Exchange option pricing under stochastic volatility: a correlation expansion

Antonelli, Fabio; Ramponi, Alessandro; Scarlatti, Sergio

doi:10.1007/s11147-009-9043-4

Cited by 36 publications

(27 citation statements)

References 17 publications

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“…Here we use a technique introduced in [2] and [3], that gives an expression of u(x, λ, t; ρ) as a power series of ρ around 0…”

Section: Correlation Expansionmentioning

confidence: 99%

“…In this paper we propose an alternative method, introduced in the papers [2] and [3], which expands theoretically the solution of the PDE system in a Taylor's series with respect to the correlation parameters. Indeed, under quite general hypotheses, it is straightforward to verify that the solution to the PDE is regular with respect to the correlation parameters and therefore it can be expanded in series around the zero value for all of them.The coefficients of the series are characterized, by using Duhamel's principle, as solutions to a chain of PDE problems and they are therefore identified by means of Feynman-Kac formulas and expressed as expectations, that turn to be easier to compute or to approximate.…”

Section: Introductionmentioning

confidence: 99%

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CVA and vulnerable options pricing by correlation expansions

2019

Self Cite

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We consider the problem of computing the Credit Value Adjustment (CVA) of a European option in presence of the Wrong Way Risk (WWR) in a default intensity setting. Namely we model the asset price evolution as solution to a linear equation that might depend on different stochastic factors and we provide an approximate evaluation of the option's price, by exploiting a correlation expansion approach, introduced in [2]. We compare the numerical performance of such a method with that recently proposed by Brigo et al. ([8], [10]) in the case of a call option driven by a GBM correlated with the CIR default intensity. We additionally report some numerical evaluations obtained by other methods.

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“…Here we use a technique introduced in [2] and [3], that gives an expression of u(x, λ, t; ρ) as a power series of ρ around 0…”

Section: Correlation Expansionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

CVA and vulnerable options pricing by correlation expansions

2019

Self Cite

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“…1 Cheang, Chiarella, and Ziogas (2006), Cheang and Chiarella (2011), Caldana et al (2015), Cufaro-Petroni and Sabino (2018), and Ma, Pan, and Wang (2020) analyzed European exchange options when asset prices are modelled using jump-diffusion processes. Antonelli and Scarlatti (2010), Alòs and Rheinlander (2017), and Kim and Park (2017) priced European exchange options where underlying assets are driven by stochastic volatility models. Cheang and Chiarella (2011) also considered the case of American exchange options in their analysis.…”

Section: Introductionmentioning

confidence: 99%

A numerical approach to pricing exchange options under stochastic volatility and jump-diffusion dynamics

Garces

Cheang

2021

Quantitative Finance

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We consider a method of lines (MOL) approach to determine prices of European and American exchange options when underlying asset prices are modelled with stochastic volatility and jump-diffusion dynamics. As the MOL, as with any other numerical scheme for PDEs, becomes increasingly complex when higher dimensions are involved, we first simplify the problem by transforming the exchange option into a call option written on the ratio of the yield processes of the two assets. This is achieved by taking the second asset yield process as the numéraire. We also characterize the near-maturity behavior of the early exercise boundary of the American exchange option and analyze how model parameters affect this behavior. Using the MOL scheme, we conduct a numerical comparative static analysis of exchange option prices with respect to the model parameters and investigate the impact of stochastic volatility and jumps to option prices. We also consider the effect of boundary conditions at far-but-finite limits of the computational domain on the overall efficiency of the MOL scheme. Toward these objectives, a brief exposition of the MOL and how it can be implemented on computing software are provided.

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“…(1) All underlying assets are assumed to be driven by one stochastic volatility factor, which is not reasonable in practice. A more reasonable model is to assume that each underlying asset is driven by its own stochastic volatility factor (see Antonelli et al [60], Shiraya and Takahashi [61], and Park et al [62]).…”

Section: Introductionmentioning

confidence: 99%

Variance and Dimension Reduction Monte Carlo Method for Pricing European Multi-Asset Options with Stochastic Volatilities

Liang

2019

Sustainability

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Pricing multi-asset options has always been one of the key problems in financial engineering because of their high dimensionality and the low convergence rates of pricing algorithms. This paper studies a method to accelerate Monte Carlo (MC) simulations for pricing multi-asset options with stochastic volatilities. First, a conditional Monte Carlo (CMC) pricing formula is constructed to reduce the dimension and variance of the MC simulation. Then, an efficient martingale control variate (CV), based on the martingale representation theorem, is designed by selecting volatility parameters in the approximated option price for further variance reduction. Numerical tests illustrated the sensitivity of the CMC method to correlation coefficients and the effectiveness and robustness of our martingale CV method. The idea in this paper is also applicable for the valuation of other derivatives with stochastic volatility.

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Exchange option pricing under stochastic volatility: a correlation expansion

Cited by 36 publications

References 17 publications

CVA and vulnerable options pricing by correlation expansions

CVA and vulnerable options pricing by correlation expansions

A numerical approach to pricing exchange options under stochastic volatility and jump-diffusion dynamics

Variance and Dimension Reduction Monte Carlo Method for Pricing European Multi-Asset Options with Stochastic Volatilities

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