Related papers: Option pricing under stochastic volatility on a qu…
Multi-asset option pricing under local- and stochastic-volatility models leads naturally to high-dimensional parabolic PDEs. We develop an end-to-end quantum PDE framework for European option pricing under local-volatility Black--Scholes…
In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. For European options we could improve the…
We introduce two quantum algorithms to compute the Value at Risk (VaR) and Conditional Value at Risk (CVaR) of financial derivatives using quantum computers: the first by applying existing ideas from quantum risk analysis to derivative…
In this paper we reformulate the problem of pricing options in a quantum setting. Our proposed algorithm involves preparing an initial state, representing the option price, and then evolving it using existing imaginary time simulation…
The multidimensional Uncertain Volatility Model leads to robust option pricing problems under joint volatility and correlation uncertainty. Their numerical resolution quickly becomes challenging because the associated stochastic control…
Variational hybrid quantum-classical algorithms are some of the most promising workloads for near-term quantum computers without error correction. The aim of these variational algorithms is to guide the quantum system to a target state that…
Hamiltonian approach in quantum mechanics provides a new thinking for barrier option pricing. For proportional floating barrier step options, the option price changing process is similar to the one dimensional trapezoid potential barrier…
We propose a new, data-driven approach for efficient pricing of - fixed- and float-strike - discrete arithmetic Asian and Lookback options when the underlying process is driven by the Heston model dynamics. The method proposed in this…
The Heston stochastic volatility model is a widely used tool in financial mathematics for pricing European options. However, its calibration remains computationally intensive and sensitive to local minima due to the model's nonlinear…
In this paper an improved Cuckoo Search Algorithm is developed to allow for an efficient and robust calibration of the Heston option pricing model for American options. Calibration of stochastic volatility models like the Heston is…
This paper presents an algorithm for a complete and efficient calibration of the Heston stochastic volatility model. We express the calibration as a nonlinear least squares problem. We exploit a suitable representation of the Heston…
The financial sector is anticipated to be one of the first industries to benefit from the increased computational power of quantum computers, in areas such as portfolio optimisation and risk management to financial derivative pricing.…
This dissertation develops and justifies a novel method for deriving approximate formulas to estimate two parameters in stochastic volatility diffusion models with exponentially-affine characteristic functions and single- or two-factor…
We propose a hybrid quantum-classical algorithm, originated from quantum chemistry, to price European and Asian options in the Black-Scholes model. Our approach is based on the equivalence between the pricing partial differential equation…
Quantum Amplitude Estimation (QAE) can achieve a quadratic speed-up for applications classically solved by Monte Carlo simulation. A key requirement to realize this advantage is efficient state preparation. If state preparation is too…
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…
This study provides a consistent and efficient pricing method for both Standard & Poor's 500 Index (SPX) options and the Chicago Board Options Exchange's Volatility Index (VIX) options under a multiscale stochastic volatility model. To…
We derive a semi-analytical pricing formula for European VIX call options under the Heston-Hawkes stochastic volatility model introduced in arXiv:2210.15343. This arbitrage-free model incorporates the volatility clustering feature by adding…
We develop the general integral transforms (GIT) method for pricing barrier options in the time-dependent Heston model (also with a time-dependent barrier) where the option price is represented in a semi-analytical form as a two-dimensional…
In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and…