Pricing of mountain range derivatives under a principal component stochastic volatility model

Escobar, Marcos; Olivares, Pablo

doi:10.1002/asmb.936

Cited by 19 publications

(12 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The work of Venkatramanan and Alexander in [16] is hereby used as reference. We aim to visualize the flexibility of the surface under our model and compare it with the two-dimensional PCSV model in [8], which incorporates stochastic eigenvalues but no stochastic MRL of the eigenvalues. ** In all these plotting, we have ensured the Feller condition, that is, j2 j2 ⩾ c 2 j2 ∕2, j = 1, 2, choosing the range of values conveniently.…”

Section: Implied Volatility and Correlation Surfacesmentioning

confidence: 99%

“…For each pair (c 11 , c 21 ), we vary ( 12 , 22 , c 12 , c 22 ). In the case of 12 = 22 = c 12 = c 22 = 0, we simply have the two-dimensional PCSV model in [8].…”

Section: 53mentioning

confidence: 99%

“…In particular, and rely on Monte Carlo (MC) simulations and tree‐based methods to provide pricing and risk management analyses. Some early work in the 2000s introduced stochastic correlation and volatility via modeling of the covariance matrix, for example, the Wishart process, first treated in and later on introduced to finance in and , as well as the principal component stochastic volatility process (PCSV), introduced in and further discussed in . These models allow for some tractability, as they provide closed‐form expressions for the characteristic function, hence making pricing analytical.…”

Section: Introductionmentioning

confidence: 99%

“…Modeling a third level of stochasticity can be achieved in one dimension by means of modeling both the stochastic volatility and the MRL of the volatilities using Cox–Ingersoll–Ross (CIR) processes . In higher dimensions, we rely on the convenient structure of the principal components stochastic volatility (PCSV) model . The PCSV process decomposes the total variance of the asset processes into several principal components, while the stochastic eigenvalues drive the volatility of the principal components.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Escobar

Goetz

et al. 2016

Appl Stoch Models Bus & Ind

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Implied Volatility and Correlation Surfacesmentioning

confidence: 99%

“…For each pair (c 11 , c 21 ), we vary ( 12 , 22 , c 12 , c 22 ). In the case of 12 = 22 = c 12 = c 22 = 0, we simply have the two-dimensional PCSV model in [8].…”

Section: 53mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Escobar

Goetz

et al. 2016

Appl Stoch Models Bus & Ind

Self Cite

View full text Add to dashboard Cite

show abstract

“…The best solution to this challenge is a stochastic covariance model, as those stochastic matrices tackle both features, volatility and correlation, simultaneously (see [1][2][3]). In such a context, when it comes to the actual pricing of products, practitioners either determine model parameters from option prices (usually called calibration) or obtain the parameters from historical observations of the underlying (estimation methodology).…”

Section: Introductionmentioning

confidence: 99%

A Note on the Impact of Parameter Uncertainty on Barrier Derivatives

Escobar

Panz

2016

Risks

Self Cite

View full text Add to dashboard Cite

This paper presents a comprehensive extension of pricing two-dimensional derivatives depending on two barrier constraints. We assume randomness on the covariance matrix as a way of generalizing. We analyse common barrier derivatives, enabling us to study parameter uncertainty and the risk related to the estimation procedure (estimation risk). In particular, we use the distribution of empirical parameters from IBM and EURO STOXX50. The evidence suggests that estimation risk should not be neglected in the context of multidimensional barrier derivatives, as it could cause price differences of up to 70%.

show abstract