scholarly journals Analytical Approximation of the Transition Density in a Local Volatility Model

2011 ◽  
Author(s):  
Andrea Pascucci ◽  
Stefano Pagliarani
Keyword(s):  
Transition Density ◽  
Analytical Approximation ◽  
Local Volatility ◽  
Local Volatility Model ◽  
Volatility Model

Analytical approximation for spread option pricing in local volatility model

2017 ◽  
Vol 04 (04) ◽  
pp. 1750022
Author(s):  
Ying Yang
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Option Pricing ◽  
Difference Method ◽  
Analytical Approximation ◽  
Second Order ◽  
Local Volatility ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Spread Option

This paper introduces a methodology of analytical approximation in general European option-pricing case based on local volatility model and then apply it to price a European Spread Option. The approximation procedure is flexible in pricing financial derivatives with any form of volatility, drift rate, risk-free rate and payoff function. We also work out the explicit pricing formula up to the second-order approximation of spread option which is good-fitting compared with finite difference method and Monte Carlo simulation. The relative error compared to finite difference method is no more than 5%, which attests to the accuracy of our second-order closed-form formulas.

Calibration of the Heston stochastic local volatility model: A finite volume scheme

2021 ◽  
pp. 2050048
Author(s):  
Bernd Engelmann ◽  
Frank Koster ◽  
Daniel Oeltz
Keyword(s):  
Finite Volume ◽  
Numerical Test ◽  
Transition Density ◽  
Heston Model ◽  
Finite Volume Scheme ◽  
Local Volatility ◽  
Volume Scheme ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Stochastic Local Volatility

The two most popular equity and FX derivatives pricing models in banking practice are the local volatility model and the Heston model. While the former has the appealing property that it can be calibrated exactly to any given set of arbitrage free European vanilla option prices, the latter delivers more realistic smile dynamics. In this paper, we combine both modeling approaches to the Heston stochastic local volatility model. We build upon a theoretical framework that has been already developed and focus on the numerical model calibration which requires special care in the treatment of mixed derivatives and in cases where the Feller condition is not met in the Heston model leading to a singular transition density at zero volatility. We propose a finite volume scheme to calibrate the model after a suitable transformation of the model equation and demonstrate its accuracy in numerical test cases using real market data.

Libor Local Volatility Model: A New Interest Rate Smile Model

Wilmott ◽  
2016 ◽  
Vol 2016 (82) ◽  
pp. 78-87 ◽  
Author(s):  
Dingqiu Zhu ◽  
Dong Qu
Keyword(s):  
Interest Rate ◽  
Local Volatility ◽  
Local Volatility Model ◽  
Volatility Model
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