A Closed Form Approach to the Valuation and Hedging of Basket and Spread Option

Borovkova, Svetlana; Permana, Ferry Jaya; Weide, Hans van der

doi:10.3905/jod.2007.686420

Cited by 71 publications

(69 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Concerning the basket spread option case, we compare Table 7 with the results obtained for different approximation methods in Deelstra et al (2010) (see tables reported in that paper). On the same parameter setting, the lower bound C G K (t) is less accurate than the best methods they considered for a basket spread option (Borovkova et al (2007) and Deelstra et al (2010)). …”

Section: Numerical Resultsmentioning

confidence: 99%

“…They derive an analytic approximation for the price of the compound exchange option, first under the assumption that the underlying assets of these options follow correlated lognormal processes, and then under more general assumptions for the asset price processes. The case of a basket where not all assets have positive weights (w k < 0 for some k) is discussed by Borovkova et al (2007), Li et al (2010) and Deelstra et al (2010) in a lognormal setting. Borovkova et al (2007) approximate the basket distribution by using a generalized family of lognormal distributions.…”

mentioning

confidence: 99%

“…The case of a basket where not all assets have positive weights (w k < 0 for some k) is discussed by Borovkova et al (2007), Li et al (2010) and Deelstra et al (2010) in a lognormal setting. Borovkova et al (2007) approximate the basket distribution by using a generalized family of lognormal distributions. Li et al (2010) provide an extended Kirk approximation and a second-order boundary approximation for pricing spread options on a basket.…”

mentioning

confidence: 99%

See 2 more Smart Citations

General Closed-Form Basket Option Pricing Bounds

et al. 2014

View full text Add to dashboard Cite

This is the accepted version of the paper.This version of the publication may differ from the final published version. This article presents lower and upper bounds on the prices of basket options for a general class of continuous-time financial models. The techniques we propose are applicable whenever the joint characteristic function of the vector of log-returns is known. Moreover, the basket value is not required to be positive. We test our new price approximations on different multivariate models, allowing for jumps and stochastic volatility. Numerical examples are discussed and benchmarked against Monte Carlo simulations. All bounds are general and do not require any additional assumption on the characteristic function, so our methods may be employed also to non-affine models. All bounds involve the computation of one-dimensional Fourier transforms, hence they do not suffer from the curse of dimensionality and can be applied also to high dimensional problems where most existing methods fail. In particular we study two kinds of price approximations: an accurate lower bound based on an approximating set and a fast bounded approximation based on the arithmetic-geometric mean inequality. We also show how to improve Monte Carlo accuracy by using one of our bounds as a control variate. Permanent repository link

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

General Closed-Form Basket Option Pricing Bounds

et al. 2014

View full text Add to dashboard Cite

show abstract

“…For the purposes of the numerical study in this paper, we model a single composite output, whose parameters are estimated by combining the prices of the soymeal and oil in the proportion in which they are produced upon processing one unit of the input commodity. Such approximations Borovkova et al 2007, for instance) and are sufficient to illustrate the main goals of the numerical study. The average of the estimated parameters obtained over each trading day are given in Table 2.…”

Section: Numerical Study Implementationmentioning

confidence: 99%

Dynamic Risk Management of Commodity Operations: Model and Analysis

Devalkar

Anupindi

Sinha

2018

M&SOM

View full text Add to dashboard Cite

We consider the dynamic risk management problem for a commodity processor facing risk costs. The firm procures an input commodity and processes it to produce an output commodity over a multi-period horizon. The processed commodity is sold using forward contracts while the input itself can be traded at the end of the horizon. The firm can also trade financial instruments to manage the commodity price risk, but cannot hedge the risk completely. Using the concept of conditional risk mappings, we extend the single period conditional value at risk (CVaR) measure to a dynamic setting and ensure a time-consistent representation of the firm's risk management objective. In a partially complete market framework, we show that the optimal financial trading policy is a CVaR-replicating portfolio. Contingent on optimal financial trading, we show that the optimal procurement and processing policies are characterized by price and horizon dependent inventory thresholds. We show, analytically, that the procurement threshold increases with risk costs during the horizon. Our numerical studies show that optimizing a time-consistent risk measure results in better risk control over the entire horizon when compared to optimizing the CVaR of total profits. We also find that myopic and risk-neutral optimal policies are poor substitutes for the optimal risk management policy, especially when the firm faces significant risk costs.

show abstract

“…There are basically two approaches to address this issue. The first is by modelling the (unidimensinal) distribution of the basket value (e.g., Borovkova et al, 2007). The second approach, which is perhaps more intuitive, is by focusing directly on the joint density of the basket's constituent assets.…”

Section: Some Applications Of Mvar Frameworkmentioning

confidence: 99%

Co-Dependence of Extreme Events in High Frequency FX Returns

Polanski

Stoja

2013

SSRN Journal

View full text Add to dashboard Cite

b s t r a c tIn this paper, we investigate extreme events in high frequency, multivariate FX returns within a purposely built framework. We generalize univariate tests and concepts to multidimensional settings and employ these novel techniques for parametric and nonparametric analysis. In particular, we investigate and quantify the co-dependence of cross-sectional and intertemporal extreme events. We find evidence of the cubic law of extreme returns, their increasing and asymmetric dependence and of the scaling property of extreme risk in joint symmetric tails.

show abstract

A Closed Form Approach to the Valuation and Hedging of Basket and Spread Option

Cited by 71 publications

References 9 publications

General Closed-Form Basket Option Pricing Bounds

General Closed-Form Basket Option Pricing Bounds

Dynamic Risk Management of Commodity Operations: Model and Analysis

Co-Dependence of Extreme Events in High Frequency FX Returns

Contact Info

Product

Resources

About