Second Order Expansion for Implied Volatility in Two Factor Local Stochastic Volatility Models and Applications to the Dynamic $$\lambda $$ -Sabr Model

2015 ◽  
pp. 89-136 ◽  
Author(s):  
Gérard Ben Arous ◽  
Peter Laurence
Keyword(s):  
Stochastic Volatility ◽  
Implied Volatility ◽  
Second Order ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Order Expansion ◽  
Sabr Model

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.

Pricing timer options: second-order multiscale stochastic volatility asymptotics

2021 ◽  
Vol 63 ◽  
pp. 249-267
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

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. doi:10.1017/S1446181121000249

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.

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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