Closed-Form Partial Transform of Triple Joint Density for Pricing Exotic Options and Variance Derivatives Under the 3/2 Model

Zheng, Wendong; Zeng, Pingping

doi:10.2139/ssrn.2421268

Cited by 1 publication

(3 citation statements)

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“…For instance, it has been documented (see or more recently that variance premium (market price of volatility risk) could be stochastic: this translates into a stochastic MRL either under both measures, historical and risk‐neutral, or under one of them; in our case, we focus on the risk‐neutral modeling. The recent analysis of the variance‐inspired VIX index is another case where stochastic MRLs have been documented . A third rationale, part of our insight, is that the third level leads to richer structures of implied correlation and implied volatility (both as functions of strike prices).…”

Section: Introductionmentioning

confidence: 84%

“…. For the numerical implementation in Section 4, the trapezoid rule is used for the integrals in (13). Let 1 and 2 be the integration steps and N 1 and N 2 the integration limits.…”

Section: Propositionmentioning

confidence: 99%

“…In particular, we focus on plain vanilla European Call options on two underlyings: the S&P 500 Index (SPX, SECID: 108105) and Dow Jones Industrial Average (DJX, Security ID: 102456). The data set is composed of 8 days and 15 strike prices spread over roughly a 2-year period: 13 The calibration example consists of calibrating each one of the eight available days, every one-dimensional underlying (S&P500 and DowJones) to the Heston as well as to the MRL-Heston model. In order to simplify the presentation and to gain clarity, two sets of results are displayed.…”

Section: Calibrationmentioning

confidence: 99%

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Principal component models with stochastic mean‐reverting levels. Pricing and covariance surface improvements

Escobar

Goetz

et al. 2016

Appl Stoch Models Bus & Ind

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a In this work, we create a family of simple stochastic covariance models, which display stochastic mean-reverting levels of covariance as an additional level of stochastic behavior beyond well-known stochastic volatility and correlation. The one-dimensional version of our model is inspired by Heston model, while the multidimensional model generalizes the principal component stochastic volatility model. Their main contribution is that they capture stochastic mean-reversion levels on the volatility and on the eigenvalues of the instantaneous covariance matrix of the vector of stock prices, with direct implications on the correlations as well. Our focus is on the multidimensional model; we investigate its properties and derive a closed-form expression for the characteristic function. This allows us to study the pricing of financial derivatives, such as correlation and spread options. Those prices are compared with simulated Monte Carlo prices for correctness. A sensitivity analysis is performed on the parameters of the stochastic mean-reverting level of volatilities to study their impact on the price. Finally, implied volatility curves and correlation surfaces are built to reveal the additional flexibility gained within the new model.

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Section: Introductionmentioning

confidence: 84%

“…. For the numerical implementation in Section 4, the trapezoid rule is used for the integrals in (13). Let 1 and 2 be the integration steps and N 1 and N 2 the integration limits.…”

Section: Propositionmentioning

confidence: 99%

Section: Calibrationmentioning

confidence: 99%

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