Valuation of Barrier Options Using Sequential Monte Carlo

Shevchenko, Pavel V.; Moral, Pierre Del

doi:10.2139/ssrn.2529539

Cited by 8 publications

(9 citation statements)

References 27 publications

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“…11. It is worth noting that for typical business cases, the number of paths required for acceptable pricing accuracy goes from tens of thousands to millions (depending on the option underlyings) [42,43], so they are well within the range where amplitude estimation becomes more efficient than Monte Carlo, as shown in Fig. 11.…”

Section: Basket Optionsmentioning

confidence: 94%

Option Pricing using Quantum Computers

Stamatopoulos

Egger

Sun

et al. 2020

Quantum

210

207

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We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.

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Section: Basket Optionsmentioning

confidence: 94%

Option Pricing using Quantum Computers

Stamatopoulos

Egger

Sun

et al. 2020

Quantum

210

207

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show abstract

“…This motivates the development of more advanced stochastic simulation methods which inherit the robustness of MCS, and yet are more efficient in estimating barrier option prices. A range of stochastic simulation techniques for speeding up the convergence have been proposed, such as the MCS approximation correction for constant single barrier options (Beaglehole et al, 1997), the simulation method based on the large deviations theory (Baldi et al, 1999) and the sequential MCS method (Shevchenko and Del Moral, 2017).…”

Section: Literature Reviewmentioning

confidence: 99%

Pricing discretely-monitored double barrier options with small probabilities of execution

Kontosakos

Mendonca

Pantelous

et al. 2021

European Journal of Operational Research

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In this paper, we propose a new stochastic simulation-based methodology for pricing discretely-monitored double barrier options and estimating the corresponding probabilities of execution. We develop our framework by employing a versatile tool for the estimation of rare event probabilities known as subset simulation algorithm. In this regard, considering plausible dynamics for the price evolution of the underlying asset, we are able to compare and demonstrate clearly that our treatment always outperforms the standard Monte Carlo approach and becomes substantially more efficient (measured in terms of the sample coefficient of variation) when the underlying asset has high volatility and the barriers are set close to the spot price of the underlying asset. In addition, we test and report that our approach performs better when it is * We are extremely grateful to the three anonymous reviewers and handling editor Emanuele Borgonovo who have afforded us considerable assistance in enhancing both the quality of the findings and the clarity of their presentation. The authors would like to thank

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“…g n (s n−1 , s n ) is probability of no barrier hit within [t n−1 , t n ] conditional on asset taking values s n−1 and s n at t n−1 and t n respectively with s n−1 ∈ (L n , U n ) and s n ∈ (L n , U n ); it is the socalled Brownian bridge correction often used in the literature on pricing barrier options, see e.g. Andersen and Brotherton-Racliffe (1996); Shevchenko (2003); Beaglehole et al (1997); Shevchenko and Del Moral (2014)…”

Section: Barrier Optionmentioning

confidence: 99%

Fast and Simple Method for Pricing Exotic Options Using Gauss-Hermite Quadrature on a Cubic Spline Interpolation

Luo

Shevchenko

2014

SSRN Journal

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There is a vast literature on numerical valuation of exotic options using Monte Carlo, binomial and trinomial trees, and finite difference methods. When transition density of the underlying asset or its moments are known in closed form, it can be convenient and more efficient to utilize direct integration methods to calculate the required option price expectations in a backward time-stepping algorithm. This paper presents a simple, robust and efficient algorithm that can be applied for pricing many exotic options by computing the expectations using Gauss-Hermite integration quadrature applied on a cubic spline interpolation. The algorithm is fully explicit but does not suffer the inherent instability of the explicit finite difference counterpart. A 'free' bonus of the algorithm is that it already contains the function for fast and accurate interpolation of multiple solutions required by many discretely monitored path dependent options. For illustrations, we present examples of pricing a series of American options with either Bermudan or continuous exercise features, and a series of exotic pathdependent options of target accumulation redemption note (TARN). Results of the new method are compared with Monte Carlo and finite difference methods, including some of the most advanced or best known finite difference algorithms in the literature. The comparison shows that, despite its simplicity, the new method can rival with some of the best finite difference algorithms in accuracy and at the same time it is significantly faster. Virtually the same algorithm can be applied to price other path-dependent financial contracts such as Asian options and variable annuities.

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Valuation of Barrier Options Using Sequential Monte Carlo

Cited by 8 publications

References 27 publications

Option Pricing using Quantum Computers

Option Pricing using Quantum Computers

Pricing discretely-monitored double barrier options with small probabilities of execution

Fast and Simple Method for Pricing Exotic Options Using Gauss-Hermite Quadrature on a Cubic Spline Interpolation

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