Closed-Form Implied Volatility Surfaces for Stochastic Volatility Models

2017 ◽  
Author(s):  
Yacine Ait-Sahalia ◽  
Chenxu Li ◽  
Chen Xu Li
Keyword(s):  
Closed Form ◽  
Stochastic Volatility ◽  
Implied Volatility ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Implied Volatility Surfaces

scholarly journals TIME-CHANGED FAST MEAN-REVERTING STOCHASTIC VOLATILITY MODELS

2011 ◽  
Vol 14 (08) ◽  
pp. 1355-1383 ◽  
Author(s):  
MATTHEW LORIG
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Perturbation Techniques ◽  
European Option ◽  
Stochastic Volatility Models ◽  
Multiple Factors ◽  
Price Process ◽  
Volatility Models ◽  
Time Changes ◽  
Implied Volatility Surfaces

We introduce a class of randomly time-changed fast mean-reverting stochastic volatility (TC-FMR-SV) models. Using spectral theory and singular perturbation techniques, we derive an approximation for the price of any European option in the TC-FMR-SV setting. Three examples of random time-changes are provided and are shown to induce distinct implied volatility surfaces. The key features of the TC-FMR-SV framework are that (i) it is able to incorporate jumps into the price process of the underlying asset (ii) it allows for the leverage effect and (iii) it can accommodate multiple factors of volatility, which operate on different time-scales.

PRICING TIMER OPTIONS: SECOND-ORDER MULTISCALE STOCHASTIC VOLATILITY ASYMPTOTICS

2021 ◽  
pp. 1-19
Author(s):  
XUHUI WANG ◽  
SHENG-JHIH WU ◽  
XINGYE YUE
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Option Price ◽  
Second Order ◽  
Approximation Formula ◽  
Stochastic Volatility Models ◽  
Regular Perturbation ◽  
Volatility Models ◽  
Order Expansion ◽  
High Level

Abstract We study the pricing of timer options in a class of stochastic volatility models, where the volatility is driven by two diffusions—one fast mean-reverting and the other slowly varying. Employing singular and regular perturbation techniques, full second-order asymptotics of the option price are established. In addition, we investigate an implied volatility in terms of effective maturity for the timer options, and derive its second-order expansion based on our pricing asymptotics. A numerical experiment shows that the price approximation formula has a high level of accuracy, and the implied volatility in terms of its effective maturity is illustrated.

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.

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