Narrow Results

The paper analyzes alternative mathematical techniques, which can be used to derive hedging strategies for credit derivatives in models with totally unexpected default. The stochastic calculus approach is used to establish abstract characterization results for hedgeable contingent claims in a fairly general set-up. In the Markovian framework, we use the PDE approach to show that the arbitrage price and the hedging strategy for an attainable contingent claim can be described in terms of solutions of a pair of coupled PDEs.

We consider reduced-form models for portfolio credit risk with interacting default intensities. In this class of models default intensities are modeled as functions of time and of the default state of the entire portfolio, so that phenomena such as default contagion or counterparty risk can be modeled explicitly. In the present paper this class of models is analyzed by Markov process techniques. We study in detail the pricing and the hedging of portfolio-related credit derivatives such as basket default swaps and collaterized debt obligations (CDOs) and discuss the calibration to market data.

This paper examines the major determinants of a firm's derivatives use for companies listed in Taiwan Stock Exchange in the period from 1997 to 1999. The study finds that the proportion of derivatives use in Taiwan, ranging from 31% to 37%, is comparable to that of the US (35%), but less than that of New Zealand (53%). Firms' derivatives use in Taiwan asymmetrically focuses on currency/forwards derivatives. Industry breakdown illustrates that the electronic industry stands for the heavy user both in terms of number and amount. We show that the vital determinants of a firm's derivatives use are size, the ratio of long-term debt to total debt, the electronic industry dummy, and the export ratio. The fact that firms' derivatives use positively correlated with size and the long-term-debt-to-total-debt ratio implies the capability-willingness hypothesis: only large firms are affordable to engage in derivatives use due to the concern of economies of scale in establishing and maintaining expertise, and these firms demand more derivatives use when they face with high financial risk in debt structure.

Dollar cost averaging (DCA) is a widely employed investment strategy in financial markets. At the same time it is also well documented that such gradual policy is sub-optimal from the point of view of risk averse decision makers with a fixed investment horizon T > 0. However, an explicit strategy that would be preferred by all risk averse decision makers did not yet appear in the literature. In this paper, we give a novel proof for the suboptimality of DCA when (log) returns are governed by Lévy processes and we construct a dominating strategy explicitly. The optimal strategy we propose is static and consists in purchasing a suitable portfolio of path-independent options. Next, we discuss a market governed by a Brownian motion in more detail. We show that the dominating strategy amounts to setting up a portfolio of power options. We provide evidence that the relative performance of DCA becomes worse in volatile markets, but also give some motivation to support its use. We also analyse DCA in presence of a minimal guarantee, explore the continuous setting and discuss the (non) uniqueness of the dominating strategy.

Agricultural futures markets were the backbone of early futures trading and continue to play a vital role in today's global economy. For more than a century following the founding of the Chicago Board of Trade in 1848, the United States dominated the world's futures markets with agricultural commodities such as wheat, corn, oats, and soybeans. Today, the global agricultural futures markets include not only grains but also livestock such as cattle and hogs; dairy products such as milk, butter, and cheese; “soft” or tropical commodities such as cotton, coffee, sugar, and orange juice; and industrial products such as soybean oil, soybean meal, and lumber.

We hereby present an explicit formula for European options on coupon bearing bonds in the Heath–Jarrow–Morton one factor model with non-stochastic volatility. The formula extends the Jamshidian formula for zero-coupon bonds for special form of volatility. Moreover we present a formula for zero-coupon bonds without condition on the volatility. We provide also an explicit way to compute the hedging ratio (Δ) in order to hedge the options individually.

It is known that the market in a Markovian regime-switching model is, in general, incomplete, so not all contingent claims can be perfectly hedged. We show, in this paper, how certain contingent claims are attainable in the regime-switching market using a money market account, a share and a zero-coupon bond. General contingent claims with payoffs depending on both the share price and the state of the regime-switching process are considered. We apply a martingale representation result to show the attainability of a European-style contingent claim. We also extend our analysis to Asian-style and American-style contingent claims.

The hedging of a European-style contingent claim is studied in a continuous-time doubly Markov-modulated financial market, where the interest rate of a bond is modulated by an observable, continuous-time, finite-state, Markov chain and the appreciation rate of a risky share is modulated by a continuous-time, finite-state, hidden Markov chain. The first chain describes the evolution of credit ratings of the bond over time while the second chain models the evolution of the hidden state of an underlying economy over time. Stochastic flows of diffeomorphisms are used to derive some hedge quantities, or Greeks, for the claim. A mixed filter-based and regime-switching Black–Scholes partial differential equation is obtained governing the price of the claim. It will be shown that the delta hedge ratio process obtained from stochastic flows is a risk-minimizing, admissible mean-self-financing portfolio process. Both the first-order and second-order Greeks will be considered.

This paper aims to investigate the return and volatility spillover between world oil prices and the sectoral stock of Pakistan. We estimate a bivariate VAR(1)-AGARCH (1,1) model using weekly data sampled from January 1, 2001 to December 31, 2015. The model results are used to estimate the optimal portfolio weights and hedge ratios. The empirical findings suggest no short-run price transmission between world oil prices and stock sectors of Pakistan Stock Exchange. Only the past unexpected shocks in world oil prices has significant effect on the volatility of sectoral stock returns of Pakistan Stock Exchange, and no volatility spillover exist between world oil price and stock sectors. The optimal portfolio weights and hedge ratios for oil/stock holdings are sensitive to sectors considered. These findings are of great interest for policy makers, hedge fund managers, $i$ investors and market participants.

Alternative approaches to hedging swaptions are explored and tested by simulation. Hedging methods implied by the Black swaption formula are compared with a lognormal forward LIBOR model approach encompassing all the relevant forward rates. The simulation is undertaken within the LIBOR model framework for a range of swaptions and volatility structures. Despite incompatibilities with the model assumptions, the Black method performs equally well as the LIBOR method, yielding very similar distributions for the hedging profit and loss — even at high rehedging frequencies. This result demonstrates the robustness of the Black hedging technique and implies that — being simpler and generally better understood by financial practitioners — it would be the preferred method in practice.

A quantum field theory generalization, Baaquie [1], of the Heath, Jarrow and Morton (HJM) [10] term structure model parsimoniously describes the evolution of imperfectly correlated forward rates. Field theory also offers powerful computational tools to compute path integrals which naturally arise from all forward rate models. Specifically, incorporating field theory into the term structure facilitates hedge parameters that reduce to their finite factor HJM counterparts under special correlation structures. Although investors are unable to perfectly hedge against an infinite number of term structure perturbations in a field theory model, empirical evidence using market data reveals the effectiveness of a low dimensional hedge portfolio.

The paper provides simple and rigorous, albeit fairly general, derivations of valuation formulae for credit default swaptions and credit default index swaptions. Results of this work cover as special cases the pricing formulae derived previously by Jamshidian [Finance and Stochastics8 (2004) 343–371], Pedersen [Quantitative Credit Research (2003)], Brigo and Morini (2005), and Morini and Brigo (2007). Most results presented in this work are completely independent of a particular convention regarding the specification of the fee and protection legs and thus they can also be used for valuation of other credit derivatives that exhibit similar features (for instance, options on CDO tranches). The main tools are a judicious choice of the reference filtration and a suitable specification of the risk-neutral dynamics for the pre-default (loss-adjusted) fair market spread.

In order to dynamize the static Gaussian copula model of portfolio credit risk, we introduce a model filtration made of a reference Brownian filtration progressively enlarged by the default times. This yields a multidimensional density model of default times, where, as opposed to the classical situation of the Cox model, the reference filtration is not immersed into the enlarged filtration. In mathematical terms this lack of immersion means that martingales in the reference filtration are not martingales in the enlarged filtration. From the point of view of financial interpretation this means default contagion, a good feature in the perspective of modeling counterparty wrong-way risk on credit derivatives. Computational tractability is ensured by invariance of multivariate Gaussian distributions through conditioning by some components, the ones corresponding to past defaults. Moreover the model is Markov in an augmented state-space including past default times. After a discussion of different notions of deltas, the model is applied to the valuation of counterparty risk on credit derivatives.

We examine the pricing and hedging of general contracts in an extension of the market model proposed by [B-1995]. We study both problems from the perspectives of the hedger and the counterparty with arbitrary initial endowments. We derive inequalities satisfied by unilateral prices of a contract and we give the range for its fair bilateral prices. Our study hinges on results for backward stochastic differential equations (BSDEs) driven by multi-dimensional continuous martingales obtained in Nie & Rutkowski (2014b). We also derive the pricing partial differential equations (PDEs) for path-independent contingent claims of European style in a Markovian framework.

In this paper, we propose a novel method of hedging path-dependent options in a discrete-time setup. Assuming that prices are given by the Black–Scholes model, we first describe the residual risk when hedging a path-dependent option using only an European option. Then, for a fixed hedging interval, we find the hedging option that minimizes the shortfall risk, which we define as the expectation of the shortfall weighted by some loss function. We illustrate the method using Asian options, but the methodology is applicable to other path-dependent contacts.

How should one construct a portfolio from multiple mean-reverting assets? Should one add an asset to a portfolio even if the asset has zero mean reversion? We consider a position management problem for an agent trading multiple mean-reverting assets. We solve an optimal control problem for an agent with power utility, and present an explicit solution for several important special cases and a semi-explicit solution for the general case. The near-explicit nature of the solution allows us to study the effects of parameter misspecification, and derive a number of properties of the optimal solution.

Understanding mortgage prepayment is crucial for any financial institution providing mortgages, and it is important for hedging the risk resulting from such unexpected cash flows. Here, in the setting of a Dutch mortgage provider, we propose to include nonlinear financial instruments in the hedge portfolio when dealing with mortgages with the option to prepay part of the notional early. Based on the assumption that there is a correlation between prepayment and the interest rates in the market, a model is proposed which is based on a specific refinancing incentive. The linear and nonlinear risks are addressed by a set of tradeable instruments in a static hedge strategy. We will show that a stochastic model for the notional of a mortgage unveils nonlinear risk embedded in a prepayment option. Based on a calibration of the refinancing incentive on a data set of more than thirty million observations, a functional form of the prepayments is defined, which accurately reflects the borrowers’ behavior. We compare this functional form with a fully rational model, where the option to prepay is assumed to be exercised rationally.

We examine how information asymmetry affects a firm's incentive to hedge versus speculate by using foreign currency derivatives. We find a quadratic relation between asymmetric information and a firm's risk management activities. In particular, we find that the firms facing medium level of information asymmetry are more likely to hedge, while firms with very high and low levels of asymmetric information tend to speculate. Moreover, we find that our results hold primary for firms operating in highly competitive industries.

In this paper, we investigate the applicability of the comonotonicity approach in the context of various benchmark models for equities and commodities. Instead of classical Lévy models as in Albrecher et al. we focus on the Heston stochastic volatility model, the constant elasticity of variance (CEV) model and Schwartz’ 1997 stochastic convenience yield model. We show how the technical difficulties of inverting the distribution function of the sum of the comonotonic random vector can be overcome and that the method delivers rather tight upper bounds for the prices of Asian Options in these models, at least for strikes which are not too large. As a by-product the method delivers super-hedging strategies which can be easily implemented.

Derivatives have been blamed in recent years for many financial disasters and there is evidence that disclosure influences hedging activity and corporate value. Nevertheless, standards for the mandatory disclosure of derivatives usage have been very controversial. This paper examines the nature and determinants of voluntary disclosures of currency derivatives usage by large industrial firms under SFAS 107 and has implications for the new derivatives disclosures under SFAS 133. This study documents that, consistent with higher disclosure levels being associated with lower cost of capital and higher shareholder value, firms with higher quality voluntary disclosures have higher market/book value ratios. However, consistent with agency, political, and disclosure cost arguments, industry leaders and firms with higher executive compensation in the form of stock options are more likely to have poor voluntary disclosure. In addition, we do not find any evidence indicating firms with more exposure to currency risk or firms with higher levels of currency derivatives usage provide increased disclosure of derivatives activity.