scholarly journals Semi-static variance-optimal hedging in stochastic volatility models with Fourier representation

2019 ◽  
Vol 56 (3) ◽  
pp. 787-809 ◽  
Author(s):  
Paolo Di Tella ◽  
Martin Haubold ◽  
Martin Keller-Ressel
Keyword(s):  
Factor Model ◽  
Heston Model ◽  
Market Model ◽  
Stochastic Volatility Models ◽  
Hedging Strategy ◽  
Static Hedging ◽  
Hedging Strategies ◽  
Optimal Hedging ◽  
Volatility Models ◽  
Set Up

AbstractWe introduce variance-optimal semi-static hedging strategies for a given contingent claim. To obtain a tractable formula for the expected squared hedging error and the optimal hedging strategy we use a Fourier approach in a multidimensional factor model. We apply the theory to set up a variance-optimal semi-static hedging strategy for a variance swap in the Heston model, which is affine, in the 3/2 model, which is not, and in a market model including jumps.

VAR-BASED OPTIMAL PARTIAL HEDGING

2013 ◽  
Vol 43 (3) ◽  
pp. 271-299 ◽  
Author(s):  
Jianfa Cong ◽  
Ken Seng Tan ◽  
Chengguo Weng
Keyword(s):  
Financial Market ◽  
Value At Risk ◽  
Risk Measure ◽  
Market Model ◽  
Risk Exposure ◽  
Hedging Strategy ◽  
Quantile Hedging ◽  
Hedging Strategies ◽  
Optimal Hedging ◽  
Partial Hedging

AbstractHedging is one of the most important topics in finance. When a financial market is complete, every contingent claim can be hedged perfectly to eliminate any potential future obligations. When the financial market is incomplete, the investor may eliminate his risk exposure by superhedging. In practice, both hedging strategies are not satisfactory due to their high implementation costs, which erode the chance of making any profit. A more practical and desirable strategy is to resort to the partial hedging, which hedges the future obligation only partially. The quantile hedging of Föllmer and Leukert (Finance and Stochastics, vol. 3, 1999, pp. 251–273), which maximizes the probability of a successful hedge for a given budget constraint, is an example of the partial hedging. Inspired by the principle underlying the partial hedging, this paper proposes a general partial hedging model by minimizing any desirable risk measure of the total risk exposure of an investor. By confining to the value-at-risk (VaR) measure, analytic optimal partial hedging strategies are derived. The optimal partial hedging strategy is either a knock-out call strategy or a bull call spread strategy, depending on the admissible classes of hedging strategies. Our proposed VaR-based partial hedging model has the advantage of its simplicity and robustness. The optimal hedging strategy is easy to determine. Furthermore, the structure of the optimal hedging strategy is independent of the assumed market model. This is in contrast to the quantile hedging, which is sensitive to the assumed model as well as the parameter values. Extensive numerical examples are provided to compare and contrast our proposed partial hedging to the quantile hedging.

scholarly journals INTEGRAL REPRESENTATION OF PROBABILITY DENSITY OF STOCHASTIC VOLATILITY MODELS AND TIMER OPTIONS

2017 ◽  
Vol 20 (08) ◽  
pp. 1750055 ◽  
Author(s):  
ZHENYU CUI ◽  
J. LARS KIRKBY ◽  
GUANGHUA LIAN ◽  
DUY NGUYEN
Keyword(s):  
Stochastic Volatility ◽  
Probabilistic Method ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Model Parameters ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Volatility Model ◽  
Probability Densities ◽  
Special Case

This paper contributes a generic probabilistic method to derive explicit exact probability densities for stochastic volatility models. Our method is based on a novel application of the exponential measure change in [Z. Palmowski & T. Rolski (2002) A technique for exponential change of measure for Markov processes, Bernoulli 8(6), 767–785]. With this generic approach, we first derive explicit probability densities in terms of model parameters for several stochastic volatility models with nonzero correlations, namely the Heston 1993, [Formula: see text], and a special case of the [Formula: see text]-Hypergeometric stochastic volatility models recently proposed by [J. Da Fonseca & C. Martini (2016) The [Formula: see text]-Hypergeometric stochastic volatility model, Stochastic Processes and their Applications 126(5), 1472–1502]. Then, we combine our method with a stochastic time change technique to develop explicit formulae for prices of timer options in the Heston model, the [Formula: see text] model and a special case of the [Formula: see text]-Hypergeometric model.

COMPUTATION OF VOLATILITY IN STOCHASTIC VOLATILITY MODELS WITH HIGH FREQUENCY DATA

2010 ◽  
Vol 13 (05) ◽  
pp. 767-787 ◽  
Author(s):  
EMILIO BARUCCI ◽  
MARIA ELVIRA MANCINO
Keyword(s):  
Stochastic Volatility ◽  
High Frequency ◽  
Asset Price ◽  
Heston Model ◽  
High Frequency Data ◽  
Monte Carlo Experiment ◽  
Price Model ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Correlation Parameters

We consider general stochastic volatility models driven by continuous Brownian semimartingales, we show that the volatility of the variance and the leverage component (covariance between the asset price and the variance) can be reconstructed pathwise by exploiting Fourier analysis from the observation of the asset price. Specifying parametrically the asset price model we show that the method allows us to compute the parameters of the model. We provide a Monte Carlo experiment to recover the volatility and correlation parameters of the Heston model.

A comparison of option pricing models

2017 ◽  
Vol 04 (02n03) ◽  
pp. 1750024
Author(s):  
Elham Dastranj ◽  
Roghaye Latifi
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Heston Model ◽  
Pricing Models ◽  
Stochastic Volatility Models ◽  
Numerical Examples ◽  
Call Options ◽  
Volatility Models ◽  
Premium Income

Option pricing under two stochastic volatility models, double Heston model and double Heston with three jumps, is done. Firstly, the efficiency of the second model is shown via FFT method, and numerical examples using power call options. Then it is shown that power option yields more premium income under the second model, double Heston with three jumps, than another one.

Long-Time Trajectorial Large Deviations and Importance Sampling for Affine Stochastic Volatility Models

2021 ◽  
Vol 53 (1) ◽  
pp. 220-250
Author(s):  
Zorana Grbac ◽  
David Krief ◽  
Peter Tankov
Keyword(s):  
Monte Carlo ◽  
Stochastic Volatility ◽  
Variance Reduction ◽  
Large Deviation ◽  
Heston Model ◽  
Stochastic Volatility Models ◽  
Monte Carlo Computation ◽  
Volatility Models ◽  
Long Time ◽  
Path Dependent

AbstractWe establish a pathwise large deviation principle for affine stochastic volatility models introduced by Keller-Ressel (2011), and present an application to variance reduction for Monte Carlo computation of prices of path-dependent options in these models, extending the method developed by Genin and Tankov (2020) for exponential Lévy models. To this end, we apply an exponentially affine change of measure and use Varadhan’s lemma, in the fashion of Guasoni and Robertson (2008) and Robertson (2010), to approximate the problem of finding the measure that minimizes the variance of the Monte Carlo estimator. We test the method on the Heston model with and without jumps to demonstrate its numerical efficiency.

scholarly journals Variance-Optimal Hedging in General Affine Stochastic Volatility Models

2010 ◽  
Vol 42 (1) ◽  
pp. 83-105 ◽  
Author(s):  
Jan Kallsen ◽  
Arnd Pauwels
Keyword(s):  
Stochastic Volatility ◽  
Continuous Time ◽  
Stock Price ◽  
Forthcoming Paper ◽  
Parametric Models ◽  
Stochastic Volatility Models ◽  
Optimal Hedging ◽  
Volatility Models ◽  
Optimal Hedge ◽  
General Affine

We consider variance-optimal hedging in general continuous-time affine stochastic volatility models. The optimal hedge and the associated hedging error are determined semiexplicitly in the case that the stock price follows a martingale. The integral representation of the solution opens the door to efficient numerical computation. The setup includes models with jumps in the stock price and in the activity process. It also allows for correlation between volatility and stock price movements. Concrete parametric models will be illustrated in a forthcoming paper.

scholarly journals Variance-Optimal Hedging in General Affine Stochastic Volatility Models

2010 ◽  
Vol 42 (01) ◽  
pp. 83-105 ◽  
Author(s):  
Jan Kallsen ◽  
Arnd Pauwels
Keyword(s):  
Stochastic Volatility ◽  
Continuous Time ◽  
Stock Price ◽  
Forthcoming Paper ◽  
Parametric Models ◽  
Stochastic Volatility Models ◽  
Optimal Hedging ◽  
Volatility Models ◽  
Optimal Hedge ◽  
General Affine

We consider variance-optimal hedging in general continuous-time affine stochastic volatility models. The optimal hedge and the associated hedging error are determined semiexplicitly in the case that the stock price follows a martingale. The integral representation of the solution opens the door to efficient numerical computation. The setup includes models with jumps in the stock price and in the activity process. It also allows for correlation between volatility and stock price movements. Concrete parametric models will be illustrated in a forthcoming paper.

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