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The depth and breadth of the market for contingent claims, including exotic options, has expanded dramatically. Regulators have expressed concern regarding the risks of exotics to the financial system, due to the difficulty of hedging these instruments. Recent literature focuses on the difficulties in hedging exotic options, e.g., liquidity risk and other violations of the standard Black‐Scholes model. This article provides insight into hedging problems associated with exotic options: 1) hedging in discrete versus continuous time, 2) transaction costs, 3) stochastic volatility, and 4) non‐constant correlation. The author applies simulation analysis of these problems to a variety of exotics, including Asian options, barrier options, look‐back options, and quanto options.

The volatility of a financial asset is an important input for financial decision‐making in the context of asset allocation, option pricing, and risk management. The authors compare and contrast four approaches to stochastic volatility to determine which is most appropriate to each of these various needs.

This paper studies the performance of commonly employed stochastic volatility and jump models in the consistent pricing of The CBOE Volatility Index (VIX) and The S&P 500 Index (SPX) options. With the existence of active markets for volatility derivatives and options on the underlying instrument, the need for models that are able to price these markets consistently has increased. Although pricing formulas for VIX and vanilla options are now available for commonly used models exhibiting stochastic volatility and/or jumps, it remains to be shown whether these are able to price both markets consistently. This paper fills this vacuum.

In particular, the Heston model, the Heston model with jumps in returns and the Heston model with simultaneous jumps in returns and variance (SVJJ) are jointly calibrated to market quotes on SPX and VIX options together with VIX futures.

The full flexibility of having jumps in both returns and volatility added to a stochastic volatility model is essential. Moreover, we find that the SVJJ model with the Feller condition imposed and calibrated jointly to SPX and VIX options fits both markets poorly. Relaxing the Feller condition in the calibration improves the performance considerably. Still, the fit is not satisfactory, and we conclude that one needs more flexibility in the model to jointly fit both option markets.

Compared to existing literature, we derive numerically simpler VIX option and futures pricing formulas in the case of the SVJ model. Moreover, the paper is the first to study the pricing performance of three widely used models to SPX options and VIX derivatives.

The purpose of this paper is to derive semi‐closed‐form solutions to a wide variety of interest rate derivatives prices under stochastic volatility in affine‐term structure models.

The paper first derives the Frobenius series solution to the cross‐moment generating function, and then inverts the related characteristic function using the Gauss‐Laguerre quadrature rule for the corresponding cumulative probabilities.

This paper values options on discount bonds, coupon bond options, swaptions, interest rate caps, floors, and collars, etc. The valuation approach suggested in this paper is found to be both accurate and fast and the approach compares favorably with some alternative methods in the literature.

Future research could extend the approach adopted in this paper to some non‐affine‐term structure models such as quadratic models.

The valuation approach in this study can be used to price mortgage‐backed securities, asset‐backed securities and credit default swaps. The approach can also be used to value derivatives on other assets such as commodities. Finally, the approach in this paper is useful for the risk management of fixed‐income portfolios.

This paper utilizes a new approach to value many of the most commonly traded interest rate derivatives in a stochastic volatility framework.

The purpose of this article is to propose a detailed methodology to estimate, model and incorporate the non-constant volatility onto a numerical tree scheme, to evaluate a real option, using a quadrinomial multiplicative recombination.

This article uses the multiplicative quadrinomial tree numerical method with non-constant volatility, based on stochastic differential equations of the GARCH-diffusion type to value real options when the volatility is stochastic.

Findings showed that in the proposed method with volatility tends to zero, the multiplicative binomial traditional method is a particular case, and results are comparable between these methodologies, as well as to the exact solution offered by the Black–Scholes model.

The originality of this paper lies in try to model the implicit (conditional) market volatility to assess, based on that, a real option using a quadrinomial tree, including into this valuation the stochastic volatility of the underlying asset. The main contribution is the formal derivation of a risk-neutral valuation as well as the market risk premium associated with volatility, verifying this condition via numerical test on simulated and real data, showing that our proposal is consistent with Black and Scholes formula and multiplicative binomial trees method.

The development of standardized measures of institution‐wide volatility exposures has so far lagged that for measures of asset price and interest‐rate exposure—largely because it is difficult to reconcile the various mathematical models used to value options. Recent mathematical results, however, can be used to construct standardized measures of volatility exposure. We consider here techniques for reconciling “vegas” for financial options valued using stochastic models that may be mathematically inconsistent with each other.

The purpose of this paper is to propose a model for ruin‐contingent life annuity (RCLA) contracts under a jump diffusion model, where the dynamics of volatility is governed by the Heston stochastic volatility framework. The paper aims to illustrate that the proposed jump diffusion process, for both asset price and stochastic volatility, will provide a more realistic pricing model for RCLA contracts in comparison to existing models.

Under the assumption of the deterministic withdrawals, the authors use a partial integro differential equation (PIDE) approach to develop the pricing scheme for the fair value of the lump sum charges of RCLA contracts. Consequently, the authors employ an elegant numerical scheme, finite difference method, for solving the PIDEs for the reference portfolio, as well as the volatility. The findings show that a different pricing behaviour of the RCLA contracts under the authors' model parameters is obtained compared to that in the existing literature.

RCLA pricing in the complete market often underestimates the jump risk and the persistent factor in the volatility process. The authors' generalized model shows how these two random sources of risks can be precisely characterized.

The parameter values used in the numerical analysis require more empirical evidence. Hence, in order for more precise pricing practice, the calibration from real data is needed.

The model, as adopted in this study, for pricing of RCLA contracts should provide a general guideline for the commercialization of this product by insurance companies.

The demand for RCLA contracts as an alternative to the commonly‐practised annuitization option has recently increased, rapidly, among the soon‐to‐retire baby boomers. This paper investigates the fair value of this particular product, which could be beneficial to researchers for a better understanding of the product design.

This is the first research paper which prices the RCLA contracts in the incomplete market. The gap between RCLA contract pricing and studies of jump diffusion models for derivative pricing, in the literature, is therefore filled.

This paper aims to study whether the industry indexes predict the evolution of the broad stock market in the USA.

The study uses industry indexes to predict the equity premium in the USA. It considers several types of predictive models: constant coefficients and constant volatility, drifting coefficients and constant volatility, constant coefficients and stochastic volatility and drifting coefficients and stochastic volatility. The models are estimated through the particle learning algorithm, which is suitable for dealing with the problem that an investor faces in practice, given that it allows the investor to revise the parameters as new information arrives. The individual forecasts are combined based on their past performance.

The results reveal that models exhibit significant predictive ability. The models with constant volatility exhibit better performance, at the statistical level, but the models with stochastic volatility generate higher gains for a mean–variance investor.

This study’s findings are valuable not only for finance researchers but also for private investors and mutual fund managers, who can use these forecasts to improve the performance of their portfolios.

To the best of the knowledge of the author, this is the first paper that uses particle learning and combination of forecasts to predict the equity premium in the USA based on industry indexes. The study shows that the models generate valuable forecasts over the long time span that is considered.

In this paper we make an analysis of KOSPI 200 index options listed in Korea Stock and Futures Exchange whose trading volume is world best these days. We adopt the stochastic volatility model suggested by Heston (1993) for the dynamics of the underlying asset and use EMM to estimate the parameters of option pricing kernel. The SNP distribution of the implied volatility contains AR (2) and ARCH effects, and the skewness of the distribution is much higher than normal distribution. The distribution has thinner left tail and fatter right tail than normal distribution, which is opposite to the case of S&P 500 options market. The result of estimation shows that Implied volatility series of KOSPI 200 options have weak mean reverting property and are almost nonstationary. The correlation coefficient between the implied volatility and returns is estimated to have negligible negative number. These features are also opposite to the case of S&P 500 options market where implied volatility is reported to have strong mean reversion, and the correlation between the implied VIatilIty and retturns is reported to have large negative number.

Cryptocurrency markets are notoriously noisy, but not all markets might behave in the exact same way. Therefore, the aim of this paper is to investigate which one of the cryptocurrency markets contributes the most to the common volatility component inherent in the market.

The paper extracts each of the cryptocurrency's markets' latent volatility using a stochastic volatility model and, subsequently, models their dynamics in a fractionally cointegrated vector autoregressive model. The authors use the refinement of Lien and Shrestha (2009, J. Futures Mark) to come up with unique Hasbrouck (1995, J. Finance) information shares.

The authors’ findings indicate that Bitfinex is the leading market for Bitcoin and Ripple, while Bitstamp dominates for Ethereum and Litecoin. Based on the dominant market for each cryptocurrency, the authors find that the volatility of Bitcoin explains most of the volatility among the different cryptocurrencies.

The authors’ findings are limited by the availability of the cryptocurrency data. Apart from Bitcoin, the data series for the other cryptocurrencies are not long enough to ensure the precision of the authors’ estimates.

To date, only price discovery in cryptocurrencies has been studied and identified. This paper extends the current literature into the realm of volatility discovery. In addition, the authors propose a discrete version for the evolution of a markets fundamental volatility, extending the work of Dias et al. (2018).