The transition from interbank offered rates (IBOR) to the new risk-free rates, and in particular the adoption of the backward-looking approach in place of the forward-looking one, affects the interest rate modeling and the pricing of interest rate derivatives. In this article, we introduce the pricing formula for caplets/floorlets with backward-looking risk-free rates under the one- and two-factor Hull-White model. In particular, we derive the appropriate volatility function for caplets/floorlets to be used in the pricing formula under the two-factor Hull-White model and, implicitly, under the one-factor Hull-White model. Our formulation allows us to obtain, as a particular case, the caplet/floorlet formula under the IBOR environment with a forward-looking rates approach. A numerical analysis is performed to illustrate the main feature of the proposed model and in order to provide a comparison in evaluating caplets/floorlets under both forward-looking and backward-looking approaches.
{"title":"Caplets/Floorlets with Backward-Looking Risk-Free Rates under the One- and Two-Factor Hull-White Models","authors":"Vincenzo Russo, Frank J. Fabozzi","doi":"10.3905/jod.2023.1.186","DOIUrl":"https://doi.org/10.3905/jod.2023.1.186","url":null,"abstract":"The transition from interbank offered rates (IBOR) to the new risk-free rates, and in particular the adoption of the backward-looking approach in place of the forward-looking one, affects the interest rate modeling and the pricing of interest rate derivatives. In this article, we introduce the pricing formula for caplets/floorlets with backward-looking risk-free rates under the one- and two-factor Hull-White model. In particular, we derive the appropriate volatility function for caplets/floorlets to be used in the pricing formula under the two-factor Hull-White model and, implicitly, under the one-factor Hull-White model. Our formulation allows us to obtain, as a particular case, the caplet/floorlet formula under the IBOR environment with a forward-looking rates approach. A numerical analysis is performed to illustrate the main feature of the proposed model and in order to provide a comparison in evaluating caplets/floorlets under both forward-looking and backward-looking approaches.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"31 1","pages":"96 - 110"},"PeriodicalIF":0.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44901450","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 article discusses a new lattice approach for pricing options when the underlying asset price process follows the exponential Lévy model. The article proposes a new lattice method that can be applied to a wide range of Lévy processes. Lévy processes include various models, such as Brownian motion, the compound Poisson process, and the infinite intensity jump model with finite and infinite variation. We introduce a versatile algorithm for option pricing in the exponential Lévy process models. Numerical experiments show that the proposed method accurately calculates options prices.
{"title":"Lattice Approach for Option Pricing under Lévy Processes","authors":"Yoshifumi Muroi, Shintaro Suda","doi":"10.3905/jod.2023.1.185","DOIUrl":"https://doi.org/10.3905/jod.2023.1.185","url":null,"abstract":"This article discusses a new lattice approach for pricing options when the underlying asset price process follows the exponential Lévy model. The article proposes a new lattice method that can be applied to a wide range of Lévy processes. Lévy processes include various models, such as Brownian motion, the compound Poisson process, and the infinite intensity jump model with finite and infinite variation. We introduce a versatile algorithm for option pricing in the exponential Lévy process models. Numerical experiments show that the proposed method accurately calculates options prices.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"31 1","pages":"34 - 48"},"PeriodicalIF":0.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43370429","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 show how a three-strike option portfolio can be used to trade the difference between the instantaneous variance rate and the implied variance rate, the difference between the instantaneous covariation rate and the implied slope, or the difference between the instantaneous variance rate of volatility and the implied convexity. We label each one of these strategies as vol, skew, and smile trades. Our results yield precise financial interpretations of particular measures of the level, slope, and curvature of a BMS implied variance curve. We provide empirical evidence that the average returns of the vol and smile (skew) trades are negative (positive) and that the returns of the skew and smile trades cannot be explained by the CAPM.
{"title":"Vol, Skew, and Smile Trading","authors":"Aşty Al-Jaaf, P. Carr","doi":"10.3905/jod.2023.1.183","DOIUrl":"https://doi.org/10.3905/jod.2023.1.183","url":null,"abstract":"We show how a three-strike option portfolio can be used to trade the difference between the instantaneous variance rate and the implied variance rate, the difference between the instantaneous covariation rate and the implied slope, or the difference between the instantaneous variance rate of volatility and the implied convexity. We label each one of these strategies as vol, skew, and smile trades. Our results yield precise financial interpretations of particular measures of the level, slope, and curvature of a BMS implied variance curve. We provide empirical evidence that the average returns of the vol and smile (skew) trades are negative (positive) and that the returns of the skew and smile trades cannot be explained by the CAPM.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"31 1","pages":"64 - 95"},"PeriodicalIF":0.0,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41339398","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}
Hsuan-Ling Chang, Hung-Wen Cheng, Yifei Lei, J. T. Tsai
This article develops a nonmonotonic pricing kernel with long-run and short-run variance risk premiums for option valuation, with a proposed pricing kernel retaining a U-shaped pattern that significantly improves the fitting ability for index options pricing and implied volatility. The estimation results show that the long-run volatility component is critical in generating the negative risk premium. In the in-sample and out-of-sample tests, the model with the new pricing kernel has more accurate predictions, especially the year around the financial crisis, wherein there is a decrease of an average of 35% root mean square error relative to the benchmark. Considering the bull and bear market states, our model improves implied volatility root mean square error by 23% on average.
{"title":"Option Valuation with Nonmonotonic Pricing Kernel and Embedded Volatility Component Premiums","authors":"Hsuan-Ling Chang, Hung-Wen Cheng, Yifei Lei, J. T. Tsai","doi":"10.3905/jod.2023.1.184","DOIUrl":"https://doi.org/10.3905/jod.2023.1.184","url":null,"abstract":"This article develops a nonmonotonic pricing kernel with long-run and short-run variance risk premiums for option valuation, with a proposed pricing kernel retaining a U-shaped pattern that significantly improves the fitting ability for index options pricing and implied volatility. The estimation results show that the long-run volatility component is critical in generating the negative risk premium. In the in-sample and out-of-sample tests, the model with the new pricing kernel has more accurate predictions, especially the year around the financial crisis, wherein there is a decrease of an average of 35% root mean square error relative to the benchmark. Considering the bull and bear market states, our model improves implied volatility root mean square error by 23% on average.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"30 1","pages":"105 - 127"},"PeriodicalIF":0.0,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49582411","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}
A two-factor approach to asset pricing based on averaged historical and instantaneous volatility defined by a marginal investor’s beliefs and herding behaviour is proposed. For the two-side filtration, backward SDE-defined stochastic dynamics under the risk-neutral probability measure are determined by a target price distribution at given horizon with parameters averaged over a subset of active market agents. For the current price at market equilibrium and instantaneous volatility, the distribution of acceptable price of risk is obtained. The found implied volatility dependencies on strike and maturity are corresponding to the historical data for options by Carr and Wu (2016). The liquidity discount for bonds and options is derived. A generalized solution for the FBSDE and a partial solution for the stochastic terminal conditions are found. The developed two-factor approach is well-suited to deep learning pricing algorithms.
{"title":"Instantaneous and Averaged Volatility in Two-Side Filtration Model of Financial Asset Pricing","authors":"Pavel Levin","doi":"10.3905/jod.2023.1.182","DOIUrl":"https://doi.org/10.3905/jod.2023.1.182","url":null,"abstract":"A two-factor approach to asset pricing based on averaged historical and instantaneous volatility defined by a marginal investor’s beliefs and herding behaviour is proposed. For the two-side filtration, backward SDE-defined stochastic dynamics under the risk-neutral probability measure are determined by a target price distribution at given horizon with parameters averaged over a subset of active market agents. For the current price at market equilibrium and instantaneous volatility, the distribution of acceptable price of risk is obtained. The found implied volatility dependencies on strike and maturity are corresponding to the historical data for options by Carr and Wu (2016). The liquidity discount for bonds and options is derived. A generalized solution for the FBSDE and a partial solution for the stochastic terminal conditions are found. The developed two-factor approach is well-suited to deep learning pricing algorithms.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"31 1","pages":"49 - 63"},"PeriodicalIF":0.0,"publicationDate":"2023-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44288919","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}
In this study, the author investigates the positive spread between option-implied and realized volatility (i.e., variance risk premiums) for dividend versus non-dividend-paying stocks. The author finds, unconditionally, dividend-paying stocks have lower implied volatilities and variance risk premiums compared with nonpayers. However, using subsamples based on implied volatility levels, the author documents that dividend-paying firms have higher conditional variance risk premiums relative to nonpaying firms. Stated differently, for the same level of implied volatility, the spread between implied and future realized volatilities is higher for firms that pay dividends compared with firms that do not. Multivariate tests suggest this result is not explained by option-implied skewness and kurtosis, a proxy for option mispricing, and fundamental risk factors. The results suggest that traders can generate higher risk-adjusted returns from shorting options on dividend-paying firms relative to nonpayers and investors should adjust dividend-paying firms’ implied volatilities down more compared with non-dividend-paying firms’ implied volatilities before performing portfolio optimizations.
{"title":"Biased Implied Volatilities and Dividend-Paying Stocks","authors":"Thaddeus Neururer","doi":"10.3905/jod.2023.1.181","DOIUrl":"https://doi.org/10.3905/jod.2023.1.181","url":null,"abstract":"In this study, the author investigates the positive spread between option-implied and realized volatility (i.e., variance risk premiums) for dividend versus non-dividend-paying stocks. The author finds, unconditionally, dividend-paying stocks have lower implied volatilities and variance risk premiums compared with nonpayers. However, using subsamples based on implied volatility levels, the author documents that dividend-paying firms have higher conditional variance risk premiums relative to nonpaying firms. Stated differently, for the same level of implied volatility, the spread between implied and future realized volatilities is higher for firms that pay dividends compared with firms that do not. Multivariate tests suggest this result is not explained by option-implied skewness and kurtosis, a proxy for option mispricing, and fundamental risk factors. The results suggest that traders can generate higher risk-adjusted returns from shorting options on dividend-paying firms relative to nonpayers and investors should adjust dividend-paying firms’ implied volatilities down more compared with non-dividend-paying firms’ implied volatilities before performing portfolio optimizations.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"30 1","pages":"91 - 103"},"PeriodicalIF":0.0,"publicationDate":"2023-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47245759","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 present a tree-based approach to the Pull-to-Par model for call options on zero-coupon bonds presented in Tomas and Yu (2021). The binomial approach presented is a simple alternative to the original model solution. The model presented converges to the stochastic process given in Tomas and Yu. Some illustrative comparison values to the original model for calls and puts are given. A discussion of American option pricing and the addition of coupons is also presented and illustrated.
{"title":"A Pull-to-Par Binomial Model for Pricing Options on Bonds","authors":"Michael J. Tomas, Jun Yu","doi":"10.3905/jod.2023.1.180","DOIUrl":"https://doi.org/10.3905/jod.2023.1.180","url":null,"abstract":"We present a tree-based approach to the Pull-to-Par model for call options on zero-coupon bonds presented in Tomas and Yu (2021). The binomial approach presented is a simple alternative to the original model solution. The model presented converges to the stochastic process given in Tomas and Yu. Some illustrative comparison values to the original model for calls and puts are given. A discussion of American option pricing and the addition of coupons is also presented and illustrated.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"31 1","pages":"111 - 127"},"PeriodicalIF":0.0,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47220208","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}
Across credit classes for alternative financial scenarios, this study estimates the term structure of credit default swap liquidity premiums (LPs) using dual estimation. The authors find that the term structures of LPs were positively sloped and concave in the first three of the four economic epochs considered but that they became negatively sloped and convex during the Dodd-Frank era. LPs were disproportionally large across the time to maturity for both grades of swaps examined during the financial crisis. In addition, for a given epoch and time to maturity, speculative grade swaps uniformly suffered greater LPs than investment grade default swaps.
{"title":"Term Structure of Credit Default Swap Liquidity Premiums","authors":"Diego Leal, Bryan E. Stanhouse","doi":"10.3905/jod.2023.1.179","DOIUrl":"https://doi.org/10.3905/jod.2023.1.179","url":null,"abstract":"Across credit classes for alternative financial scenarios, this study estimates the term structure of credit default swap liquidity premiums (LPs) using dual estimation. The authors find that the term structures of LPs were positively sloped and concave in the first three of the four economic epochs considered but that they became negatively sloped and convex during the Dodd-Frank era. LPs were disproportionally large across the time to maturity for both grades of swaps examined during the financial crisis. In addition, for a given epoch and time to maturity, speculative grade swaps uniformly suffered greater LPs than investment grade default swaps.","PeriodicalId":34223,"journal":{"name":"Jurnal Derivat","volume":"30 1","pages":"47 - 73"},"PeriodicalIF":0.0,"publicationDate":"2023-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47543206","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：