{"title":"A Short Note on Application of Bachelier Option Model to FRAs; with Comment on Black 1976","authors":"I. Thomson","doi":"10.2139/ssrn.3464749","DOIUrl":"https://doi.org/10.2139/ssrn.3464749","url":null,"abstract":"This Short Note arises from questions about applying the Bachelier model to FRAs which arose as interest rates went negative leading to a failure of the Black 1976 model used by convention as the market price model.<br><br>The paper reviews the Black ’76 model form highlighting reasons for this failure. Alternate Bachelier model based on log normal and yield standard error measures are shown to have similar limitations. Other extant models derived from the Black-Scholes model form have consistent failings.<br><br>Given this, the author defines a Bachelier spread model in terms of yields and the related note price. It is shown these create the same price outcomes for all positive, negative and nil values of the note yield. It can then be shown the Black ’76 model for instance systematically misprices as the Note yields go to zero and fails below zero. Recommendation is the price model be moved from the log normal, yield standard error model form to the Bachelier style spread model formulated consistent with that detailed in this paper.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132505969","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":"Bitcoin Futures and Option Markets: Searching for Completeness","authors":"H. Geman, H. Price","doi":"10.2139/ssrn.3457167","DOIUrl":"https://doi.org/10.2139/ssrn.3457167","url":null,"abstract":"Cryptocurrencies have emerged in the last decade as a new asset class unlikely to disappear despite its extraordinary volatility. Futures contracts on Bitcoins were introduced in December 2017 by the Chicago Mercantile Exchange and options are being traded on crypto exchanges. Our goal in this paper is threefold: i) present the main features of cryptocurrency spot and derivative markets; ii) argue that storability of Bitcoins implies the existence of a convenience yield and infer from traded Future prices the risk neutral drift of the Bitcoin price in the continuous time Black-Scholes setting quite appropriate to continuously traded bitcoins. We use the prices of options traded on the Deribit Exchange to build the volatility smiles and skews observed at different dates of 2019 for short and long dated maturities and compare them to forward curves. Lastly, the robustness of the Black-Scholes formula allows capturing in our approach the stochastic volatility displayed by price trajectories and provides some answers to the incompleteness of the bitcoin market.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115308416","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}
Rhys ap Gwilym, Muhammed Shahid Ebrahim, A. O. EL ALAOUI, Hamid Rahman, A. Taamouti
{"title":"Financial Frictions and the Futures Pricing Puzzle","authors":"Rhys ap Gwilym, Muhammed Shahid Ebrahim, A. O. EL ALAOUI, Hamid Rahman, A. Taamouti","doi":"10.2139/ssrn.3451791","DOIUrl":"https://doi.org/10.2139/ssrn.3451791","url":null,"abstract":"Abstract In perfect capital markets, the futures price of an asset should be an unbiased forecast of its realized spot price when the contract matures. In reality, futures prices are often higher for some assets and lower for others. However, there is no stability in the relationship between futures prices and the realized spot prices. This instability has been a puzzle in the existing financial literature. The key to this puzzle may lie in the nature of the model and the lack of market imperfections. In this study, we take a theoretical approach in a dynamic multi-period environment. We incorporate competition between disparate economic agents and impose financial frictions (i.e., imperfections) that are in the form of hedging and borrowing limits on them. Our model gives rise to multiple equilibria, each with unique market clearing prices, with the market switching between these equilibria. Our analysis incorporates a comprehensive consideration of the risks faced by the futures markets participants (i.e., speculators and hedgers) and leads to a better understanding of the puzzle.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115139829","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":"Supplement to 'Market Selection with Differential Financial Constraints'","authors":"Ani Guerdjikova, J. Quiggin","doi":"10.2139/ssrn.3372292","DOIUrl":"https://doi.org/10.2139/ssrn.3372292","url":null,"abstract":"In this Supplement we provide foundations for the asset structures used in the main part of the paper, as well as in Appendix A. We use results by Choquet (1966), Kendall (1962) and Polyrakis (1999) to demonstrate how these asset structures can be generated from a general set of assets available in the economy and a general set of financial constraints. A sufficient condition called \"internal completeness\" is for the set of assets to contain an appropriate set of put and call options so that the implied set of payoffs is a sublattice of the Euclidean space.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"368 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122151080","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":"On the Valuation of Equity Options with Dividend-Protection Features","authors":"Ghislain Vong","doi":"10.2139/ssrn.3357971","DOIUrl":"https://doi.org/10.2139/ssrn.3357971","url":null,"abstract":"This note describes the various techniques used to protect the writer of an equity option against the risk of dividend uncertainty. We first explicitly formulate the PnL tracking error in presence of dividend misspecification. We then describe various ways to offset the dividend risk: for vanilla options practitioners usually adjust the strike and notional across an ex-div date. We justify this approximation. We then introduce an alternative way that does not require a change in the strike and that involves an extra exchange of cash flow across the ex-div date.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114678647","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 Information Content of Commodity Futures Markets","authors":"R. Alves, M. Szymanowska","doi":"10.2139/ssrn.3352822","DOIUrl":"https://doi.org/10.2139/ssrn.3352822","url":null,"abstract":"textabstractWe find that commodity futures returns contain information relevant to stock market returns and macroeconomic fundamentals for a large number of countries. Commodity futures returns predict stock market returns in 59 out of 70 countries and macroeconomic fundamentals in 62 countries. This predictability is not concentrated in the Energy and Industrial Metals sectors, as it is economically and statistically significant across all sectors. Surprisingly, we find that the role of countries’ dependence on commodity trade is limited in its ability to account for this predictability. This holds true even when considering new measures that take into account indirect exposures through financial and trade linkages between countries. We find much stronger evidence of predictability being related to the ability of commodities to forecast inflation rates. Overall, our evidence is consistent with commodity markets having a truly global information discovery role in relation to financial markets and the real economy.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134356429","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":"Bilateral Defaultable Financial Derivatives Pricing and Credit Valuation Adjustment","authors":"Tim Xiao","doi":"10.2139/ssrn.3412478","DOIUrl":"https://doi.org/10.2139/ssrn.3412478","url":null,"abstract":"The one-side defaultable financial derivatives valuation problems have been studied extensively, but the valuation of bilateral derivatives with asymmetric credit qualities is still lacking convincing mechanism. This paper presents an analytical model for valuing derivatives subject to default by both counterparties. The default-free interest rates are modeled by the Market Models, while the default time is modeled by the reduced-form model as the first jump of a time-inhomogeneous Poisson process. All quantities modeled are market-observable. The closed-form solution gives us a better understanding of the impact of the credit asymmetry on swap value, credit value adjustment, swap rate and swap spread.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"117 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134009163","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":"Looking Forward to Backward-Looking Rates: A Modeling Framework for Term Rates Replacing LIBOR","authors":"A. Lyashenko, F. Mercurio","doi":"10.2139/ssrn.3330240","DOIUrl":"https://doi.org/10.2139/ssrn.3330240","url":null,"abstract":"In this paper, we define and model forward risk-free term rates, which appear in the payoff definition of derivatives, and possibly cash instruments, based on the new interest-rate benchmarks that will be replacing IBORs globally. We show that the classical interest rate modeling framework can be naturally extended to describe the evolution of both the forward-looking (IBOR-like) and backward-looking (setting-in-arrears) term rates using the same stochastic process. In particular, we show that the extension of the popular LIBOR Market Model (LMM) to the backward-looking rates completes the model by providing additional information about the rate dynamics not accessible in the LMM.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"40 1-8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123376156","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":"Characteristic Function-Based Estimation of Affine Option Pricing Models","authors":"Yannick Dillschneider","doi":"10.2139/ssrn.3328584","DOIUrl":"https://doi.org/10.2139/ssrn.3328584","url":null,"abstract":"In this paper, we derive explicit expressions for certain joint moments of stock prices and option prices within a generic affine stochastic volatility model. Evaluation of each moment requires weighted inverse Fourier transformation of a function that is determined by the risk-neutral and real-world characteristic functions of the state vector. Explicit availability of such moment expressions allows to devise a novel GMM approach to jointly estimate real-world and risk-neutral parameters of affine stochastic volatility models using observed individual option prices. Moreover, the moment expressions may be used to include option price information into other existing moment-based estimation approaches.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"34 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124643205","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":"Analytic Swaption Pricing in the Black-Karasinski Model","authors":"C. Turfus","doi":"10.2139/ssrn.3253866","DOIUrl":"https://doi.org/10.2139/ssrn.3253866","url":null,"abstract":"We present a Green's function solution to the Black-Karasinski (lognormal) short rate model as a perturbation expansion valid in the limit of small deviations of the rates from the forward curve. We use this to derive analytic formulae for the prices of European swaptions to second order accuracy.","PeriodicalId":177064,"journal":{"name":"ERN: Other Econometric Modeling: Derivatives (Topic)","volume":"48 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122805431","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}