Calendar Spread Exchange Options Pricing with Gaussian Random Fields
Most of the models leading to an analytical expression for option prices are based on the assumption that underlying asset returns evolve according to a Brownian motion with drift. For some asset classes like commodities, a Brownian model does not fit empirical covariance and autocorrelation structu...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-08-01
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| Series: | Risks |
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| Online Access: | http://www.mdpi.com/2227-9091/6/3/77 |
| _version_ | 1828520886670458880 |
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| author | Donatien Hainaut |
| author_facet | Donatien Hainaut |
| author_sort | Donatien Hainaut |
| collection | DOAJ |
| description | Most of the models leading to an analytical expression for option prices are based on the assumption that underlying asset returns evolve according to a Brownian motion with drift. For some asset classes like commodities, a Brownian model does not fit empirical covariance and autocorrelation structures. This failure to replicate the covariance introduces a bias in the valuation of calendar spread exchange options. As the payoff of these options depends on two asset values at different times, particular care must be taken for the modeling of covariance and autocorrelation. This article proposes a simple alternative model for asset prices with sub-exponential, exponential and hyper-exponential autocovariance structures. In the proposed approach, price processes are seen as conditional Gaussian fields indexed by the time. In general, this process is not a semi-martingale, and therefore, we cannot rely on stochastic differential calculus to evaluate options. However, option prices are still calculable by the technique of the change of numeraire. A numerical illustration confirms the important influence of the covariance structure in the valuation of calendar spread exchange options for Brent against WTI crude oil and for gold against silver. |
| first_indexed | 2024-12-11T19:38:56Z |
| format | Article |
| id | doaj.art-c07b467bafa34cdfbc930de1ad126aaf |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-12-11T19:38:56Z |
| publishDate | 2018-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-c07b467bafa34cdfbc930de1ad126aaf2022-12-22T00:53:04ZengMDPI AGRisks2227-90912018-08-01637710.3390/risks6030077risks6030077Calendar Spread Exchange Options Pricing with Gaussian Random FieldsDonatien Hainaut0Institute of Statistics, Biostatistics and Actuarial Sciences, University Catholique de Louvain, Voie du Roman Pays 20, 1348 Louvain-la-Neuve, BelgiumMost of the models leading to an analytical expression for option prices are based on the assumption that underlying asset returns evolve according to a Brownian motion with drift. For some asset classes like commodities, a Brownian model does not fit empirical covariance and autocorrelation structures. This failure to replicate the covariance introduces a bias in the valuation of calendar spread exchange options. As the payoff of these options depends on two asset values at different times, particular care must be taken for the modeling of covariance and autocorrelation. This article proposes a simple alternative model for asset prices with sub-exponential, exponential and hyper-exponential autocovariance structures. In the proposed approach, price processes are seen as conditional Gaussian fields indexed by the time. In general, this process is not a semi-martingale, and therefore, we cannot rely on stochastic differential calculus to evaluate options. However, option prices are still calculable by the technique of the change of numeraire. A numerical illustration confirms the important influence of the covariance structure in the valuation of calendar spread exchange options for Brent against WTI crude oil and for gold against silver.http://www.mdpi.com/2227-9091/6/3/77Gaussian fieldsExchange optionsCalendar options |
| spellingShingle | Donatien Hainaut Calendar Spread Exchange Options Pricing with Gaussian Random Fields Risks Gaussian fields Exchange options Calendar options |
| title | Calendar Spread Exchange Options Pricing with Gaussian Random Fields |
| title_full | Calendar Spread Exchange Options Pricing with Gaussian Random Fields |
| title_fullStr | Calendar Spread Exchange Options Pricing with Gaussian Random Fields |
| title_full_unstemmed | Calendar Spread Exchange Options Pricing with Gaussian Random Fields |
| title_short | Calendar Spread Exchange Options Pricing with Gaussian Random Fields |
| title_sort | calendar spread exchange options pricing with gaussian random fields |
| topic | Gaussian fields Exchange options Calendar options |
| url | http://www.mdpi.com/2227-9091/6/3/77 |
| work_keys_str_mv | AT donatienhainaut calendarspreadexchangeoptionspricingwithgaussianrandomfields |