Target volatility option pricing in lognormal fractional SABR model

Alòs, Elisa; Chatterjee, Rupak; Tudor, Sebastian F.; Wang, Tai‐Ho

doi:10.48550/arxiv.1801.08215

Cited by 1 publication

(3 citation statements)

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“…We present in Table 1 a comprehensive comparison between QuEST QRNs, ID Quantique (IDQ) 3 , and Australian National University (ANU) Quantum Random Numbers Server 4 QRNs.…”

Section: Nist and Dieharder Testsmentioning

confidence: 99%

“…We price target volatility options (TVO) under a fBM stochastic process via MC methods using the QRNs described in the previous sections. A similar problem was approached in [3], where the authors derived two analytic approximations of TVO prices. The Python implementation using PRNs (similar to our MC pricing presented here) is available online on the GitHub platform 6 .…”

Section: Target Volatility Options Pricing Via Quantum Random Numbersmentioning

confidence: 99%

“…Note that the target volatility is in the denominator instead of the numerator, see [3] for comparison. MC methods via PRNs and QRNs were implemented and the results are shown in Figures 19 and 20.…”

Section: Target Volatility Options Pricing Via Quantum Random Numbersmentioning

confidence: 99%

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Quantum systems for Monte Carlo methods and applications to fractional stochastic processes

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Physica A: Statistical Mechanics and its Applications

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Random numbers are a fundamental and useful resource in science and engineering with important applications in simulation, machine learning and cyber-security. Quantum systems can produce true random numbers because of the inherent randomness at the core of quantum mechanics. As a consequence, quantum random number generators are an efficient method to generate random numbers on a large scale. We study in this paper the applications of a viable source of unbiased quantum random numbers (QRNs) whose statistical properties can be arbitrarily programmed without the need for any post-processing and that pass all standard randomness tests of the NIST and Dieharder test suites without any randomness extraction. Our method is based on measuring the arrival time of single photons in shaped temporal modes that are tailored with an electro-optical modulator. The advantages of our QRNs are shown via two applications: simulation of a fractional Brownian motion, which is a non-Markovian process, and option pricing under the fractional SABR model where the stochastic volatility process is assumed to be driven by a fractional Brownian motion. The results indicate that using the same number of random units, our QRNs achieve greater accuracy than those produced by standard pseudo-random number generators. Moreover, we demonstrate the advantages of our method via an increase in computational speed, efficiency, and convergence.

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“…We present in Table 1 a comprehensive comparison between QuEST QRNs, ID Quantique (IDQ) 3 , and Australian National University (ANU) Quantum Random Numbers Server 4 QRNs.…”

Section: Nist and Dieharder Testsmentioning

confidence: 99%

Section: Target Volatility Options Pricing Via Quantum Random Numbersmentioning

confidence: 99%