Fast Numerical Pricing of Barrier Options under Stochastic Volatility and Jumps

Guardasoni, C.; Sanfelici, Simona

doi:10.1137/15100504x

Cited by 21 publications

(28 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In contrast, the evaluation of the first-order approximation takes less than half of a second when the Mathematica function NIntegrate is used to compute the integral in (23). This computation time is also clearly lower to that of other numerical schemes such as finite elements [9] or boundary elements [10]. The first-order asymptotic expansion proposed in this paper therefore provides a fast way of obtaining barrier option prices which capture the common financial market phenomena of volatility randomness and mean reversion.…”

Section: Numerical Examplesmentioning

confidence: 94%

Barrier option pricing under the 2-hypergeometric stochastic volatility model

Sousa

Cruzeiro

Guerra

2018

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

We investigate the pricing of financial options under the 2-hypergeometric stochastic volatility model. This is an analytically tractable model that reproduces the volatility smile and skew effects observed in empirical market data.Using a regular perturbation method from asymptotic analysis of partial differential equations, we derive an explicit and easily computable approximate formula for the pricing of barrier options under the 2hypergeometric stochastic volatility model. The asymptotic convergence of the method is proved under appropriate regularity conditions, and a multi-stage method for improving the quality of the approximation is discussed. Numerical examples are also provided.A natural way to address this issue is to introduce randomness in the volatility. For this reason, option pricing under stochastic volatility has been the subject of a great deal of research in recent years. Here we focus on the 2-hypergeometric stochastic volatility model, which was introduced by Da Fonseca and Martini [1] as a model which ensures that the volatility is strictly positive -this is an important property which is not present in some other well-established stochastic volatility models. In a very recent paper, Privault and She [2] demonstrated that, under this model, a closed-form asymptotic vanilla option pricing formula can be determined through a regular perturbation method. This is a notable result because their formulas are analytically very simple, which is rarely the case in models with stochastic volatility: as discussed by Zhu [3], the higher complexity of these models usually yields the need for rather sophisticated numerical implementations.The literature on barrier option pricing methods is extensive. Exact closed-form pricing formulas have been derived for only a few models other than that of Black and Scholes, none of which reproduces satisfactorily the market phenomena. (For explicit formulas under one-dimensional models see e.g. Davydov and Linestky [4], Hui and Lo [5]; for an explicit solution under the Heston stochastic volatility model see Lipton [6].) Given the unavailability of explicit formulas, to price barrier options under more complex models one needs to resort to numerical methods. The main approaches are the use of numerical partial differential equation (PDE) techniques and of Monte Carlo methods (we refer the reader to the books of Seydel [7] and of Glasserman [8]), which are often combined with other analytical or numerical techniques (for recent work see for instance Zhang et al. [9], Guardasoni and Sanfelici [10]). Unfortunately, the computational times are nowadays still largely incompatible with the demands of the financial industry.An alternative strategy for pricing under more general models is to derive approximate (or asymptotic) analytical solutions: this has been proposed not only for vanilla options (cf. Privault and She [2]) but also for barrier options, see e.g. Fouque et al. [11], Alos et al. [12]. These asymptotic methods are intrinsically computationally much less expen...

show abstract

Section: Numerical Examplesmentioning

confidence: 94%

Barrier option pricing under the 2-hypergeometric stochastic volatility model

Sousa

Cruzeiro

Guerra

2018

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

show abstract

“…SABO is the acronym of semianalytical method for pricing of barrier options, and it has been introduced for European options both in Black‐Scholes and in Heston and Bates frameworks. For geometric Asian option, a formal and deep argumentation was described in the work of Aimi and Guardasoni, and it proceeds as follows.…”

Section: Semianalytical Methods For Barrier Options Pricingmentioning

confidence: 99%

“…The existence and uniqueness for (6) are stated in the work of Polidoro, 13 and the exact option value V(S, A, t ) is known to be the payoff expected value…”

Section: The Differential Model Problemmentioning

confidence: 99%

“…Semianalytical method for pricing of barrier options has been recently introduced for the computation of European barrier options within various differential models in other works . This new approach, based on boundary element method, turns out to be stable and efficient, especially when the differential problem is defined in an unbounded domain and the data is assigned on a limited boundary (which is the case of the “barrier options”).…”

Section: Introductionmentioning

confidence: 99%

“…2 Barrier options are largely exchanged as they are good products for hedging and investment and they are cheaper than vanilla options, but, for Asian options, we found in literature only the analysis of the work of Atkinson and Kazantzaki, 3 which provides rigorous bounds in the arithmetic mean case.Semianalytical method for pricing of barrier options has been recently introduced for the computation of European barrier options within various differential models in other works. [4][5][6] This new approach, based on boundary element method, 7,8 turns out to be stable and efficient, especially when the differential problem is defined in an unbounded domain and the data is assigned on a limited boundary (which is the case of the "barrier options"). The method is particularly advantageous for its high accuracy, for the implicit satisfaction of the far-field behavior of the solution, and for the low discretization costs.…”

mentioning

confidence: 99%

See 2 more Smart Citations