scholarly journals Small-time expansions of the distributions, densities, and option prices of stochastic volatility models with Lévy jumps

2012 ◽  
Vol 122 (4) ◽  
pp. 1808-1839 ◽  
Author(s):  
José E. Figueroa-López ◽  
Ruoting Gong ◽  
Christian Houdré
Keyword(s):  
Stochastic Volatility ◽  
Small Time ◽  
Option Prices ◽  
Stochastic Volatility Models ◽  
Volatility Models ◽  
Lévy Jumps

LOCAL STOCHASTIC VOLATILITY WITH JUMPS: ANALYTICAL APPROXIMATIONS

2013 ◽  
Vol 16 (08) ◽  
pp. 1350050 ◽  
Author(s):  
STEFANO PAGLIARANI ◽  
ANDREA PASCUCCI
Keyword(s):  
Characteristic Function ◽  
Stochastic Volatility ◽  
Fourier Space ◽  
Stochastic Volatility Models ◽  
Fourier Methods ◽  
Analytical Approximations ◽  
Volatility Models ◽  
Approximation Formulas ◽  
Real Market ◽  
Lévy Jumps

We present new approximation formulas for local stochastic volatility models, possibly including Lévy jumps. Our main result is an expansion of the characteristic function, which is worked out in the Fourier space. Combined with standard Fourier methods, our result provides efficient and accurate formulas for the prices and the Greeks of plain vanilla options. We finally provide numerical results to illustrate the accuracy with real market data.

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.

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.

A Tractable Framework for Option Pricing with Dynamic Market Maker Inventory and Wealth

2019 ◽  
Vol 55 (4) ◽  
pp. 1117-1162
Author(s):  
Mathieu Fournier ◽  
Kris Jacobs
Keyword(s):  
Stochastic Volatility ◽  
Risk Premium ◽  
Reduced Form ◽  
Market Maker ◽  
Option Prices ◽  
Stochastic Volatility Models ◽  
Variance Risk Premium ◽  
Volatility Models ◽  
Variance Risk ◽  
Index Option

We develop a tractable dynamic model of an index option market maker with limited capital. We solve for the variance risk premium and option prices as a function of the asset dynamics and market maker option holdings and wealth. The market maker absorbs end users’ positive demand and requires a more negative variance risk premium when she incurs losses. We estimate the model using returns, options, and inventory and find that it performs well, especially during the financial crisis. The restrictions imposed by nested existing reduced-form stochastic-volatility models are strongly rejected in favor of the model with a market maker.

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