This paper considers loans containing implicit options according to §489 of the German civil code. Assuming a risk neutral framework a generalisation of the simple case of a 1:1 micro-hedge to the more advanced case of a macro-hedge will be presented. For this purpose, the proposed hedging strategy will be described and examined. The question which of the several components of a macro hedge should be finally taken into account is answered in a step by step approach. Firstly, by means of a methodological discussion and secondly, by means of a cost/benefit analysis. A useful by-product of the analysis conducted here is a generic method for quantifying the materiality of risks of §489 options.
{"title":"A Macro Hedge for Implicit Options of Type §489","authors":"A. Miemiec","doi":"10.2139/ssrn.3926361","DOIUrl":"https://doi.org/10.2139/ssrn.3926361","url":null,"abstract":"This paper considers loans containing implicit options according to §489 of the German civil code. Assuming a risk neutral framework a generalisation of the simple case of a 1:1 micro-hedge to the more advanced case of a macro-hedge will be presented. For this purpose, the proposed hedging strategy will be described and examined. The question which of the several components of a macro hedge should be finally taken into account is answered in a step by step approach. Firstly, by means of a methodological discussion and secondly, by means of a cost/benefit analysis. A useful by-product of the analysis conducted here is a generic method for quantifying the materiality of risks of §489 options.","PeriodicalId":293888,"journal":{"name":"Econometric Modeling: Derivatives eJournal","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115577507","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
How do supply and demand from informed traders drive market prices of bitcoin options? Deribit options tick-level data supports the limits-to-arbitrage hypothesis about market maker’s supply. The main demand-side effects are that at-the-money option prices are largely driven by volatility traders and out-of-the-money options are simultaneously driven by volatility traders and those with proprietary information about the direction of future bitcoin price movements. The demand-side trading results contrast with prior studies on established options markets in the US and Asia, but we also show that Deribit is rapidly evolving into a more efficient channel for aggregating information from informed traders.
{"title":"Net Buying Pressure and the Information in Bitcoin Option Trades","authors":"C. Alexander, Jun Deng, J. Feng, Huning Wan","doi":"10.2139/ssrn.3915901","DOIUrl":"https://doi.org/10.2139/ssrn.3915901","url":null,"abstract":"How do supply and demand from informed traders drive market prices of bitcoin options? Deribit options tick-level data supports the limits-to-arbitrage hypothesis about market maker’s supply. The main demand-side effects are that at-the-money option prices are largely driven by volatility traders and out-of-the-money options are simultaneously driven by volatility traders and those with proprietary information about the direction of future bitcoin price movements. The demand-side trading results contrast with prior studies on established options markets in the US and Asia, but we also show that Deribit is rapidly evolving into a more efficient channel for aggregating information from informed traders.","PeriodicalId":293888,"journal":{"name":"Econometric Modeling: Derivatives eJournal","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125591047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Defining a futures return as the rate of change of futures prices, as done in many empirical studies, implicitly implies that a futures contract is fully collateralized. We adjust futures' returns to explicitly account for holding the minimum margin (collateral) and the return to this collateral. Different collateral choices of the futures affect the dynamic properties of returns to futures contracts and modify their risk profile. In our empirical study, we document these discrepancies under full and partial collateralization. The discrepancy is minimal except when the futures prices and minimum margins are volatile. Our findings broadly verify the common belief that commodity futures serve as a good asset class for diversification purposes.
{"title":"Futures Contract Collateralization and its Implications","authors":"R. Jarrow, S. Kwok","doi":"10.2139/ssrn.3921423","DOIUrl":"https://doi.org/10.2139/ssrn.3921423","url":null,"abstract":"Defining a futures return as the rate of change of futures prices, as done in many empirical studies, implicitly implies that a futures contract is fully collateralized. We adjust futures' returns to explicitly account for holding the minimum margin (collateral) and the return to this collateral. Different collateral choices of the futures affect the dynamic properties of returns to futures contracts and modify their risk profile. In our empirical study, we document these discrepancies under full and partial collateralization. The discrepancy is minimal except when the futures prices and minimum margins are volatile. Our findings broadly verify the common belief that commodity futures serve as a good asset class for diversification purposes.","PeriodicalId":293888,"journal":{"name":"Econometric Modeling: Derivatives eJournal","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132210984","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Manipulation in the VIX settlement can cause significant losses to investors. Analysing high-frequency data, we present indications of VIX manipulation accelerating since 2017. Deviations have an upward direction and average at around 6%. Specific effects accompany settlement days. The put/call ratio of underlying options surges by 10.9%. A time series decomposition demonstrates that this difference exceeds the day-specific variations of all other days by 80%. Data on open interest point towards leveraged funds, who systematically gather additional exposure in the seven days before settlement. All other players seem to reduce their VIX exposure before settlement. After 2017, the market seems to accustom itself and incorporate deviations more easily.
{"title":"Has Manipulation in the VIX Decreased?","authors":"T. Baumgartner, Andre Guettler","doi":"10.2139/ssrn.3874249","DOIUrl":"https://doi.org/10.2139/ssrn.3874249","url":null,"abstract":"Manipulation in the VIX settlement can cause significant losses to investors. Analysing high-frequency data, we present indications of VIX manipulation accelerating since 2017. Deviations have an upward direction and average at around 6%. Specific effects accompany settlement days. The put/call ratio of underlying options surges by 10.9%. A time series decomposition demonstrates that this difference exceeds the day-specific variations of all other days by 80%. Data on open interest point towards leveraged funds, who systematically gather additional exposure in the seven days before settlement. All other players seem to reduce their VIX exposure before settlement. After 2017, the market seems to accustom itself and incorporate deviations more easily.","PeriodicalId":293888,"journal":{"name":"Econometric Modeling: Derivatives eJournal","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129041530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the problem of dynamically trading futures in continuous time under a multifactor Gaussian framework. We present a utility maximization approach to determine the optimal futures trading st...
{"title":"Optimal Dynamic Futures Portfolio Under a Multifactor Gaussian Framework","authors":"Tim Leung, Yang Zhou","doi":"10.2139/ssrn.3905578","DOIUrl":"https://doi.org/10.2139/ssrn.3905578","url":null,"abstract":"We study the problem of dynamically trading futures in continuous time under a multifactor Gaussian framework. We present a utility maximization approach to determine the optimal futures trading st...","PeriodicalId":293888,"journal":{"name":"Econometric Modeling: Derivatives eJournal","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126996473","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Following Boukai (2021) we present the Generalized Gamma (GG) distribution as a possible RND for modeling European options prices under Heston's (1993) stochastic volatility (SV) model. This distribution is seen as especially useful in situations in which the spot's price follows a negatively skewed distribution and hence, Black-Scholes based (i.e. the log-normal distribution) modeling is largely inapt. We apply the GG distribution as RND to modeling current market option data on three large market-index ETFs, namely the SPY, IWM and QQQ as well as on the TLT (an ETF that tracks an index of long term US Treasury bonds). The current option chain of each of the three market-index ETFs shows of a pronounced skew of their volatility `smile' which indicates a likely distortion in the Black-Scholes modeling of such option data. Reflective of entirely different market expectations, this distortion appears not to exist in the TLT option data. We provide a thorough modeling of the available option data we have on each ETF (with the October 15, 2021 expiration) based on the GG distribution and compared it to the option pricing and RND modeling obtained directly from a well-calibrated Heston's (1993) SV model (both theoretically and empirically, using Monte-Carlo simulations of the spot's price). All three market-index ETFs exhibit negatively skewed distributions which are well-matched with those derived under the GG distribution as RND. The inadequacy of the Black-Scholes modeling in such instances which involve negatively skewed distribution is further illustrated by its impact on the hedging factor, delta, and the immediate implications to the retail trader. In contrast, for the TLT ETF, which exhibits no such distortion to the volatility `smile', the three pricing models (i.e. Heston's, Black-Scholes and Generalized Gamma) appear to yield similar results.
{"title":"The Generalized Gamma Distribution as a Useful RND Under Heston’s Stochastic Volatility Model","authors":"B. Boukai","doi":"10.2139/ssrn.3906918","DOIUrl":"https://doi.org/10.2139/ssrn.3906918","url":null,"abstract":"Following Boukai (2021) we present the Generalized Gamma (GG) distribution as a possible RND for modeling European options prices under Heston's (1993) stochastic volatility (SV) model. This distribution is seen as especially useful in situations in which the spot's price follows a negatively skewed distribution and hence, Black-Scholes based (i.e. the log-normal distribution) modeling is largely inapt. We apply the GG distribution as RND to modeling current market option data on three large market-index ETFs, namely the SPY, IWM and QQQ as well as on the TLT (an ETF that tracks an index of long term US Treasury bonds). The current option chain of each of the three market-index ETFs shows of a pronounced skew of their volatility `smile' which indicates a likely distortion in the Black-Scholes modeling of such option data. Reflective of entirely different market expectations, this distortion appears not to exist in the TLT option data. We provide a thorough modeling of the available option data we have on each ETF (with the October 15, 2021 expiration) based on the GG distribution and compared it to the option pricing and RND modeling obtained directly from a well-calibrated Heston's (1993) SV model (both theoretically and empirically, using Monte-Carlo simulations of the spot's price). All three market-index ETFs exhibit negatively skewed distributions which are well-matched with those derived under the GG distribution as RND. The inadequacy of the Black-Scholes modeling in such instances which involve negatively skewed distribution is further illustrated by its impact on the hedging factor, delta, and the immediate implications to the retail trader. In contrast, for the TLT ETF, which exhibits no such distortion to the volatility `smile', the three pricing models (i.e. Heston's, Black-Scholes and Generalized Gamma) appear to yield similar results.","PeriodicalId":293888,"journal":{"name":"Econometric Modeling: Derivatives eJournal","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114831832","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We build a risk management model that incorporates variable capital utilization and procyclical collateral capacity. The former means that capital utilization determines production, which affects capital depreciation and risk exposure, linking capital utilization to firms' risk management decisions. The latter means that the ability to borrow and hedge increases with expected profitability. Using a new dataset on hedging and capital utilization of oil and gas producers, we employ novel identification strategies and find that hedging is positively correlated with corporate liquidity and expected profitability, whereas utilization is negatively correlated with liquidity. These results support the key predictions of our theory.
{"title":"Risk Management with Variable Capital Utilization and Procyclical Collateral Capacity","authors":"Guojun Chen, Zhongjin Lu, Siddharth Vij","doi":"10.2139/ssrn.3719158","DOIUrl":"https://doi.org/10.2139/ssrn.3719158","url":null,"abstract":"We build a risk management model that incorporates variable capital utilization and procyclical collateral capacity. The former means that capital utilization determines production, which affects capital depreciation and risk exposure, linking capital utilization to firms' risk management decisions. The latter means that the ability to borrow and hedge increases with expected profitability. Using a new dataset on hedging and capital utilization of oil and gas producers, we employ novel identification strategies and find that hedging is positively correlated with corporate liquidity and expected profitability, whereas utilization is negatively correlated with liquidity. These results support the key predictions of our theory.","PeriodicalId":293888,"journal":{"name":"Econometric Modeling: Derivatives eJournal","volume":"63 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114608387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We develop two models for index futures arbitrage that take the financing constraints faced by real-world arbitrageurs into account. Our models predict that the price of an index futures contract and the value of its underlying index should deviate further from their theoretical cost-of-carry relationship when (a) the contract has a longtime to go before expiry, and (b) volatility is high. The fact that these predictions enjoy considerable empirical support highlights the importance of financing constraints for explaining index futures mispricing.
{"title":"Financially Constrained Index Futures Arbitrage","authors":"K. Glover, H. Hulley","doi":"10.2139/ssrn.3895655","DOIUrl":"https://doi.org/10.2139/ssrn.3895655","url":null,"abstract":"We develop two models for index futures arbitrage that take the financing constraints faced by real-world arbitrageurs into account. Our models predict that the price of an index futures contract and the value of its underlying index should deviate further from their theoretical cost-of-carry relationship when (a) the contract has a longtime to go before expiry, and (b) volatility is high. The fact that these predictions enjoy considerable empirical support highlights the importance of financing constraints for explaining index futures mispricing.","PeriodicalId":293888,"journal":{"name":"Econometric Modeling: Derivatives eJournal","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114909544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Valuation adjustments, collectively named XVA, play an important role in modern derivatives pricing. XVA are an exotic pricing component since they require the forward simulation of multiple risk factors in order to compute the portfolio exposure including collateral, leading to a significant model risk and computational effort, even in case of plain vanilla trades. This work analyses the most critical model risk factors, meant as those to which XVA are most sensitive, finding an acceptable compromise between accuracy and performance. This task has been conducted in a complete context including a market standard multi-curve G2++ model calibrated on real market data, both Variation Margin and ISDA-SIMM dynamic Initial Margin, different collateralization schemes, and the most common linear and non-linear interest rates derivatives. Moreover, we considered an alternative analytical approach for XVA in case of uncollateralized Swaps. We show that a crucial element is the construction of a parsimonious time grid capable of capturing all periodical spikes arising in collateralized exposure during the Margin Period of Risk. To this end, we propose a workaround to efficiently capture all spikes. Moreover, we show that there exists a parameterization which allows to obtain accurate results in a reasonable time, which is a very important feature for practical applications. In order to address the valuation uncertainty linked to the existence of a range of different parameterizations, we calculate the Model Risk AVA (Additional Valuation Adjustment) for XVA according to the provisions of the EU Prudent Valuation regulation. Finally, this work can serve as an handbook containing step-by-step instructions for the implementation of a complete, realistic and robust modelling framework of collateralized exposure and XVA.
{"title":"Everything You Always Wanted to Know About XVA Model Risk but Were Afraid to Ask","authors":"Lorenzo Silotto, Marco Scaringi, M. Bianchetti","doi":"10.2139/ssrn.3891120","DOIUrl":"https://doi.org/10.2139/ssrn.3891120","url":null,"abstract":"Valuation adjustments, collectively named XVA, play an important role in modern derivatives pricing. XVA are an exotic pricing component since they require the forward simulation of multiple risk factors in order to compute the portfolio exposure including collateral, leading to a significant model risk and computational effort, even in case of plain vanilla trades. This work analyses the most critical model risk factors, meant as those to which XVA are most sensitive, finding an acceptable compromise between accuracy and performance. This task has been conducted in a complete context including a market standard multi-curve G2++ model calibrated on real market data, both Variation Margin and ISDA-SIMM dynamic Initial Margin, different collateralization schemes, and the most common linear and non-linear interest rates derivatives. Moreover, we considered an alternative analytical approach for XVA in case of uncollateralized Swaps. We show that a crucial element is the construction of a parsimonious time grid capable of capturing all periodical spikes arising in collateralized exposure during the Margin Period of Risk. To this end, we propose a workaround to efficiently capture all spikes. Moreover, we show that there exists a parameterization which allows to obtain accurate results in a reasonable time, which is a very important feature for practical applications. In order to address the valuation uncertainty linked to the existence of a range of different parameterizations, we calculate the Model Risk AVA (Additional Valuation Adjustment) for XVA according to the provisions of the EU Prudent Valuation regulation. Finally, this work can serve as an handbook containing step-by-step instructions for the implementation of a complete, realistic and robust modelling framework of collateralized exposure and XVA.","PeriodicalId":293888,"journal":{"name":"Econometric Modeling: Derivatives eJournal","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114271955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper investigates the effects of the issuance of retail products with non-linear payoffs on option prices. For a given underlying asset, when the outstanding volume of products embedding a short-put position increases, implied volatility at the corresponding strike decreases. A similar pattern exists for the dividend term structure: larger outstanding volumes of retail structured products are associated with a flattened dividend term structured. A simple trading strategy exploiting this pattern leads to a Sharpe ratio above 2. These results are consistent with the existence of segmented markets and speak to the equilibrium effects of the retail demand for innovative securities.
{"title":"The Price Effects of Innovative Security Design","authors":"Claire Célérier, B. Vallée, Gordon Y. Liao","doi":"10.2139/ssrn.3881268","DOIUrl":"https://doi.org/10.2139/ssrn.3881268","url":null,"abstract":"This paper investigates the effects of the issuance of retail products with non-linear payoffs on option prices. For a given underlying asset, when the outstanding volume of products embedding a short-put position increases, implied volatility at the corresponding strike decreases. A similar pattern exists for the dividend term structure: larger outstanding volumes of retail structured products are associated with a flattened dividend term structured. A simple trading strategy exploiting this pattern leads to a Sharpe ratio above 2. These results are consistent with the existence of segmented markets and speak to the equilibrium effects of the retail demand for innovative securities.","PeriodicalId":293888,"journal":{"name":"Econometric Modeling: Derivatives eJournal","volume":"73 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120907626","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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