single Point ◽  
Option Prices ◽  
Double Barrier ◽  
Early Exercise ◽  
Put Option ◽  
Volatility Model ◽  
Uncertain Volatility ◽  
Exercise Boundary ◽  
Early Exercise Boundary ◽  
American Style

This paper aims to study the asymptotic behavior of double barrier American-style put option prices under an uncertain volatility model, which degenerates to a single point. We give an approximation of the double barrier American-style option prices with a small volatility interval, expressed by the Black–Scholes–Barenblatt equation. Then, we propose a novel representation for the early exercise boundary of American-style double barrier options in terms of the optimal stopping boundary of a single barrier contract.

scholarly journals Analysis of an uncertain volatility model

2006 ◽  
Vol 2006 ◽  
pp. 1-17 ◽  
Author(s):  
Marco Di Francesco ◽  
Paolo Foschi ◽  
Andrea Pascucci
Keyword(s):  
Parabolic Pdes ◽  
Kolmogorov Type ◽  
Volatility Model ◽  
Uncertain Volatility ◽  
Degenerate Parabolic

We examine, from both analytical and numerical viewpoints, the uncertain volatility model by Hobson-Rogers in the framework of degenerate parabolic PDEs of Kolmogorov type.

SIMPLIFIED HEDGE FOR PATH-DEPENDENT DERIVATIVES

2016 ◽  
Vol 19 (07) ◽  
pp. 1650045 ◽  
Author(s):  
CAROLE BERNARD ◽  
JUNSEN TANG
Keyword(s):  
Stochastic Volatility ◽  
Stochastic Volatility Model ◽  
Asian Option ◽  
Distributional Properties ◽  
Lookback Option ◽  
Volatility Model ◽  
Black Scholes ◽  
Delta Hedging ◽  
Path Dependent

Path-dependent derivatives are typically difficult to hedge. Traditional dynamic delta hedging does not perform well because of the difficulty to evaluate the Greeks and the high cost of constantly rebalancing. We propose to price and hedge path-dependent derivatives by constructing simplified alternatives that preserve certain distributional properties of their terminal payoffs, and that can be hedged by semi-static replication. The method is illustrated by a geometric Asian option and by a lookback option in the Black–Scholes setting, for which explicit forms of the simplified alternatives exist. Extensions to a Lévy market and to a Heston stochastic volatility model are discussed as well.

scholarly journals Asian Option Pricing under an Uncertain Volatility Model

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yuecai Han ◽  
Chunyang Liu
Keyword(s):  
Boundary Condition ◽  
Nonlinear Pde ◽  
Asian Option ◽  
Option Prices ◽  
Case Scenario ◽  
Worst Case ◽  
Volatility Model ◽  
Black Scholes ◽  
Uncertain Volatility ◽  
Fully Nonlinear Pde

In this paper, we study the asymptotic behavior of Asian option prices in the worst-case scenario under an uncertain volatility model. We derive a procedure to approximate Asian option prices with a small volatility interval. By imposing additional conditions on the boundary condition and splitting the obtained Black–Scholes–Barenblatt equation into two Black–Scholes-like equations, we obtain an approximation method to solve a fully nonlinear PDE.

European option pricing under multifactor uncertain volatility model

2020 ◽  
Vol 24 (12) ◽  
pp. 8781-8792 ◽  
Author(s):  
Sabahat Hassanzadeh ◽  
Farshid Mehrdoust
Keyword(s):  
Option Pricing ◽  
European Option ◽  
European Option Pricing ◽  
Volatility Model ◽  
Uncertain Volatility

scholarly journals Vulnerable options pricing under uncertain volatility model

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Qing Zhou ◽  
Xiaonan Li
Keyword(s):  
Nonlinear Partial Differential Equation ◽  
Options Pricing ◽  
Case Scenario ◽  
Worst Case ◽  
Volatility Model ◽  
Black Scholes ◽  
Uncertain Volatility ◽  
Default Risks ◽  
Vulnerable Option ◽  
Vulnerable Options

AbstractIn this paper, we consider the pricing problem of options with counterparty default risks. We study the asymptotic behavior of vulnerable option prices in the worst case scenario under an uncertain volatility model which contains both corporate assets and underlying assets. We propose a method to estimate the price of vulnerable options when the volatility of the underlying assets is within a small interval. By imposing additional conditions on the boundary condition and cutting the obtained Black–Scholes–Barenblatt equation into two Black–Scholes-like equations, we obtain an approximate method for solving the fully nonlinear partial differential equation satisfied by the price of vulnerable options under the uncertain volatility model.

The pricing of average options with jump diffusion processes in the uncertain volatility model

2017 ◽  
Vol 04 (01) ◽  
pp. 1750005
Author(s):  
Yulian Fan ◽  
Huadong Zhang
Keyword(s):  
Diffusion Processes ◽  
Jump Diffusion ◽  
Two Dimensional ◽  
Discrete Solution ◽  
One Dimensional ◽  
Numerical Tests ◽  
Jump Diffusion Processes ◽  
Convergence Results ◽  
Volatility Model ◽  
Uncertain Volatility

The pricing equations of the average options with jump diffusion processes can be formulated as two-dimensional partial integro-differential equations (PIDEs). In the uncertain volatility model, for options with non-convex and non-concave payoffs, such as the butterfly spread, the PIDEs are nonlinear. We use the semi-Lagrangian method to reduce the two-dimensional nonlinear PIDE to a one-dimensional nonlinear PIDE along the trajectory of the average price, and use a Newton-type iteration to guarantee the convergence of the discrete solution to the viscosity solution. Monotonicity and stability as well as the convergence results are derived. Numerical tests of convergence for a variety of cases, including average butterfly spread and ordinary butterfly spread, are presented.

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