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.

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.

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 Pricing Various Types of Power Options under Stochastic Volatility

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1911
Author(s):  
Youngrok Lee ◽  
Yehun Kim ◽  
Jaesung Lee
Keyword(s):  
Financial Markets ◽  
Stochastic Volatility ◽  
Asset Price ◽  
Stochastic Volatility Model ◽  
Exotic Options ◽  
Option Prices ◽  
Black Scholes Model ◽  
Volatility Model ◽  
Black Scholes ◽  
Pricing Power

The exotic options with curved nonlinear payoffs have been traded in financial markets, which offer great flexibility to participants in the market. Among them, power options with the payoff depending on a certain power of the underlying asset price are widely used in markets in order to provide high leverage strategy. In pricing power options, the classical Black–Scholes model which assumes a constant volatility is simple and easy to handle, but it has a limit in reflecting movements of real financial markets. As the alternatives of constant volatility, we focus on the stochastic volatility, finding more exact prices for power options. In this paper, we use the stochastic volatility model introduced by Schöbel and Zhu to drive the closed-form expressions for the prices of various power options including soft strike options. We also show the sensitivity of power option prices under changes in the values of each parameter by calculating the resulting values obtained from the formulas.

FROM THE IMPLIED VOLATILITY SKEW TO A ROBUST CORRECTION TO BLACK-SCHOLES AMERICAN OPTION PRICES

2001 ◽  
Vol 04 (04) ◽  
pp. 651-675 ◽  
Author(s):  
JEAN-PIERRE FOUQUE ◽  
GEORGE PAPANICOLAOU ◽  
K. RONNIE SIRCAR
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Stochastic Volatility ◽  
Free Boundary Problem ◽  
Implied Volatility ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
One Dimensional ◽  
Volatility Model ◽  
Black Scholes

We describe a robust correction to Black-Scholes American derivatives prices that accounts for uncertain and changing market volatility. It exploits the tendency of volatility to cluster, or fast mean-reversion, and is simply calibrated from the observed implied volatility skew. The two-dimensional free-boundary problem for the derivative pricing function under a stochastic volatility model is reduced to a one-dimensional free-boundary problem (the Black-Scholes price) plus the solution of a fixed boundary-value problem. The formal asymptotic calculation that achieves this is presented here. We discuss numerical implementation and analyze the effect of the volatility skew.

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.

Uncertain Parameters, an Empirical Stochastic Volatility Model and Confidence Limits

1998 ◽  
Vol 01 (01) ◽  
pp. 175-189 ◽  
Author(s):  
Paul Wilmott ◽  
Asli Oztukel
Keyword(s):  
Stochastic Volatility ◽  
Time Series Data ◽  
Stochastic Volatility Model ◽  
Uncertain Parameter ◽  
Series Data ◽  
Confidence Limits ◽  
Case Scenario ◽  
Worst Case ◽  
Long Run ◽  
Volatility Model

In this paper we build upon the recently developed uncertain parameter framework for valuing derivatives in a worst-case scenario. We start by deriving a stochastic volatility model based on a simple analysis of time-series data. We use this stochastic model to examine the time evolution of volatility from an initial known value to a steady-state distribution in the long run. This empirical model is then incorporated into the uncertain parameter option valuation framework to provide "confidence limits" for the option value.

THE BLACK SCHOLES BARENBLATT EQUATION FOR OPTIONS WITH UNCERTAIN VOLATILITY AND ITS APPLICATION TO STATIC HEDGING

2006 ◽  
Vol 09 (05) ◽  
pp. 673-703 ◽  
Author(s):  
GUNTER H. MEYER
Keyword(s):  
Maximum Principle ◽  
Interest Rate ◽  
Source Term ◽  
Diffusion Equations ◽  
Option Prices ◽  
Nonlinear Source ◽  
The Maximum Principle ◽  
Static Hedging ◽  
Black Scholes ◽  
Uncertain Volatility

The Black Scholes Barenblatt (BSB) equation for the envelope of option prices with uncertain volatility and interest rate is derived from the Black Scholes equation with the maximum principle for diffusion equations and shown to be equivalent to a readily solvable standard Black Scholes equation with a nonlinear source term. Analogous arguments yield the envelope for the delta of option prices. We then interpret the concept of static hedging for narrowing the envelope in terms of partial differential equations and define the optimal static hedge and computable approximations to it. We apply the BSB equation to find numerically some optimally hedged portfolios of representative European and American options.

Reducing Probabilistic Weather Forecasts to the Worst Case Scenario: Anchoring Effects

2008 ◽  
Author(s):  
Sonia Savelli ◽  
Susan Joslyn ◽  
Limor Nadav-Greenberg ◽  
Queena Chen
Keyword(s):  
Case Scenario ◽  
Worst Case ◽  
Weather Forecasts ◽  
Worst Case Scenario ◽  
Anchoring Effects

EXPEDITION TO MALI, 2020

2020 ◽  
pp. 12-28
Author(s):  
D. V. Vaniukova ◽  
◽  
P. A. Kutsenkov ◽  
Keyword(s):  
Mass Murder ◽  
The State ◽  
Case Scenario ◽  
Worst Case ◽  
Traditional Art ◽  
Peter The Great ◽  
State Museum ◽  
Bobo Dioulasso ◽  
Oriental Studies ◽  
The Village

The research expedition of the Institute of Oriental studies of the Russian Academy of Sciences has been working in Mali since 2015. Since 2017, it has been attended by employees of the State Museum of the East. The task of the expedition is to study the transformation of traditional Dogon culture in the context of globalization, as well as to collect ethnographic information (life, customs, features of the traditional social and political structure); to collect oral historical legends; to study the history, existence, and transformation of artistic tradition in the villages of the Dogon Country in modern conditions; collecting items of Ethnography and art to add to the collection of the African collection of the. Peter the Great Museum (Kunstkamera, Saint Petersburg) and the State Museum of Oriental Arts (Moscow). The plan of the expedition in January 2020 included additional items, namely, the study of the functioning of the antique market in Mali (the “path” of things from villages to cities, which is important for attributing works of traditional art). The geography of our research was significantly expanded to the regions of Sikasso and Koulikoro in Mali, as well as to the city of Bobo-Dioulasso and its surroundings in Burkina Faso, which is related to the study of migrations to the Bandiagara Highlands. In addition, the plan of the expedition included organization of a photo exhibition in the Museum of the village of Endé and some educational projects. Unfortunately, after the mass murder in March 2019 in the village of Ogossogou-Pel, where more than one hundred and seventy people were killed, events in the Dogon Country began to develop in the worst-case scenario: The incessant provocations after that revived the old feud between the Pel (Fulbe) pastoralists and the Dogon farmers. So far, this hostility and mutual distrust has not yet developed into a full-scale ethnic conflict, but, unfortunately, such a development now seems quite likely.

Risk-Based Robust Bidding Strategies for EVs’ Aggregators in Day-ahead Markets with Uncertainty

2020 ◽  
Author(s):  
Ahmed Abdelmoaty ◽  
Wessam Mesbah ◽  
Mohammad A. M. Abdel-Aal ◽  
Ali T. Alawami
Keyword(s):  
Robust Optimization ◽  
Electricity Market ◽  
Real Life ◽  
Optimization Approach ◽  
Case Scenario ◽  
Worst Case ◽  
Bidding Strategies ◽  
Wind Generators ◽  
Proposed Model ◽  
Optimal Bidding

In the recent electricity market framework, the profit of the generation companies depends on the decision of the operator on the schedule of its units, the energy price, and the optimal bidding strategies. Due to the expanded integration of uncertain renewable generators which is highly intermittent such as wind plants, the coordination with other facilities to mitigate the risks of imbalances is mandatory. Accordingly, coordination of wind generators with the evolutionary Electric Vehicles (EVs) is expected to boost the performance of the grid. In this paper, we propose a robust optimization approach for the coordination between the wind-thermal generators and the EVs in a virtual<br>power plant (VPP) environment. The objective of maximizing the profit of the VPP Operator (VPPO) is studied. The optimal bidding strategy of the VPPO in the day-ahead market under uncertainties of wind power, energy<br>prices, imbalance prices, and demand is obtained for the worst case scenario. A case study is conducted to assess the e?effectiveness of the proposed model in terms of the VPPO's profit. A comparison between the proposed model and the scenario-based optimization was introduced. Our results confirmed that, although the conservative behavior of the worst-case robust optimization model, it helps the decision maker from the fluctuations of the uncertain parameters involved in the production and bidding processes. In addition, robust optimization is a more tractable problem and does not suffer from<br>the high computation burden associated with scenario-based stochastic programming. This makes it more practical for real-life scenarios.<br>

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