scholarly journals The Heston Stochastic-Local Volatility Model: Efficient Monte Carlo Simulation

2013 ◽  
Author(s):  
Anthonie Willem van der Stoep ◽  
Lech A. Grzelak ◽  
Cornelis W. Oosterlee
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Local Volatility ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Stochastic Local Volatility

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.

scholarly journals THE TIME-DEPENDENT FX-SABR MODEL: EFFICIENT CALIBRATION BASED ON EFFECTIVE PARAMETERS

2015 ◽  
Vol 18 (06) ◽  
pp. 1550042 ◽  
Author(s):  
ANTHONIE W. VAN DER STOEP ◽  
LECH A. GRZELAK ◽  
CORNELIS W. OOSTERLEE
Keyword(s):  
Monte Carlo ◽  
Time Dependent ◽  
Barrier Options ◽  
Constant Parameter ◽  
Effective Parameters ◽  
Local Volatility ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Sabr Model

We present a framework for efficient calibration of the time-dependent SABR model (Fernández et al. (2013) Mathematics and Computers in Simulation94, 55–75; Hagan et al. (2002) Wilmott Magazine 84–108; Osajima (2007) Available at SSRN 965265.) in an foreign exchange (FX) context. In a similar fashion as in (Piterbarg (2005) Risk18 (5), 71–75) we derive effective parameters, which yield an accurate and efficient calibration. On top of the calibrated FX-SABR model, we add a non-parametric local volatility component, which naturally compensates for possible calibration errors. By means of Monte Carlo pricing experiments, we show that the time-dependent FX-SABR model enables an accurate and consistent pricing of barrier options and outperforms the constant-parameter SABR model and the traditional local volatility model (Derman & Kani (1998) International Journal of Theoretical and Applied Finance1 (1), 61–110; Dupire (1994) Risk7 (1), 18–20). We also discuss the role of the local volatility component in pricing barrier options.

A new calibration of the Heston Stochastic Local Volatility Model and its parallel implementation on GPUs

2020 ◽  
Vol 177 ◽  
pp. 467-486
Author(s):  
Ana María Ferreiro-Ferreiro ◽  
José A. García-Rodríguez ◽  
Luis Souto ◽  
Carlos Vázquez
Keyword(s):  
Parallel Implementation ◽  
Local Volatility ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Stochastic Local Volatility
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