scholarly journals Pricing Arithmetic Asian Options under Hybrid Stochastic and Local Volatility

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Min-Ku Lee ◽  
Jeong-Hoon Kim ◽  
Kyu-Hwan Jang
Keyword(s):  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Asian Options ◽  
Partial Differential ◽  
Constant Elasticity ◽  
Local Volatility ◽  
Constant Elasticity Of Variance ◽  
Arithmetic Average ◽  
Volatility Model

Recently, hybrid stochastic and local volatility models have become an industry standard for the pricing of derivatives and other problems in finance. In this study, we use a multiscale stochastic volatility model incorporated by the constant elasticity of variance to understand the price structure of continuous arithmetic average Asian options. The multiscale partial differential equation for the option price is approximated by a couple of single scale partial differential equations. In terms of the elasticity parameter governing the leverage effect, a correction to the stochastic volatility model is made for more efficient pricing and hedging of Asian options.

On the Performance of the Comonotonicity Approach for Pricing Asian Options in Some Benchmark Models from Equities and Commodities

2017 ◽  
Vol 20 (01) ◽  
pp. 1750005
Author(s):  
Jilong Chen ◽  
Christian Ewald
Keyword(s):  
Upper Bounds ◽  
Stochastic Volatility Model ◽  
Asian Options ◽  
Convenience Yield ◽  
Yield Model ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Hedging Strategies ◽  
Volatility Model

In this paper, we investigate the applicability of the comonotonicity approach in the context of various benchmark models for equities and commodities. Instead of classical Lévy models as in Albrecher et al. we focus on the Heston stochastic volatility model, the constant elasticity of variance (CEV) model and Schwartz’ 1997 stochastic convenience yield model. We show how the technical difficulties of inverting the distribution function of the sum of the comonotonic random vector can be overcome and that the method delivers rather tight upper bounds for the prices of Asian Options in these models, at least for strikes which are not too large. As a by-product the method delivers super-hedging strategies which can be easily implemented.

scholarly journals Turbo Warrants under Hybrid Stochastic and Local Volatility

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Min-Ku Lee ◽  
Ji-Hun Yoon ◽  
Jeong-Hoon Kim ◽  
Sun-Hwa Cho
Keyword(s):  
Stochastic Volatility ◽  
Uhlenbeck Process ◽  
Variance Model ◽  
Constant Elasticity ◽  
Local Volatility ◽  
Constant Elasticity Of Variance ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Ornstein Uhlenbeck Process ◽  
Sensitive Structure

This paper considers the pricing of turbo warrants under a hybrid stochastic and local volatility model. The model consists of the constant elasticity of variance model incorporated by a fast fluctuating Ornstein-Uhlenbeck process for stochastic volatility. The sensitive structure of the turbo warrant price is revealed by asymptotic analysis and numerical computation based on the observation that the elasticity of variance controls leverage effects and plays an important role in characterizing various phases of volatile markets.

Option pricing under the fractional stochastic volatility model

2021 ◽  
Vol 63 ◽  
pp. 123-142
Author(s):  
Yuecai Han ◽  
Zheng Li ◽  
Chunyang Liu
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
European Call Option ◽  
Volatility Model ◽  
The Impact

We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented. doi:10.1017/S1446181121000225

A STOCHASTIC VOLATILITY MODEL FOR RISK-REVERSALS IN FOREIGN EXCHANGE

2009 ◽  
Vol 12 (06) ◽  
pp. 877-899 ◽  
Author(s):  
CLAUDIO ALBANESE ◽  
ALEKSANDAR MIJATOVIĆ
Keyword(s):  
Stochastic Volatility ◽  
Foreign Exchange ◽  
Continuous Time ◽  
Efficient Algorithms ◽  
Stochastic Volatility Model ◽  
Foreign Exchange Markets ◽  
Local Volatility ◽  
Volatility Model ◽  
Exchange Markets

It is a widely recognized fact that risk-reversals play a central role in the pricing of derivatives in foreign exchange markets. It is also known that the values of risk-reversals vary stochastically with time. In this paper we introduce a stochastic volatility model with jumps and local volatility, defined on a continuous time lattice, which provides a way of modeling this kind of risk using numerically stable and relatively efficient algorithms.

OPTION PRICING UNDER THE FRACTIONAL STOCHASTIC VOLATILITY MODEL

2021 ◽  
pp. 1-20
Author(s):  
Y. HAN ◽  
Z. LI ◽  
C. LIU
Keyword(s):  
Brownian Motion ◽  
Option Pricing ◽  
Fractional Brownian Motion ◽  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Option Prices ◽  
European Call Option ◽  
Volatility Model ◽  
The Impact

Abstract We investigate the European call option pricing problem under the fractional stochastic volatility model. The stochastic volatility model is driven by both fractional Brownian motion and standard Brownian motion. We obtain an analytical solution of the European option price via the Itô’s formula for fractional Brownian motion, Malliavin calculus, derivative replication and the fundamental solution method. Some numerical simulations are given to illustrate the impact of parameters on option prices, and the results of comparison with other models are presented.

scholarly journals Local volatility in the Heston model: a Malliavin calculus approach

2005 ◽  
Vol 2005 (3) ◽  
pp. 307-322 ◽  
Author(s):  
Christian-Oliver Ewald
Keyword(s):  
Stochastic Volatility ◽  
Malliavin Calculus ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Explicit Formulas ◽  
Local Volatility ◽  
Girsanov Transformation ◽  
Volatility Model ◽  
Log Price ◽  
Derivatives Of

We implement the Heston stochastic volatility model by using multidimensional Ornstein-Uhlenbeck processes and a special Girsanov transformation, and consider the Malliavin calculus of this model. We derive explicit formulas for the Malliavin derivatives of the Heston volatility and the log-price, and give a formula for the local volatility which is approachable by Monte-Carlo methods.

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