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A Primer on Hedging with Stock Index Futures The Journal of Derivatives (IF 0.647) Pub Date : 2022-04-07 Frank J. Fabozzi,Francesco A. Fabozzi
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Option Pricing Models: From Black-Scholes-Merton to Present The Journal of Derivatives (IF 0.647) Pub Date : 2022-03-25 Ahmet K. Karagozoglu
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Applications of FX Derivatives in Active Currency Risk Management The Journal of Derivatives (IF 0.647) Pub Date : 2022-03-21 Frank J. Fabozzi,Suprita Vohra
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Delta-Gamma-Like Hedging with Transaction Cost under Reinforcement Learning Technique The Journal of Derivatives (IF 0.647) Pub Date : 2022-03-16 Wei Xu,Bing Dai
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Wavelet Multiscale and Spillover Analyses of Volatility and Correlation The Journal of Derivatives (IF 0.647) Pub Date : 2022-03-09 Sofiane Aboura
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Handling the Use of Derivatives in Performance Attribution The Journal of Derivatives (IF 0.647) Pub Date : 2022-03-01 Bruce J. Feibel
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SOFR Term Rates from Treasury Repo Pricing The Journal of Derivatives (IF 0.647) Pub Date : 2022-02-15 Wujiang Lou
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The Time Dimension of Volatility: Implications for Option Strategy Design The Journal of Derivatives (IF 0.647) Pub Date : 2022-02-15 Joanne M. Hill
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Pricing Dynamics of Oil Futures with Tail Risk The Journal of Derivatives (IF 0.647) Pub Date : 2022-02-14 Xinglin Yang,Ji Chen,Yiming Xu
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Tail Risk Hedging in a Low-Rate Environment The Journal of Derivatives (IF 0.647) Pub Date : 2022-02-11 Robert L. Harlow,Stefan Hubrich,Sébastien Page
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Taxes and Derivatives: An Investor’s Perspective The Journal of Derivatives (IF 0.647) Pub Date : 2022-02-03 Paul Bouchey,Benjamin T. Hood,Andrea S. Kramer,Clint Talmo
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Is Risk-Neutral Skewness an Indicator of Downside Risk? Evidence from Tail Risk Taking of Hedge Funds The Journal of Derivatives (IF 0.647) Pub Date : 2022-01-18 Thorsten Lehnert
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American Option Pricing and Filtering with a Hidden Regime-Switching Jump Diffusion The Journal of Derivatives (IF 0.647) Pub Date : 2022-01-07 Tak Kuen Siu,Robert J. Elliott
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Do Options Belong in the Portfolios of Individual Investors? The Journal of Derivatives (IF 0.647) Pub Date : 2022-01-06 Victor Haghani,Vladimir Ragulin,James White
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Application of Credit Derivatives in Portfolio Management The Journal of Derivatives (IF 0.647) Pub Date : 2022-01-06 Sameer Kackar,Kelly Rogal
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Term Risk-Free Rates: Methodologies, Challenges, and the Future The Journal of Derivatives (IF 0.647) Pub Date : 2022-01-05 Xi (Figo) Liu,Yudi Bai
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Equity Portfolio Trading with Volatility and Dividend Derivatives The Journal of Derivatives (IF 0.647) Pub Date : 2021-12-23 Radu Tunaru
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Negative WTI Price: What Really Happened and What Can We Learn? The Journal of Derivatives (IF 0.647) Pub Date : 2021-12-23 Lingjie Ma
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Cosine Willow Tree Structure under Lévy Processes with Application to Pricing Variance Derivatives The Journal of Derivatives (IF 0.647) Pub Date : 2021-09-25 Junmei Ma,Wei Xu,Yi Yao
Lévy process models can capture the large price changes on sudden exogenous events and can better demonstrate the high peak and heavy tail characteristics of financial data. The Fourier transformation method is famous for pricing derivatives under the Lévy processes beause of its efficiency, how it separates models from payoff function, and how it handles models with characteristic functions, but it
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Analytical Valuation of Compound Options under Regime-Switching Dynamics The Journal of Derivatives (IF 0.647) Pub Date : 2021-07-30 Michèle Breton,Mbaye Ndoye
We propose an analytical formula for the evaluation of compound options when the underlying asset is described by a two-states Markov regime-switching log-normal model. One specific application of interest of such a formula is the pricing of principal protected callable notes with an early redemption feature. This approach provides practitioners with a Black-Scholes-type formula under a realistic assumption
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Option Pricing with Greed and Fear Factor: The Rational Finance Approach The Journal of Derivatives (IF 0.647) Pub Date : 2021-07-20 Abootaleb Shirvani,Frank J. Fabozzi,Boryana Racheva-Iotova,Svetlozar T. Rachev
In this article, we explain main concepts of prospect theory and cumulative prospect theory within the rational dynamic asset pricing framework. We derive option pricing formulas when asset returns are altered by a generalized prospect theory value function or a modified Prelec’s weighting probability function. We introduce new parametric classes for prospect theory value functions and probability
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A Model-Free Fourier Cosine Method for Estimating the Risk-Neutral Density The Journal of Derivatives (IF 0.647) Pub Date : 2021-07-12 Zhenyu Cui,Zixiao Yu
In this article, we present a new nonparametric method to extract the risk-neutral density from market-observed options prices. The method is based on novelly combining the Fourier cosine series method and the Carr-Madan spanning formula. In contrast to the seminal Breeden-Litzenberger formula, which is based on twice differentiating the options prices with respect to the strikes, our method is based
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Pricing of Adverse Development Covers Using Option Pricing Methods The Journal of Derivatives (IF 0.647) Pub Date : 2021-05-11 Eric Dal Moro
The market for Adverse Development Covers and Loss Portfolio Transfer has been growing in the past few years. Despite this growth, reinsurers are still struggling to define a standard method for pricing such covers. In this context, this article aims at providing an innovative method for pricing such contracts. The proposed method is based on the famous Mack model and fits a Constant Elasticity of
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Cover’s Rebalancing Option with Discrete Hindsight Optimization The Journal of Derivatives (IF 0.647) Pub Date : 2021-04-20 Alex Garivaltis
The author studies T. Cover’s rebalancing option (Ordentlich and Cover 1998) under discrete hindsight optimization in continuous time. The payoff in question is equal to the final wealth that would have accrued to an initial deposit of 1 unit of the numéraire into the best of some finite set of (perhaps levered) rebalancing rules determined in hindsight. A rebalancing rule (or fixed-fraction betting
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Testing and Mapping an Empirical Exercise Boundary for the American Put Option The Journal of Derivatives (IF 0.647) Pub Date : 2021-04-13 Joseph M. Pimbley
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Semi-Analytical Solutions for Barrier and American Options Written on a Time-Dependent Ornstein–Uhlenbeck Process The Journal of Derivatives (IF 0.647) Pub Date : 2021-04-12 Peter Carr,Andrey Itkin
In this article, we develop semi-analytical solutions for the barrier (perhaps, time-dependent) and American options written on the underlying stock that follows a time-dependent Ornstein–Uhlenbeck process with a lognormal drift. Semi-analytical means that given the time-dependent interest rate, continuous dividend and volatility functions, one need to solve a linear (for the barrier option) or nonlinear
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Pricing and Hedging Options on Assets with Options on Related Assets The Journal of Derivatives (IF 0.647) Pub Date : 2021-04-08 Dilip B. Madan,King Wang
The question addressed is the pricing of options on the CBOE Skew Index. The option pricing theory developed partially hedges risk by taking positions in the market for options on a related asset. The option is then priced at the cost of this hedge. The theory is applied to pricing Volatility Index (VIX) options hedged by the SPDR S&P 500 ETF Trust (SPY) options and pricing options on JPMorgan hedged
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Price Discovery in a New Futures Market: Micro E-Mini Index Futures The Journal of Derivatives (IF 0.647) Pub Date : 2021-04-05 Athanasios P. Fassas
This article revisits the role of futures contracts in price discovery, studying one of the most successful product debuts in derivatives markets, the Micro E-mini index futures. These contracts (sized at the one-tenth of their E-mini counterpart value) allow investors to gain a more affordable exposure to the S&P 500, Nasdaq 100, Dow Jones Industrial Average, and Russell 2000 indices. Using intraday
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Evergreen Trees: The Likelihood Ratio Method for Binomial and Trinomial Trees The Journal of Derivatives (IF 0.647) Pub Date : 2021-04-02 Tom P. Davis
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Bias Correction for Bond Option Greeks via Jackknife The Journal of Derivatives (IF 0.647) Pub Date : 2021-03-30 Jinyu Zhang,Kang Gao,Yong Li
The underlying models for bond options are often based on some linear drift functions such that the option Greeks depend crucially on the mean reversion parameters. Substantial estimation bias may arise when these parameters are estimated using standard methods such as maximum likelihood estimation, leading to a bias in estimating the Greeks. To address this issue, following Phillips and Yu (2005)
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An Arbitrage-Free Real-World Model for Fractional Option Prices The Journal of Derivatives (IF 0.647) Pub Date : 2021-03-25 Holger Fink
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A Closed-Form Model-Free Implied Volatility Formula through Delta Families The Journal of Derivatives (IF 0.647) Pub Date : 2020-12-26 Zhenyu Cui,Justin Kirkby,Duy Nguyen,Stephen Taylor
In this article, we derive a closed-form explicit model-free formula for the (Black-Scholes) implied volatility. The method is based on the novel use of the Dirac Delta function, corresponding delta families, and the change of variable technique. The formula is expressed through either a limit or as an infinite series of elementary functions, and we establish that the proposed formula converges to
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A Derivatives Pricing Model with Non-Cash Collateralization The Journal of Derivatives (IF 0.647) Pub Date : 2020-12-14 Kazuhiro Takino
This article proposes a derivatives pricing model with both cash and a non-cash asset posted as collateral for a derivatives contract. We assume that the participant sources funds from the repo market for the posted non-cash collateral. Our pricing formula is based on the investment of the received collaterals. For the pricing formula, we discount the future derivatives value using a combination of
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Model Risk in Risk Analysis for No-Negative-Equity-Guarantees The Journal of Derivatives (IF 0.647) Pub Date : 2020-11-25 Jr-Wei Huang,Sharon S. Yang,Chuang-Chang Chang
Understanding the risk for No-Negative-Equity-Guarantees (NNEGs) requires the proper modeling of the housing return, interest rate, and mortality rate dynamics. This article investigates the model risk for the risk measures of NNEGs by calculating the Value-at-Risk (VaR) and Conditional-Tail-Expectation (CTE) from the provider perspective, with an emphasis on the housing price return model. Therefore
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Jump, Diffusion, and Long-Term Volatility Risks with Incremental Information in VIX Assets The Journal of Derivatives (IF 0.647) Pub Date : 2020-11-23 Sonnan Chen,Yuchi Gu
A reduced-form model is proposed to disentangle the dynamics of positive-jump, diffusion, and long-term risks in VIX assets. A dissection of the three component risks in volatility is undertaken to determine their distinctive dynamics, risk prices, and market information. The dynamics of three component volatility risks play important and distinctive roles in the VIX derivatives market. The risk dissection
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Universal Arbitrage-Free Estimation of State Price Density The Journal of Derivatives (IF 0.647) Pub Date : 2020-11-21 Qi Hu,David Newton
Given the valuable information content of Arrow–Debreu prices, the recovery of a well-behaved state price density is of considerable importance. However, this is a nontrivial task because of data limitation and the complex arbitrage-free constraints. In this article, the authors develop a more effective linear programming support vector machine estimator for state price density, which incorporates
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Optimal Volatility Dependent Derivatives in the Stochastic Volatility Model The Journal of Derivatives (IF 0.647) Pub Date : 2020-11-20 Artem Dyachenko,Marc Oliver Rieger
We consider derivatives that maximize an investor’s expected utility in the stochastic volatility model. We show that the optimal derivative that depends on the stock and its variance significantly outperforms the optimal derivative that depends on the stock only. Such derivatives yield a much higher certainty equivalent return. This result implies that investors could benefit from structured financial
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Can the Improved CMBO Strategies Beat the CMBO Index? The Journal of Derivatives (IF 0.647) Pub Date : 2020-11-12 Wei-Han Liu,Jow-Ran Chang
The authors aim to improve the CMBO strategy, a covered-call strategy based on the Chicago Board of Exchange Covered Combo (CMBO) Index. They modify the major issues that determine risk and return: aggregate market status and the degree of moneyness of options. The empirical analyses indicate that the four CMBO strategy portfolios they designed, with their respective degrees of moneyness of options
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An Arbitrage-Free Interpolation of Class C2 for Option Prices The Journal of Derivatives (IF 0.647) Pub Date : 2020-11-12 Fabien Le Floc’h
This article presents simple formulae for the local variance gamma model of Carr and Nadtochiy (2017), extended with a piecewise-linear local variance function. The new formulae allow us to calibrate the model efficiently to market option quotes. On a small set of quotes, exact calibration is achieved under one millisecond. This effectively results in an arbitrage-free interpolation of class . The
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Analytical Valuation of Exotic Double Barrier Options The Journal of Derivatives (IF 0.647) Pub Date : 2020-11-11 Jui-Jane Chang,Hui-Ming Pai,Ting-Pin Wu
This article derives the bivariate joint probability distribution functions of a geometric Brownian motion and the extreme values of another geometric Brownian. Based on the probability distribution functions, the authors develop the analytical pricing formulas of three exotic double barrier options (DBOs) with continuously monitored barriers, including rainbow DBOs, protected DBOs, and protected rainbow
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Pricing Discretely Monitored Barrier Options under Markov Processes through Markov Chain Approximation The Journal of Derivatives (IF 0.647) Pub Date : 2020-11-10 Zhenyu Cui,Stephen Taylor
The authors propose an explicit closed-form approximation formula for the price of discretely monitored single or double barrier options with an underlying asset that evolves according to a one-dimensional Markov process, which includes diffusion and jump-diffusion processes. The prices and Greeks of a discretely monitored double barrier option are explicitly expressed in terms of rudimentary matrix
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A Bivariate Lattice Model to Compute Risk Measures in Life Insurance Policies The Journal of Derivatives (IF 0.647) Pub Date : 2020-11-10 Massimo Costabile
This article considers the problem of computing risk measures in a life insurance context by means of a lattice-based approach. The main advantage of the proposed model relies on the fact that the dynamics of the risk factors may be approximated by a unique lattice along the whole time horizon, thus guaranteeing the same computational cost of a standard pricing problem. This allows the author to develop
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The Premium Reduction of European, American, and Perpetual Log Return Options The Journal of Derivatives (IF 0.647) Pub Date : 2020-11-04 Stephen Taylor,Jan Vecer
Traditional plain vanilla options may be regarded as contingent claims whose value depends upon the simple returns of an underlying asset. These options have convex payoffs, and as a consequence of Jensen’s inequality, their prices increase as a function of maturity in the absence of interest rates. This results in long-dated call option premia being excessively expensive in relation to the fraction
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The Free Boundary For The American Put Option The Journal of Derivatives (IF 0.647) Pub Date : 2020-08-29 Thomas Little
The free boundary of the American put option is analytically characterized via new and exact formulae. New accurate short-time asymptotics are an immediate corollary of these analytical results. The free boundary is also represented formulaically throughout all tenors by a simple two-parameter generalized Gaussian functional form. TOPICS:Options, fundamental equity analysis, statistical methods Key
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Semi-Closed Form Prices of Barrier Options in the Time-Dependent CEV and CIR Models The Journal of Derivatives (IF 0.647) Pub Date : 2020-07-10 Peter Carr, Andrey Itkin, Dmitry Muravey
The authors continue a series of articles where prices of the barrier options written on the underlying, whose dynamics follow a one-factor stochastic model with time-dependent coefficients and the barrier, are obtained in semi-closed form; see Carr and Itkin (2020) and Itkin and Muravey (2020). This article extends this methodology to the Cox–Ingersoll–Ross model for zero-coupon bonds and to the constant
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Editor’s Letter The Journal of Derivatives (IF 0.647) Pub Date : 2020-05-31 Joseph M. Pimbley
I’m pleased to write that The Journal of Derivatives will publish its special issue in the next quarter: Fall 2020. Speaking for our publisher, the guest editors, and myself, we’re proud to bring this fusion of two great fields to our readers. The guest editors for the “Physics and Financial Derivatives” special issue are Andrey Itkin (also a JOD board member), Alexander Bogdanov, and Alex Lipton.
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Quantum Option Pricing and Quantum Finance The Journal of Derivatives (IF 0.647) Pub Date : 2020-05-28 Sergio Focardi, Frank J. Fabozzi, Davide Mazza
In this article, the authors discuss the use of quantum probability, that is, the probability theory of quantum mechanics, for option pricing and for finance in general. The authors discuss the motivations for applying quantum probability to finance. The critical issues are replacing random variables with operators, self-reflexivity of markets, and the existence of incompatible observations. The authors
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Model-Free Backward and Forward Nonlinear PDEs for Implied Volatility The Journal of Derivatives (IF 0.647) Pub Date : 2020-04-29 Peter Carr, Andrey Itkin, Sasha Stoikov
The authors derive backward and forward nonlinear partial differential equations that govern the implied volatility of a contingent claim whenever the latter is well defined. This would include at least any contingent claim written on a positive stock price whose payoff at a possibly random time is convex. The authors also discuss suitable initial and boundary conditions for those partial differential
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Risk Metrics Evaluation for Variable Annuities with Various Guaranteed Benefits The Journal of Derivatives (IF 0.647) Pub Date : 2020-04-28 Bing Dong, Jindong Wang, Wei Xu
Variable annuities (VA) are popularly traded around the world. Thus, the risk metrics for VAs are critical in risk management, reserves, and risk-based capital calculation for insurance companies. However, there is no efficient method to compute these metrics of VAs with various benefits, except for nested simulations. In this article, we apply a derivative pricing technique, the willow tree, to solve
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QLBS: Q-Learner in the Black-Scholes(-Merton) Worlds The Journal of Derivatives (IF 0.647) Pub Date : 2020-04-25 Igor Halperin
This article presents a discrete-time option pricing model that is rooted in reinforcement learning (RL), and more specifically in the famous Q-Learning method of RL. We construct a risk-adjusted Markov Decision Process for a discrete-time version of the classical Black-Scholes-Merton (BSM) model, where the option price is an optimal Q-function, while the optimal hedge is a second argument of this
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Physics and Derivatives: Effective-Potential Path-Integral Approximations of Arrow-Debreu Densities The Journal of Derivatives (IF 0.647) Pub Date : 2020-04-25 Luca Capriotti, Ruggero Vaia
The authors show how effective-potential path-integrals methods, stemming from a simple and nice idea originally due to Feynman and successfully employed in physics for a variety of quantum thermodynamics applications, can be used to develop an accurate and easy-to-compute semianalytical approximation of transition probabilities and Arrow-Debreu densities for arbitrary diffusions. The authors illustrate
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Information Content of Options Trading Prior to Dividend Initiations The Journal of Derivatives (IF 0.647) Pub Date : 2020-04-25 Qin Emma Wang
This article utilizes options markets to determine the information content of dividend initiation announcements. Pre-event informed options trading, measured by abnormal implied volatility spread and skew, predicts the cumulative abnormal returns around dividend initiation announcements. Options trading is more informative on dividend initiation announcement returns when the options market is more
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Widening the Range of Underlyings for Derivatives Pricing with QUAD by Using Finite Difference to Calculate Transition Densities—Demonstrated for the No-Arbitrage SABR Model The Journal of Derivatives (IF 0.647) Pub Date : 2020-04-23 Haozhe Su, David P. Newton
The QUAD method is a fast, flexible numerical pricing technique, widely applicable to many option types in its QUAD I and QUAD II versions where the underlying process has a closed-form density function or characteristic function. In its most advanced version, QUAD III, sacrificing only a little speed, it retains all the flexibility and applicability of earlier versions while covering an even greater
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Closed-Form Solution for Defaultable Bond Options under a Two-Factor Gaussian Model for Risky Rates Modeling The Journal of Derivatives (IF 0.647) Pub Date : 2020-04-21 Vincenzo Russo, Rosella Giacometti, Frank J. Fabozzi
In this article, the authors provide a closed-form solution for defaultable bond options under a two-factor Gaussian model for risky rates. The key feature of the proposed stochastic model is the introduction of two stochastic dynamics to address the behavior of both risk-free interest rates and credit spreads where the two sources of risk are correlated. Moreover, the model can match exactly the term
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Pricing of Basket Options by Conditioning and Moment Matching The Journal of Derivatives (IF 0.647) Pub Date : 2020-04-17 Ping Wu, Hui Lin
The price of basket options can be represented as an exact analytical part and an approximate part by using a conditional variable. The first part is calculated by conditioning on the price process of the underlying asset and the second part is calculated by moment matching approach. In order to calculate the second part, we find a new single random variable, which has an analytically known distribution
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Option Pricing with Mixed Lévy Subordinated Price Process and Implied Probability Weighting Function The Journal of Derivatives (IF 0.647) Pub Date : 2020-04-16 Abootaleb Shirvani, Yuan Hu, Svetlozar T. Rachev, Frank J. Fabozzi
It is essential to incorporate the impact of investor behavior when modeling the dynamics of asset returns. In this article, we reconcile behavioral finance and rational finance by incorporating investor behavior within the framework of dynamic asset pricing theory. To include the views of investors, we employ the method of subordination that has been proposed in the literature by including business
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An Approximate Swaption Formula in Heath-Jarrow-Morton Models The Journal of Derivatives (IF 0.647) Pub Date : 2020-03-27 Hideharu Funahashi
This article provides an analytical approximation formula for a swaption price when the instantaneous forward rate follows a Heath–Jarrow–Morton (HJM) model. The author’s approximation strategy, based on the chaos expansion approximation, is to replicate the probability density function of the complex quasi-Gaussian process from a simpler one, which has a semi-closed form solution. It is not restricted
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Analytically Deriving Risk-Neutral Densities from Volatility Smiles The Journal of Derivatives (IF 0.647) Pub Date : 2020-02-26 Fumio Hayashi
This article develops a method for analytically deriving RNDs (risk-neutral densities) of future asset prices from volatility smiles. It extends an existing analytical method, which is for volatility smiles with respect to the strike price, to cover smiles with respect to option delta. A worked-out example on currency options shows that the analytically derived RNDs are free of approximation errors
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How Do Options Affect the Volatility of the Underlying Equity Market? Evidence from the Introduction of Weekly Options The Journal of Derivatives (IF 0.647) Pub Date : 2020-02-26 Yuan Wen
This article investigates how options affect the volatility of the underlying equity market by using a quasi-natural experiment—the introduction of weekly options on individual stocks. The author examines the change in crash risk surrounding the introduction of weekly options by using a difference-in-difference approach that incorporates a control sample identified through propensity score matching
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Physics and Derivatives: On Three Important Problems in Mathematical Finance The Journal of Derivatives (IF 0.647) Pub Date : 2020-02-20 Alexander Lipton, Vadim Kaushansky
In this article, we use recently developed extension of the classical heat potential method in order to solve three important but seemingly unrelated problems of financial engineering: (a) American put pricing, (b) default boundary determination for the structural default problem, and (c) evaluation of the hitting time probability distribution for the general time-dependent Ornstein–Uhlenbeck process