scholarly journals Closed-Form Approximation of Timer Option Prices under General Stochastic Volatility Models

2013 ◽  
Author(s):  
Minqiang Li ◽  
Fabio Mercurio
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Option Prices ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Closed Form Approximation ◽  
General Stochastic

CLOSED-FORM APPROXIMATION OF PERPETUAL TIMER OPTION PRICES

2014 ◽  
Vol 17 (04) ◽  
pp. 1450026 ◽  
Author(s):  
MINQIANG LI ◽  
FABIO MERCURIO
Keyword(s):  
Asymptotic Expansion ◽  
Closed Form ◽  
Stochastic Volatility ◽  
Option Prices ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Expansion Technique ◽  
Black Scholes ◽  
Approximation Formulas ◽  
Closed Form Approximation

We develop an asymptotic expansion technique for pricing timer options in stochastic volatility models when the effect of volatility of variance is small. Based on the pricing PDE, closed-form approximation formulas have been obtained. The approximation has an easy-to-understand Black–Scholes-like form and many other attractive properties. Numerical analysis shows that the approximation formulas are very fast and accurate, especially when the volatility of variance is not large.

scholarly journals A Stochastic Volatility Alternative to SABR

2008 ◽  
Vol 45 (04) ◽  
pp. 1071-1085
Author(s):  
L. C. G. Rogers ◽  
L. A. M. Veraart
Keyword(s):  
Brownian Motion ◽  
Stochastic Processes ◽  
Closed Form ◽  
Stochastic Volatility ◽  
Option Prices ◽  
Stochastic Volatility Models ◽  
Underlying Asset ◽  
Volatility Models ◽  
Sabr Model ◽  
Modified Dynamics

We present two new stochastic volatility models in which option prices for European plain-vanilla options have closed-form expressions. The models are motivated by the well-known SABR model, but use modified dynamics of the underlying asset. The asset process is modelled as a product of functions of two independent stochastic processes: a Cox-Ingersoll-Ross process and a geometric Brownian motion. An application of the models to options written on foreign currencies is studied.

scholarly journals A Stochastic Volatility Alternative to SABR

2008 ◽  
Vol 45 (4) ◽  
pp. 1071-1085 ◽  
Author(s):  
L. C. G. Rogers ◽  
L. A. M. Veraart
Keyword(s):  
Brownian Motion ◽  
Stochastic Processes ◽  
Closed Form ◽  
Stochastic Volatility ◽  
Option Prices ◽  
Stochastic Volatility Models ◽  
Underlying Asset ◽  
Volatility Models ◽  
Sabr Model ◽  
Modified Dynamics

We present two new stochastic volatility models in which option prices for European plain-vanilla options have closed-form expressions. The models are motivated by the well-known SABR model, but use modified dynamics of the underlying asset. The asset process is modelled as a product of functions of two independent stochastic processes: a Cox-Ingersoll-Ross process and a geometric Brownian motion. An application of the models to options written on foreign currencies is studied.

Capturing implied correlation skew from options prices via multiscale stochastic volatility models

2020 ◽  
Vol 07 (04) ◽  
pp. 2050042
Author(s):  
T. Pellegrino
Keyword(s):  
Stochastic Volatility ◽  
Calibration Procedure ◽  
Second Order ◽  
Model Parameters ◽  
Option Prices ◽  
European Options ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Order Expansion ◽  
Implied Correlation

The aim of this paper is to derive a second-order asymptotic expansion for the price of European options written on two underlying assets, whose dynamics are described by multiscale stochastic volatility models. In particular, the second-order expansion of option prices can be translated into a corresponding expansion in implied correlation units. The resulting approximation for the implied correlation curve turns out to be quadratic in the log-moneyness, capturing the convexity of the implied correlation skew. Finally, we describe a calibration procedure where the model parameters can be estimated using option prices on individual underlying assets.

APPROXIMATING LOCAL VOLATILITY FUNCTIONS OF STOCHASTIC VOLATILITY MODELS: A CLOSED-FORM EXPANSION APPROACH

2015 ◽  
Vol 29 (4) ◽  
pp. 547-563 ◽  
Author(s):  
Yu An ◽  
Chenxu Li
Keyword(s):  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Closed Form ◽  
Stochastic Volatility ◽  
Numerical Test ◽  
Stochastic Volatility Models ◽  
Marginal Distributions ◽  
Local Volatility ◽  
Volatility Models ◽  
Conditional Expectations

We propose a method for approximating equivalent local volatility functions of stochastic volatility models. Enlightened by the theory of generalized Wiener functionals proposed by Watanabe and Yoshida (1987, 1992), our key technique is to propose a closed-form expansion of conditional expectations involving marginal distributions generated by stochastic differential equations. A numerical test and an illustration of application are provided to demonstrate the efficiency of our approach.

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