The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model

@inproceedings{Choi2019TheEC,
  title={The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model},
  author={Jaehyuk Choi and Lixin Wu},
  year={2019}
}
  • Jaehyuk Choi, Lixin Wu
  • Published 2019
  • Economics
This study presents new analytic approximations of the stochastic-alpha-beta-rho (SABR) model. Unlike existing studies that focus on the equivalent Black–Scholes (BS) volatility, we instead derive the equivalent constant-elasticity-of-variance (CEV) volatility. Our approach effectively reduces the approximation error in a way similar to the control variate method because the CEV model is the zero vol-of-vol limit of the SABR model. Moreover, the CEV volatility approximation yields a finite… Expand

Figures and Tables from this paper

References

SHOWING 1-10 OF 37 REFERENCES
A Note on the Option Price and 'Mass at Zero in the Uncorrelated SABR Model and Implied Volatility Asymptotics'
Gulisashvili et al. [Quant. Finance, 2018, 18(10), 1753-1765] provide a small-time asymptotics for the mass at zero under the uncorrelated SABR model by approximating the integrated variance with aExpand
BENCHOP – SLV: the BENCHmarking project in Option Pricing – Stochastic and Local Volatility problems
TLDR
A set of benchmark problems for Stochastic and Local Volatility problems was introduced by introducing a set of methods targeted for this type of problems, with the ADI method standing out as the best performing one. Expand
The principle of not feeling the boundary for the SABR model
The stochastic alpha–beta–rho (SABR) model is widely used in fixed income and foreign exchange markets as a benchmark. The underlying process may hit zero with a positive probability and therefore anExpand
A General Valuation Framework for SABR and Stochastic Local Volatility Models
TLDR
A general framework for the valuation of options in stochastic local volatility models with a general correlation structure, which includes the Stochastic alpha beta structure, is proposed. Expand
Hyperbolic normal stochastic volatility model
For option pricing models and heavy-tailed distributions, this study proposes a continuous-time stochastic volatility model based on an arithmetic Brownian motion: a one-parameter extension of theExpand
The survival probability of the SABR model: asymptotics and application
The stochastic-alpha-beta-rho (SABR) model is widely used by practitioners in interest rate and foreign exchange markets. The probability of hitting zero sheds light on the arbitrage-free smallExpand
Exact Simulation of the SABR Model
TLDR
This paper explores the possibility of exact simulation for the SABR model and proposes an exact simulation method for the forward price and its volatility in two special but practically interesting cases, i.e., when the elasticity β = 1 and when β < 1 and the price and volatility processes are instantaneously uncorrelated. Expand
Shapes of Implied Volatility with Positive Mass at Zero
TLDR
The structural difference with the no-mass-at-zero case is investigated, showing how one can--theoretically--distinguish between mass at the origin and a heavy-left-tailed distribution. Expand
Approximate Arbitrage-Free Option Pricing Under the SABR Model
The stochastic-alpha-beta-rho (SABR) model introduced by Hagan et al. (2002) provides a popular vehicle to model the implied volatilities in the interest rate and foreign exchange markets. To excludeExpand
...
1
2
3
4
...