scholarly journals Approximating Explicitly the Mean-Reverting CEV Process

2015 ◽  
Vol 2015 ◽  
pp. 1-20 ◽  
Author(s):  
N. Halidias ◽  
I. S. Stamatiou
Keyword(s):  
Stochastic Volatility ◽  
Diffusion Coefficients ◽  
Numerical Experiments ◽  
Stochastic Volatility Model ◽  
Financial Mathematics ◽  
Two Dimensional ◽  
Nonnegative Solutions ◽  
Volatility Model ◽  
Cev Process ◽  
The Mean

We are interested in the numerical solution of mean-reverting CEV processes that appear in financial mathematics models and are described as nonnegative solutions of certain stochastic differential equations with sublinear diffusion coefficients of the form(xt)q,where1/2<q<1. Our goal is to construct explicit numerical schemes that preserve positivity. We prove convergence of the proposed SD scheme with rate depending on the parameterq. Furthermore, we verify our findings through numerical experiments and compare with other positivity preserving schemes. Finally, we show how to treat the two-dimensional stochastic volatility model with instantaneous variance process given by the above mean-reverting CEV process.

scholarly journals VARIANCE AND VOLATILITY SWAPS UNDER A TWO-FACTOR STOCHASTIC VOLATILITY MODEL WITH REGIME SWITCHING

2019 ◽  
Vol 22 (04) ◽  
pp. 1950009
Author(s):  
XIN-JIANG HE ◽  
SONG-PING ZHU
Keyword(s):  
Markov Chain ◽  
Characteristic Function ◽  
Stochastic Volatility ◽  
Regime Switching ◽  
Numerical Experiments ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Volatility Model ◽  
Significant Difference ◽  
Cir Process

In this paper, the pricing problem of variance and volatility swaps is discussed under a two-factor stochastic volatility model. This model can be treated as a two-factor Heston model with one factor following the CIR process and another characterized by a Markov chain, with the motivation originating from the popularity of the Heston model and the strong evidence of the existence of regime switching in real markets. Based on the derived forward characteristic function of the underlying price, analytical pricing formulae for variance and volatility swaps are presented, and numerical experiments are also conducted to compare swap prices calculated through our formulae and those obtained under the Heston model to show whether the introduction of the regime switching factor would lead to any significant difference.

ON PRICING CONTINGENT CLAIMS UNDER THE DOUBLE HESTON MODEL

2012 ◽  
Vol 15 (05) ◽  
pp. 1250033 ◽  
Author(s):  
M. COSTABILE ◽  
I. MASSABÒ ◽  
E. RUSSO
Keyword(s):  
Stochastic Volatility ◽  
Numerical Experiments ◽  
Contingent Claims ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Underlying Asset ◽  
State Variable ◽  
Proposed Model ◽  
Volatility Model ◽  
Asset Value

This article presents a lattice based approach for pricing contingent claims when the underlying asset evolves according to the double Heston (dH) stochastic volatility model introduced by Christoffersen et al. (2009). We discretize the continuous evolution of both squared volatilities by a "binomial pyramid", and consider the asset value as an auxiliary state variable for which a subset of possible realizations is attached to each node of the pyramid. The elements of the subset cover the range of asset prices at each time slice, and claim price is computed solving backward through the "binomial pyramid". Numerical experiments confirm the accuracy and efficiency of the proposed model.

scholarly journals PERHITUNGAN VALUE AT RISK DENGAN PENDUGA VOLATILITAS STOKASTIK HESTON

2018 ◽  
Vol 7 (4) ◽  
pp. 317
Author(s):  
DESAK PUTU DEVI DAMIYANTI ◽  
KOMANG DHARMAWAN ◽  
LUH PUTU IDA HARINI
Keyword(s):  
At Risk ◽  
Stochastic Process ◽  
Stochastic Volatility ◽  
Value At Risk ◽  
Financial Risk ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Volatility Model ◽  
The Mean ◽  
Simulation Results

Value at risk is a method that measures financial risk of an security or portfolio. The aims of the research is to find out the value at risk of an exchange rate using the Heston stochastic volatility model. Heston model is a strochastic volatility model that assumes that volatility of the security follow stochastic process and consider the mean reversion. Based on simulation results, the value of volatility using Heston volatility estimastor is 0.2887, and the value of Heston VaR with 95 percent confident level is 0.0297. Based on result of backtesting,  there are 48 violations obtained VaR using Heston model, while historical VaR there are 2 violations. Thus, VaR using Heston model is more strict in estimating risk.

scholarly journals THE HESTON STOCHASTIC-LOCAL VOLATILITY MODEL: EFFICIENT MONTE CARLO SIMULATION

2014 ◽  
Vol 17 (07) ◽  
pp. 1450045 ◽  
Author(s):  
ANTHONIE W. VAN DER STOEP ◽  
LECH A. GRZELAK ◽  
CORNELIS W. OOSTERLEE
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Error Analysis ◽  
Stochastic Volatility ◽  
Numerical Experiments ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Local Volatility ◽  
Local Volatility Model ◽  
Volatility Model

In this paper we propose an efficient Monte Carlo scheme for simulating the stochastic volatility model of Heston (1993) enhanced by a nonparametric local volatility component. This hybrid model combines the main advantages of the Heston model and the local volatility model introduced by Dupire (1994) and Derman & Kani (1998). In particular, the additional local volatility component acts as a "compensator" that bridges the mismatch between the nonperfectly calibrated Heston model and the market quotes for European-type options. By means of numerical experiments we show that our scheme enables a consistent and fast pricing of products that are sensitive to the forward volatility skew. Detailed error analysis is also provided.

A weak approximation with Malliavin weights for local stochastic volatility model

2017 ◽  
Vol 04 (01) ◽  
pp. 1750002
Author(s):  
Toshihiro Yamada
Keyword(s):  
Differential Equation ◽  
Asymptotic Expansion ◽  
Stochastic Differential Equation ◽  
Stochastic Volatility ◽  
Numerical Experiments ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Weak Approximation ◽  
Volatility Model ◽  
Sabr Model

This paper introduces a new efficient and practical weak approximation for option price under local stochastic volatility model as marginal expectation of stochastic differential equation, using iterative asymptotic expansion with Malliavin weights. The explicit Malliavin weights for SABR model are shown. Numerical experiments confirm the validity of our discretization with a few time steps.

Pricing barrier options in the Heston model using the Heath–Platen estimator

2018 ◽  
Vol 24 (1) ◽  
pp. 29-41 ◽  
Author(s):  
Sema Coskun ◽  
Ralf Korn
Keyword(s):  
Stochastic Volatility ◽  
Real Life ◽  
Theoretical Concept ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Superior Performance ◽  
Financial Mathematics ◽  
Barrier Options ◽  
Numerical Examples ◽  
Volatility Model

Abstract Both barrier options and the Heston stochastic volatility model are omnipresent in real-life applications of financial mathematics. In this paper, we apply the Heath–Platen (HP) estimator (as first introduced by Heath and Platen in [12]) to price barrier options in the Heston model setting as an alternative to conventional Monte Carlo methods and PDE based methods. We demonstrate the superior performance of the HP estimator via numerical examples and explain this performance by a detailed look at the underlying theoretical concept of the HP estimator.

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