{"title":"A Malliavin Calculus Approach to Minimal Variance Hedging","authors":"M. Hess","doi":"10.2139/ssrn.3810190","DOIUrl":"https://doi.org/10.2139/ssrn.3810190","url":null,"abstract":"In this paper, we investigate the following problem: How can a financial institution, which has sold an option to a client, optimally hedge the payoff of this option by investing into a stock and into the option itself? Optimality is measured in terms of minimal variance and the associated optimal hedging portfolio is derived by a stochastic maximum principle. Moreover, we deduce the time dynamics of the stochastic option price process by Malliavin calculus methods, particularly by an application of the Clark-Ocone formula. We finally apply our theoretical results to several examples.","PeriodicalId":348709,"journal":{"name":"ERN: Hedging (Topic)","volume":"182 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116309465","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}
{"title":"Index Design: Hedging and Manipulation","authors":"R. Jarrow, Siguang Li","doi":"10.2139/ssrn.3819072","DOIUrl":"https://doi.org/10.2139/ssrn.3819072","url":null,"abstract":"This paper studies optimal index design to both facilitate hedging and alleviate illegal manipulation in a competitive equilibrium paradigm, modified to deal with manipulation. Specifically, a large trader is trading both derivatives and stocks, and effectively hides her trades behind the competitive market clearing mechanism. Unlike the strategic game paradigm, a volume-weighted average pricing (VWAP) index both introduces basis risk and encourages manipulation because of the additional randomness in volume weight and the greater price impact enjoyed by the large trader. In contrast, an equal-weighted average pricing (EWAP) index both preserves market completeness and discourages manipulation.","PeriodicalId":348709,"journal":{"name":"ERN: Hedging (Topic)","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2021-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129513867","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}
{"title":"The Market Structure of Dealer-to-Client Interest Rate Swaps","authors":"Mohammadreza Bolandnazar","doi":"10.2139/ssrn.3752367","DOIUrl":"https://doi.org/10.2139/ssrn.3752367","url":null,"abstract":"Following the Dodd-Frank Act, central clearing and centralized trading became mandatory for a class of the most liquid interest rate swaps (IRS). Nevertheless, IRS market making in the dealer-to-client sector remained concentrated at a few regulated banks that transfer their funding costs to end users. I develop an equilibrium model of IRS markets with imperfect competition among capital-constrained dealers. Using proprietary data on cleared IRS transactions and the dealers' daily margin requirements, I empirically investigate the impact of recent regulatory changes on market liquidity. By exploiting the variation in margin requirements across swaps with different risk profiles intermediated by bank-affiliated dealers, my estimates show that a 1 percentage point increase in the supplementary leverage ratio (SLR) leads to an increase of $1.5 billion in the annual cost of hedging for the end-users.","PeriodicalId":348709,"journal":{"name":"ERN: Hedging (Topic)","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127163289","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}
{"title":"Optimal Dynamic Longevity Hedge with Basis Risk","authors":"K. S. Tan, Chengguo Weng, Jinggong Zhang","doi":"10.2139/ssrn.3638370","DOIUrl":"https://doi.org/10.2139/ssrn.3638370","url":null,"abstract":"Abstract This paper proposes an optimal dynamic strategy for hedging longevity risk in a discrete-time setting. Our proposed hedging strategy relies on standardized mortality-linked securities and minimizes the variance of the hedging error as induced by the population basis risk. While the formulation of our proposed hedging strategy is quite general, we use a stylized pension plan, together with a specified “yearly rollingǥ trading strategy involving q-forwards and a specified stochastic mortality model, to illustrate our proposed strategy. Under these specifications, we show that the resulting hedging problem can be formulated as a stochastic optimal control framework and that a semi-analytic solution can be derived through an extended Bellman equation. Extensive Monte Carlo studies are conducted to highlight the effectiveness of our proposed hedging strategy. We also consider a scheme to approximate the semi-analytic solution in order to reduce the computational time significantly while still retaining its hedge effectiveness. We benchmark our strategy against the “delta” hedging strategy as well as its robustness to q-forwards maturity, reference age, interest rate, and stochastic mortality models. The proposed strategy has many appealing features, including its discrete-time setting which is consistent with market practice and hence conducive to practical implementation, and its generality in that the underlying hedging principle can be applied to other standardized mortality-linked securities and other stochastic models.","PeriodicalId":348709,"journal":{"name":"ERN: Hedging (Topic)","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133926354","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}
{"title":"A Darwinian Theory of Model Risk","authors":"C. Albanese, S. Crépey, Stefano Iabichino","doi":"10.2139/ssrn.3544862","DOIUrl":"https://doi.org/10.2139/ssrn.3544862","url":null,"abstract":"Performance assessment of derivative pricing models revolves around a comparative model-risk analysis. From among the plethora of econometrically unrealistic models, the ones that survive Darwinian selection tend to generate systematic short term profits while exposing the bank to long term risks. \u0000 \u0000This article puts forward an ex ante methodology to analyse this pattern for the broad class of structures, whereby a dealer buys long-term convexity from investors and resells hedges to be used for risk management purposes. As a particular case, we consider callable range accruals in the US dollar, a product which has been traded in size in recent years and is currently being unwound. We find 3d animations useful to visualize sources of model risk.","PeriodicalId":348709,"journal":{"name":"ERN: Hedging (Topic)","volume":"156 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133276668","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}
{"title":"Impact of Hedging Strategy on Capital Charges for Variable Annuity Portfolios","authors":"B. Vaucher, Vivek Shah","doi":"10.2139/ssrn.3539558","DOIUrl":"https://doi.org/10.2139/ssrn.3539558","url":null,"abstract":"Efficient and robust techniques are crucial for hedging a book of variable annuities. For insurers, the profitability of variable annuity contracts heavily depend on the hedging schemes used to mitigate their associated financial liabilities. Beyond financial performance, the inclusion of protection, in the form of protective put options, in hedging portfolios contributes to reduce the capital charges imposed on the insurer. Although this external source of profit affect the total performance of the hedge, it has not been quantified in the literature. This paper fills that gap by quantifying the contribution of capital charge reductions to hedging performance for a number of hedging methodologies. We provide statistics using price simulations following normal and student distributions with fatter tails.","PeriodicalId":348709,"journal":{"name":"ERN: Hedging (Topic)","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126742672","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}
{"title":"Gold and Bitcoin Hedging against 10 Exchange Returns","authors":"Y. Hwang","doi":"10.16980/jitc.15.6.201912.49","DOIUrl":"https://doi.org/10.16980/jitc.15.6.201912.49","url":null,"abstract":"Purpose - The purpose of this study was to examine gold and bitcoin hedging against 10 exchange returns.<br><br>Design/Methodology/Approach - This study collected financial data on exchange, gold, and bitcoin from FRB, St. Louis. A multiple Vector-BEKK regression analysis was used to analyze the data.<br><br>Findings - First, strong negative effects from exchange markets onto gold were found to exist in the EU, Switzerland, Australia, Brazil, Canada, Japan, and Korea, while there were weak effects in the UK. Bitcoin shows the weak hedging against all markets. Second, the paper also revealed that in EU, the cross-shock term significantly decreased gold volatility, but not bitcoin volatility, while in Japan it decreased bitcoin volatility. The significantly negative asymmetries in gold, but insignificant asymmetries in bitcoin, were found in most exchange markets. Exchange market volatility increases gold volatility in Japan while it decreased in the Indian and Korean markets. Cross-terms among three variables with bi-directional causality are valuable.<br><br>Research Implications or Originality - The study of the hedging of gold and bitcoin against various exchanges together shows that bi-variate models are useful to reconfirm the strong hedging of gold. Bitcoin, if well prepared to be immune to its deficiencies, might be very carefully used, but not at a magnitude equal to gold as a hedge against exchange. The results may enhance strategic risk management.","PeriodicalId":348709,"journal":{"name":"ERN: Hedging (Topic)","volume":"262 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124033664","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}
{"title":"Bank Foreign Currency Hedging and the Impact on Covered Interest Parity, an Emerging Market Perspective","authors":"Georgia R. Bush","doi":"10.2139/ssrn.3478126","DOIUrl":"https://doi.org/10.2139/ssrn.3478126","url":null,"abstract":"This paper examines the role of banking sector foreign currency hedging demand in the foreign exchange market. First, the paper documents deviations from covered interest parity for a panel of emerging economies and tests whether resident bank foreign currency hedging needs affect these deviations. Next, I exploit data from Mexican regulatory filings on derivatives transactions and bank balance sheets to assess the impact of FX hedging demand from all resident banks, foreigners, and global banks operating in Mexico. These hedging demand measures are included in an econometric model of covered interest parity (under limits to arbitrage) with tenures from 1 month to 12 months, and then interacted with arbitrageur balance sheet constraint variables to test whether these amplify the impact of FX hedging demand. The main result of the paper is that bank hedging demand directly influences CIP deviations in the EM panel and the case of Mexico, while evidence of interaction effects is mixed. The direct effect of resident bank hedging demand is robust to including foreign exchange bid-ask spreads and arbitrage constraint variables in the regression model. In addition, global banks are the driver of this hedging effect. The results validate an important mechanism in the theoretical literature: that higher bank demand for foreign currency hedging, particularly from global banks, can directly increase the cost of hedging. This paper adds to the literature on CIP deviations by analyzing emerging market currencies, with the unique advantage of using regulatory data and observed FX derivatives transactions.","PeriodicalId":348709,"journal":{"name":"ERN: Hedging (Topic)","volume":"06 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130653127","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}
{"title":"The Concentration of Cleared Derivatives: Can Access to Direct Ccp Clearing for End-Users Address the Challenge?","authors":"Nahiomy Alvarez, J. McPartland","doi":"10.21033/wp-2019-06","DOIUrl":"https://doi.org/10.21033/wp-2019-06","url":null,"abstract":"Cleared derivatives contracts are now concentrated among a small and dwindling number of institutions. Many policymakers and regulators have argued that this concentration has adverse consequences, some of which may have systemic risk implications. The authors explore the benefits and challenges of encouraging major end-users of derivatives to become direct clearing members of central counterparties (CCPs). If done prudently, increasing and diversifying the pool of clearing members and redistributing outstanding derivatives contracts across them may help CCPs become more resilient.","PeriodicalId":348709,"journal":{"name":"ERN: Hedging (Topic)","volume":"46 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127750002","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}
{"title":"The Joint S&P 500/VIX Smile Calibration Puzzle Solved","authors":"Julien Guyon","doi":"10.2139/ssrn.3397382","DOIUrl":"https://doi.org/10.2139/ssrn.3397382","url":null,"abstract":"Since VIX options started trading in 2006, many researchers have tried to build a model that jointly and exactly calibrates to the prices of S&P 500 (SPX) options, VIX futures and VIX options. So far the best attempts, which used parametric continuous-time jump-diffusion models on the SPX, only produced an approximate fit. In this article we solve this longstanding puzzle using a completely different approach: a nonparametric discrete-time model. Given a VIX future maturity T1, we build a joint probability measure on the SPX at T1, the VIX at T1, and the SPX at T2 = T1 + 30 days which is perfectly calibrated to the SPX smiles at T1 and T2, and the VIX future and VIX smile at T1. Our model satisfies the martingality constraint on the SPX as well as the requirement that the VIX at T1 is the implied volatility of the 30-day log-contract on the SPX. We prove by duality that the existence of such a model means that the SPX and VIX markets are jointly arbitrage-free. \u0000 \u0000The joint calibration puzzle is cast as a dispersion-constrained martingale transport problem which is solved using (an extension of) the Sinkhorn algorithm, in the spirit of De March and Henry-Labordere (2019). The algorithm identifies joint SPX/VIX arbitrages should they arise. Our numerical experiments show that the algorithm performs very well in both low and high volatility regimes. Finally we explain how to handle the fact that the VIX future and SPX option monthly maturities do not perfectly coincide, and how to extend the two-maturity model to include all available monthly maturities.","PeriodicalId":348709,"journal":{"name":"ERN: Hedging (Topic)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128956392","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}