Valuation of FX barrier options under stochastic volatility

1996 ◽  
Vol 3 (3) ◽  
pp. 195-215 ◽  
Author(s):  
David Heath ◽  
Eckhard Platen
Keyword(s):  
Stochastic Volatility ◽  
Barrier Options

scholarly journals Efficient Simulation for Pricing Barrier Options with Two-Factor Stochastic Volatility and Stochastic Interest Rate

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Zhang Sumei ◽  
Zhao Jieqiong
Keyword(s):  
Interest Rates ◽  
Stochastic Volatility ◽  
Implied Volatility ◽  
Differential Evolution Algorithm ◽  
Extended Model ◽  
Barrier Options ◽  
Simulation Algorithm ◽  
Volatility Model ◽  
Stochastic Interest ◽  
Simulation Scheme

This paper presents an extension of the double Heston stochastic volatility model by combining Hull-White stochastic interest rates. By the change of numeraire and quadratic exponential scheme, this paper develops a new simulation scheme for the extended model. By combining control variates and antithetic variates, this paper provides an efficient Monte Carlo simulation algorithm for pricing barrier options. Based on the differential evolution algorithm the extended model is calibrated to S&P 500 index options to obtain the model parameter values. Numerical results show that the proposed simulation scheme outperforms the Euler scheme, the proposed simulation algorithm is efficient for pricing barrier options, and the extended model is flexible to fit the implied volatility surface.

AN APPROXIMATION METHOD FOR PRICING CONTINUOUS BARRIER OPTIONS UNDER MULTI-ASSET LOCAL STOCHASTIC VOLATILITY MODELS

2020 ◽  
pp. 2050051
Author(s):  
KENICHIRO SHIRAYA
Keyword(s):  
Risk Management ◽  
Stochastic Volatility ◽  
Approximation Method ◽  
Numerical Experiments ◽  
Analytical Approximation ◽  
Barrier Options ◽  
European Options ◽  
Stochastic Volatility Models ◽  
Volatility Models

This paper presents a new approximation method for pricing multi-asset continuous single-barrier options. Barrier options are frequently traded, and it is necessary for practitioners to evaluate these precisely and quickly, both for competitiveness, and for risk management. However, it is a difficult task under local stochastic volatility models. To the best of our knowledge, this paper is the first to provide an analytical approximation for continuous barrier options prices in a multi-asset environment. In numerical experiments, we examine the validity of the formula by using parameters calibrated to EURUSD European options.

PERFORMANCE OF ROBUST HEDGES FOR DIGITAL DOUBLE BARRIER OPTIONS

2012 ◽  
Vol 15 (01) ◽  
pp. 1250003 ◽  
Author(s):  
JAN OBŁÓJ ◽  
FRÉDÉRIK ULMER
Keyword(s):  
Stochastic Volatility ◽  
Model Uncertainty ◽  
Foreign Exchange Rate ◽  
Barrier Options ◽  
Double Barrier ◽  
Fixed Amount ◽  
Forward Markets ◽  
Robust Hedging ◽  
Hedging Strategies ◽  
Financial Derivative

We analyze the performance of robust hedging strategies of digital double barrier options of Cox and Obłój (2011) against that of traditional hedging methods such as delta and delta/vega hedging. Digital double barrier options are financial derivative contracts which pay out a fixed amount on the condition that the underlying asset remains within or breaks into a range defined by two distinct barrier levels. We perform the analysis in hypothetical forward markets driven by models with stochastic volatility and jumps, calibrated to the AUD/USD foreign exchange rate market. Our findings are strikingly unanimous and suggest that, in the presence of model uncertainty and/or transaction costs, robust hedging strategies typically outperform in a substantial way model-specific hedging methods.

Robust static hedging of barrier options in stochastic volatility models

2008 ◽  
Vol 70 (3) ◽  
pp. 405-433 ◽  
Author(s):  
J. H. Maruhn ◽  
E. W. Sachs
Keyword(s):  
Stochastic Volatility ◽  
Barrier Options ◽  
Stochastic Volatility Models ◽  
Static Hedging ◽  
Volatility Models

scholarly journals Efficient smoothing of Crank-Nicolson method for pricing barrier options under stochastic volatility

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 1081101-1081102 ◽  
Author(s):  
M. Yousuf
Keyword(s):  
Stochastic Volatility ◽  
Barrier Options ◽  
Crank Nicolson
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