Good-Deal Bounds for Option Prices under Value-at-Risk and Expected Shortfall Constraints
In this paper, we deal with the pricing of European options in an incomplete market. We use the common risk measures Value-at-Risk and Expected Shortfall to define good-deals on a financial market with log-normally distributed rate of returns. We show that the pricing bounds obtained from the Value-...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Risks |
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| Online Access: | https://www.mdpi.com/2227-9091/8/4/114 |
| _version_ | 1797549314934833152 |
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| author | Sascha Desmettre Christian Laudagé Jörn Sass |
| author_facet | Sascha Desmettre Christian Laudagé Jörn Sass |
| author_sort | Sascha Desmettre |
| collection | DOAJ |
| description | In this paper, we deal with the pricing of European options in an incomplete market. We use the common risk measures Value-at-Risk and Expected Shortfall to define good-deals on a financial market with log-normally distributed rate of returns. We show that the pricing bounds obtained from the Value-at-Risk admit a non-smooth behavior under parameter changes. Additionally, we find situations in which the seller’s bound for a call option is smaller than the buyer’s bound. We identify the missing convexity of the Value-at-Risk as main reason for this behavior. Due to the strong connection between good-deal bounds and the theory of risk measures, we further obtain new insights in the finiteness and the continuity of risk measures based on multiple eligible assets in our setting. |
| first_indexed | 2024-03-10T15:12:56Z |
| format | Article |
| id | doaj.art-632705ed8efe4394ad58a754d9ac1543 |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-03-10T15:12:56Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-632705ed8efe4394ad58a754d9ac15432023-11-20T19:12:00ZengMDPI AGRisks2227-90912020-10-018411410.3390/risks8040114Good-Deal Bounds for Option Prices under Value-at-Risk and Expected Shortfall ConstraintsSascha Desmettre0Christian Laudagé1Jörn Sass2Institute of Financial Mathematics and Applied Number Theory, Johannes Kepler University Linz, Altenbergerstraße 69, 4040 Linz, AustriaDepartment of Financial Mathematics, Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern, GermanyDepartment of Mathematics, University of Kaiserslautern, Erwin-Schrödinger-Straße, 67663 Kaiserslautern, GermanyIn this paper, we deal with the pricing of European options in an incomplete market. We use the common risk measures Value-at-Risk and Expected Shortfall to define good-deals on a financial market with log-normally distributed rate of returns. We show that the pricing bounds obtained from the Value-at-Risk admit a non-smooth behavior under parameter changes. Additionally, we find situations in which the seller’s bound for a call option is smaller than the buyer’s bound. We identify the missing convexity of the Value-at-Risk as main reason for this behavior. Due to the strong connection between good-deal bounds and the theory of risk measures, we further obtain new insights in the finiteness and the continuity of risk measures based on multiple eligible assets in our setting.https://www.mdpi.com/2227-9091/8/4/114good-deal boundsrisk measuresmultiple eligible assetsValue-at-RiskExpected Shortfall |
| spellingShingle | Sascha Desmettre Christian Laudagé Jörn Sass Good-Deal Bounds for Option Prices under Value-at-Risk and Expected Shortfall Constraints Risks good-deal bounds risk measures multiple eligible assets Value-at-Risk Expected Shortfall |
| title | Good-Deal Bounds for Option Prices under Value-at-Risk and Expected Shortfall Constraints |
| title_full | Good-Deal Bounds for Option Prices under Value-at-Risk and Expected Shortfall Constraints |
| title_fullStr | Good-Deal Bounds for Option Prices under Value-at-Risk and Expected Shortfall Constraints |
| title_full_unstemmed | Good-Deal Bounds for Option Prices under Value-at-Risk and Expected Shortfall Constraints |
| title_short | Good-Deal Bounds for Option Prices under Value-at-Risk and Expected Shortfall Constraints |
| title_sort | good deal bounds for option prices under value at risk and expected shortfall constraints |
| topic | good-deal bounds risk measures multiple eligible assets Value-at-Risk Expected Shortfall |
| url | https://www.mdpi.com/2227-9091/8/4/114 |
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