Search

The increased trading in multi-name financial products has required the development of state-of-the-art multivariate models. These models should be computationally tractable and, at the same time, flexible enough to explain the stylized facts of asset log-returns and of their dependence structure. The popular class of multivariate Lévy models provides a variety of tractable models, but suffers from one major shortcoming: Lévy models can replicate single-name derivative prices for a given time-to-maturity, but not for the whole range of quoted strikes and maturities, especially during periods of market turmoil. Moreover, there is a significant discrepancy between the moment term structure of Lévy models and the one observed in the market. Sato processes on the other hand exhibit a moment term structure that is more in line with empirical evidence and allow for a better replication of single-name option price surfaces. In this paper, we propose a general framework for multivariate models characterized by independent and time-inhomogeneous increments, where the asset log-return processes at unit time are modeled as linear combinations of independent self-decomposable random variables, where at least one self-decomposable random variable is shared by all the assets. As examples, we consider two general subclasses within this new framework, where we assume a normal variance-mean mixture with a one-sided tempered stable mixing density or a difference of one-sided tempered stable laws for the distribution of the risk factors. Particular attention is given to the models' ability to explain the asset dependence structure. A numerical study reveals the advantages of these new types of models. [ABSTRACT FROM AUTHOR]

We show how to compute the expectiles of the risk-neutral distribution from the prices of European call and put options. Empirical properties of these implicit expectiles are studied on a data-set of closing daily prices of FTSE MIB index options. We introduce the interexpectile difference , for , and suggest that it is a natural measure of the variability of the risk-neutral distribution. We investigate its theoretical and empirical properties and compare it with the VIX index computed by CBOE. We also discuss a theoretical comparison with implicit VaR and CVaR introduced in Barone Adesi [J. Risk Financ. Manage., 2016, 9]. [ABSTRACT FROM AUTHOR]

The rough Bergomi model introduced by Bayeret al.[Quant. Finance, 2015, 1–18] has been outperforming conventional Markovian stochastic volatility models by reproducing implied volatility smiles in a very realistic manner, in particular for short maturities. We investigate here the dynamics of the VIX and the forward variance curve generated by this model, and develop efficient pricing algorithms for VIX futures and options. We further analyse the validity of the rough Bergomi model to jointly describe the VIX and the SPX, and present a joint calibration algorithm based on the hybrid scheme by Bennedsenet al.[Finance Stoch., forthcoming]. [ABSTRACT FROM AUTHOR]

The article reports that Foreign exchange (FX) rates confined to a band with barriers is modelled as a stochastic process, where one needs to deal with the boundaries. It mentions that FX option pricing in target zones with attainable boundaries. The basic idea behind option pricing in the presence of boundaries is no different than in the case without boundaries: we must construct a self-financing hedging strategy which replicates the claim at maturity.

We optimize the asset allocation, consumption and bequest decisions of a couple with an uncertain lifetime. The asset menu consists of zero coupon bonds and pure endowments with different maturities, whole life annuities and stocks. The pure endowments pay either fixed or variable benefits, and, similarly to the whole life annuities, are contingent on either a single or a joint lifetime. We model the stock returns and the parameters for the term structure with a vector autoregressive model, thus considering time-varying investment opportunities. To find the optimal solution we use a multi-stage stochastic programming approach, which allows for including complex surrender charges on pure endowments and annuities, as well as transaction costs on stocks and bonds. Our findings indicate that despite high surrender charges, households should invest in a wide combination of life contingent products with different maturities and underlying financial risk. [ABSTRACT FROM AUTHOR]

American options are actively traded worldwide on exchanges, thus making their accurate and efficient pricing an important problem. As most financial markets exhibit randomly varying volatility, in this paper we introduce an approximation of an American option price under stochastic volatility models. We achieve this by using the maturity randomization method known as Canadization. The volatility process is characterized by fast and slow-scale fluctuating factors. In particular, we study the case of an American put with a single underlying asset and use perturbative expansion techniques to approximate its price as well as the optimal exercise boundary up to the first order. We then use the approximate optimal exercise boundary formula to price an American put via Monte Carlo. We also develop efficient control variates for our simulation method using martingales resulting from the approximate price formula. A numerical study is conducted to demonstrate that the proposed method performs better than the least squares regression method popular in the financial industry, in typical settings where values of the scaling parameters are small. Further, it is empirically observed that in the regimes where the scaling parameter value is equal to unity, fast and slow-scale approximations are equally accurate. [ABSTRACT FROM AUTHOR]

In this paper, we propose a general technique to develop first- and second-order closed-form approximation formulas for short-maturity options with random strikes. Our method is based on a change of numeraire and on Malliavin calculus techniques, which allow us to study the corresponding short-maturity implied volatility skew and to obtain simple closed-form approximation formulas depending on the derivative operator. The numerical analysis shows that these formulas are extremely accurate and improve some previous approaches for two-asset and three-asset spread options such as Kirk’s formula or the decomposition method presented in Alòset al.[Energy Risk, 2011,9, 52–57]. This methodology is not model-dependent, and it can be applied to the case of random interest rates and volatilities. [ABSTRACT FROM PUBLISHER]

We develop a switching regime version of the intensity model for credit risk pricing. The default event is specified by a Poisson process whose intensity is modeled by a switching Lévy process. This model presents several interesting features. First, as Lévy processes encompass numerous jump processes, our model can duplicate the sudden jumps observed in credit spreads. Also, due to the presence of jumps, probabilities do not vanish at very short maturities, contrary to models based on Brownian dynamics. Furthermore, as the parameters of the Lévy process are modulated by a hidden Markov chain, our approach is well suited to model changes of volatility trends in credit spreads, related to modifications of unobservable economic factors. [ABSTRACT FROM PUBLISHER]

The article discusses a study on the pricing of corporate debt with finite maturity under Chapter 11 of the U.S. Bankruptcy Code. The study distinguishes the bankruptcy declaring boundary from the bankruptcy boundary enabling the authors to develop a continuous-rime pricing model by optimal stopping theory. The authors proposed a numerical procedure based on the partial differential equation formulations. The model yields higher equity values of optimal bankruptcy declaring boundary.

This paper explores the advantages of pricing American options using the first-passage density of a Brownian motion to a curved barrier. First, we demonstrate that, under this approach, the exact computation of the optimal boundary becomes secondary. Consequently, a simple approximation to the optimal boundary suffices to obtain accurate prices. Moreover, thefirst-passage approachtends to give more accurate prices than theearly-exercise-premium integral representation. We present two ways of implementing the approach. The first is based on an exact representation of the first-passage density. The second exploits themethod of images, which gives us a family of barriers with first-passage densities given in closed form. Both methods are very easy to implement and give accurate prices. In particular, the images-based method is extremely accurate. [ABSTRACT FROM PUBLISHER]

Studies of the term structure of interest rates try to explain the relationship between the yield to maturity on zero-coupon bonds and their time to maturity. Over the years, many theoretical models have been developed to explain the stylized facts of U.S. Treasury yields; however, model comparison, parameter estimation and hypothesis testing remain thorny issues. The purpose of this paper is to show that Bayesian methods and Markov Chain Monte Carlo (MCMC) methods, in particular, may help resolve a number of these problems, especially those related to model comparison. We use MCMC to compare the seminal models of Vasicek and Cox, Ingersoll and Ross (CIR). The most surprising result of our analysis is that one of these two models is almost 50 000 times more likely than the other. In contrast, results in the previous literature have been much more ambiguous because they are based on a variety of goodness-of-fit measures. A Monte Carlo study shows that these results are not spurious: the MCMC method is able to select the correct data generation model, whereas goodness-of-fit measures are virtually indistinguishable regardless of whether the data were generated from Vasicek or CIR. [ABSTRACT FROM AUTHOR]

The article focuses on the comparison between the Asian and European stock option. It says that the underlying asset on which the Asian option is based is equal to a stock with price St in the classical Black-Scholes settings. It adds that the payoff in the European-and American-style option is determined by the underlying price at maturity as compared to the Asian option, which is established by the average underlying price over some pre-set period of time.

This paper extends the literature on Risk-Neutral Valuation Relationships (RNVRs) to derive valuation formulae for options on zero coupon bonds when interest rates are stochastic. We develop Forward-Neutral Valuation Relationships (FNVRs) for the transformed-bounded random walk class. Our transformed-bounded random walk family of forward bond price processes implies that (i) the prices of the zero coupon bonds are bounded below at zero and above at one, and (ii) negative continuously compounded interest rates are ruled out. FNVRs are frameworks for option pricing, where the forward prices of the options are martingales independent of the market prices of risk. We illustrate the generality and flexibility of our approach with models that yield several new closed-form solutions for call and put options on discount bonds. [ABSTRACT FROM PUBLISHER]

In this paper we construct arbitrage-free call price surfaces from observed market data by locally constrained least squares approximations. The algorithm computes derivatives of the call surface accurately so that implied volatility, local volatility and transition probability density can be obtained at no additional cost. Observed input data are afflicted by a price uncertainty due to the bid–ask spread, quote imprecision and non-synchrony and cause an input data risk on the computed call surface and subsequently on the implied volatility surface. We model the input risk and perform an analysis to study and measure the effect of the input risk on the surfaces. With this analysis we can determine the trustworthiness of the computed results and their implications for option pricing a posteriori. [ABSTRACT FROM AUTHOR]

In this work we propose a new multivariate pure jump model. We fully characterize a multivariate Lévy process with finite- and infinite-activity components in positive and negative jumps. This process generalizes the variance gamma process, featuring a ‘stochastic volatility’ effect due to Poisson randomized intensities of positive and negative gamma jumps. Linear and nonlinear dependence is introduced, without restrictions on marginal properties, separately on both positive and negative jumps and on both finite- and infinite-activity jumps. Such a new approach provides greater flexibility in calibrating nonlinear dependence than in other comparable Lévy models in the literature. The model is very tractable and a straightforward multivariate simulation procedure is available. An empirical analysis shows an almost perfect fit of option prices across a span of moneyness and maturities and a very accurate multivariate fit of stock returns in terms of both linear and nonlinear dependence. A sensitivity analysis of multi-asset option prices emphasizes the importance of the proposed new approach for modeling dependence. [ABSTRACT FROM AUTHOR]

In general, geometric additive models are incomplete and the perfect replication of derivatives, in the usual sense, is not possible. In this paper we complete the market by introducing the so-called power-jump assets. Using a static hedging formula, in order to relate call options and power-jump assets, we show that this market can also be completed by considering portfolios with a continuum of call options with different strikes and the same maturity. [ABSTRACT FROM AUTHOR]

The objective of this paper is to develop a generic, yet practical, framework for the construction of Markov models for commodity derivatives. We aim for sufficient richness to permit applications to a broad variety of commodity markets, including those that are characterized by seasonality and by spikes in the spot process. In the first, largely theoretical, part of the paper we derive a series of useful results concerning the low-dimensional Markov representation of the dynamics of an entire term structure of futures prices. Extending previous results in the literature, we cover jump-diffusive models with stochastic volatility as well as several classes of regime-switching models. To demonstrate the process of building models for a specific commodity market, the second part of the paper applies a selection of our theoretical results to the exercise of constructing and calibrating derivatives trading models for USD natural gas. Special attention is paid to the incorporation of empirical seasonality effects in futures prices, in implied volatilities and their 'smile', and in correlations between futures contracts of different maturities. European option pricing in our proposed gas model is closed form and of the same complexity as the Black-Scholes formula. [ABSTRACT FROM AUTHOR]

When comparing standard bond market models with practice we observe that, whereas the literature places no restrictions on the time to maturity of traded bonds, this is actually the case in practice. Hence, standard models ignore the reinvestment risk present in practice when considering contacts with longer time to maturity than the longest bond traded in the market. In this paper we propose a model including this reinvestment risk. We place a restriction on the bonds traded in the market by limiting the time to maturity of traded bonds. At fixed times, new bonds are issued in the market, thus extending the time of maturity of traded bonds. The initial prices of the new bonds issued in the market depend on the information generated by the market and a stochastic variable independent thereof describing the reinvestment risk. In order to quantify and control the reinvestment risk we apply the criterion of risk-minimization. [ABSTRACT FROM AUTHOR]

The article explores the concepts of the Lévy volatility. It notes that is based on the well-established Lévy processes, which are typically known to fit option price surfaces per maturity well, however, not over all the maturities simultaneously. It introduces two kinds of alternative volatilities, the implied Lévy space volatility and the implied Lévy time volatility. Specifications and calculations of these two alternative volatilities are provided. Several charts depicting the functions of these volatilities are also presented.

Barrier options are considered for Asian options using a differential equation method. Solutions are obtained in the form of Fourier series for barriers which expand or contract as they approach maturity. Rigorous bounds are obtained. It is shown that by differentiating with respect to a parameter, solutions for more general payoffs can be obtained. [ABSTRACT FROM AUTHOR]

The present paper addresses the problem of computing implied volatilities of options written on a domestic asset based on implied volatilities of options on the same asset expressed in a foreign currency and the exchange rate. It proposes an original method together with explicit formulae to compute the at-the-money implied volatility, the smile's skew, convexity, and term structure for short maturities. The method is completely free of any model specification or Markov assumption; it only assumes that jumps are not present. We also investigate how the method performs on the particular example of the currency triplet dollar, euro, yen. We find a very satisfactory agreement between our formulae and the market at one week and one month maturities. [ABSTRACT FROM AUTHOR]