Vulnerable options,risky corporate bond,and credit spread

In the current literature, the focus of credit‐risk analysis has been either on the valuation of risky corporate bond and credit spread or on the valuation of vulnerable options, but never both in the same context. There are two main concerns with existing studies. First, corporate bonds and credit spreads are generally analyzed in a context where corporate debt is the only liability of the firm and a firm’s value follows a continuous stochastic process. This setup implies a zero short‐term spread, which is strongly rejected by empirical observations. The failure of generating non‐zero short‐term credit spreads may be attributed to the simplified assumption on corporate liabilities. Because a corporation generally has more than one type of liability, modeling multiple liabilities may help to incorporate discontinuity in a firm’s value and thereby lead to realistic credit term structures. Second, vulnerable options are generally valued under the assumption that a firm can fully pay off the option if the firm’s value is above the default barrier at the option’s maturity. Such an assumption is not realistic because a corporation can find itself in a solvent position at option’s maturity but with assets insufficient to pay off the option. The main contribution of this study is to address these concerns. The proposed framework extends the existing equity‐bond capital structure to an equity‐bond‐derivative setting and encompasses many existing models as special cases. The firm under study has two types of liabilities: a corporate bond and a short position in a call option. The risky corporate bond, credit spreads, and vulnerable options are analyzed and compared with their counterparts from previous models. Numerical results show that adding a derivative type of liability can lead to positive short‐term credit spreads and various shapes of credit‐spread term structures that were not possible in previous models. In addition, we found that vulnerable options need not always be worth less than their default‐free counterparts. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:301–327, 2001     

The effect of multiple listings on the bid–ask spread in option markets: The case of Montreal Exchange

In this article, we examine the effect of multiple listings of options on their bid–ask spread, by comparing options contracts listed only on the Montreal Exchange with those interlisted on that exchange and on a U.S. exchange as well. Using a statistical procedure adapted to panel data and two models for the determination of the bid–ask spread, we find that the bid–ask spreads of Montreal options interlisted in U.S. markets are narrower than those of non‐interlisted options. That advantage tends to disappear, however, with an increase in option price and to increase with its volatility, but is not affected by the volume of transactions in the option market. The analysis also shows that interlisting may result in time lags in the convergence of quotes between Montreal and the U.S. markets. Moreover, our evidence shows that with interlisting, volume shifts to the option market where trading in the underlying security is concentrated, irrespective of the location where the option was first introduced. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:939–957, 2002     

An Analytic Solution for Interest Rate Swap Spreads

This paper argues that liquidity differences between government securities and short–term Eurodollar borrowings account for interest rate swap spreads. It then models the convenience of liquidity as a linear function of two mean–reverting state variables and values it. The interest rate swap spread for a swap of particular maturity is the annuitized equivalent of this value. It has a closed form solution: a simple integral. Special cases examined include the Vasicek and Cox–Ingersoll–Ross one–factor term structure models. Numerical values for the parameters in both special cases illustrate that many realistic ‘swap spread term structures’ can be replicated. Model parameters are estimated using weekly data on the term structure of swap spreads from several countries. The model fits the data well.     

Delivery risk and the hedging role of options

Multiple delivery specifications exist on nearly all commodity futures contracts. Sellers typically are allowed to deliver any of several grades of the underlying commodity and at any of several locations. On the delivery day, the futures price as such needs not converge to the spot price of the par‐delivery grade at the par‐delivery location, thereby imposing an additional delivery risk on hedgers. This article derives the optimal hedging strategy for a risk‐averse hedger in the presence of delivery risk. In particular, it is shown that the hedger optimally uses options on futures for hedging purposes. This article provides a rationale for the hedging role of options when futures markets allow for multiple delivery specifications. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:339–354, 2002     

Valuation of futures and commodity options with information costs

In this article, futures and commodity options are analyzed in the context of Merton's (1987) model of capital market equilibrium with incomplete information. First, following Dusak (1973) and Black (1976), the conditions under which Merton's model can be applied to the valuation of forward and futures contracts are proposed. Then an application to futures markets is given. We provide a partial differential equation and the formulas for European commodity options, futures contracts, and American options in the same context. The models are simulated and compared to standard models with no information costs. We find that model prices are not significantly different from standard model prices. However, our models correct for some pricing biases in standard models. In particular, they reduce the overvaluation bias for European and American commodity options. It seems that the costs of gathering and processing information regarding the option and its underlying asset play a role in explaining the biases observed in standard models. This work can be applied to other futures markets. © 1999 John Wiley & Sons, Inc. Jrl Fut Mark 19: 645–664, 1999     

Stochastic Volatility Corrections for Interest Rate Derivatives

We study simple models of short rates such as the Vasicek or CIR models, and compute corrections that come from the presence of fast mean-reverting stochastic volatility. We show how these small corrections can affect the shape of the term structure of interest rates giving a simple and efficient calibration tool. This is used to price other derivatives such as bond options. The analysis extends the asymptotic method developed for equity derivatives in Fouque, Papanicolaou, and Sircar (2000b) . The assumptions and effectiveness of the theory are tested on yield curve data.     

When trading options is not the only option: The effects of single-stock futures trading on options market quality

We use the 2008 short-selling ban to examine the impact of single-stock futures (SSFs) trading on options market quality. We show that there is a substitution effect between options trading and SSFs trading during the ban period. In addition, our results show that SSFs trading had a significant effect in narrowing the bid-ask spreads of options contracts. Moreover, compared to stocks without SSFs, stocks with SSFs were less likely to violate put-call parity during the ban period. Our results suggest that SSFs trading helps mitigate the negative effect of the short-selling ban on options market quality documented in the literature.     

The information content of implied volatility in agricultural commodity markets

In this article we compare the incremental information content of lagged implied volatility to GARCH models of conditional volatility for a collection of agricultural commodities traded on the New York Board of Trade. We also assess the relevance of the additional information provided by the implied volatility in a risk management framework. It is first shown that past squared returns only marginally improve the information content provided by the lagged implied volatility. Secondly, value‐at‐risk (VaR) models that rely exclusively on lagged implied volatility perform as well as VaR models where the conditional variance is modelled according to GARCH type processes. These results indicate that the implied volatility for options on futures contracts in agricultural commodity markets provides relevant volatility information that can be used as an input to VaR models. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:441–454, 2003     

Pricing Options On Risky Assets In A Stochastic Interest Rate Economy1

This paper studies contingent claim valuation of risky assets in a stochastic interest rate economy. the model employed generalizes the approach utilized by Heath, Jarrow, and Morton (1992) by imbedding their stochastic interest rate economy into one containing an arbitrary number of additional risky assets. We derive closed form formulae for certain types of European options in this context, notably call and put options on risky assets, forward contracts, and futures contracts. We also value American contingent claims whose payoffs are permitted to be general functions of both the term structure and asset prices generalizing Bensoussan (1984) and Karatzas (1988) in this regard. Here, we provide an example where an American call's value is well defined, yet there does not exist an optimal trading strategy which attains this value. Furthermore, this example is not pathological as it is a generalization of Roll's (1977) formula for a call option on a stock that pays discrete dividends.     

The Relation Between Market Liquidity and Anonymity in the Presence of Tick Size Constraints

In February 2004, the Sydney Futures Exchange removed broker identifiers from the electronic limit order book for interest rate futures contracts, with the stated objective of maintaining transparency and improving market participation and liquidity. We show how the Exchange's aims were generally met by documenting an increase in volume and frequency of trades and a decline in time‐weighted quoted spreads. Although daily effective spreads do not decline, intraday analysis demonstrates that there are improvements in effective spreads which are concentrated to those points in time where the bid–ask spread is not constrained by the size of the minimum tick, and where information asymmetries are present. © 2012 Wiley Periodicals, Inc. Jrl Fut Mark 34:56–73, 2014     

The pricing of stock index futures spreads at contract expiration

This paper conducts an empirical analysis of the mispricing of calendar spreads for stock index futures. Using recent data drawn from the Sydney Futures Exchange, a sharp increase in the magnitude of spread mispricing immediately prior to maturity of the near contract is documented. This pattern in mispricing is related to a sharp decline in open interest in the near contract and an increase in open interest in the deferred contract. Further, the direction of mispricing of the near and deferred contracts are more likely to move in opposite directions as the near contract approaches maturity. These findings are consistent with the hypothesis that traders seeking to roll‐over their positions from near to deferred futures contracts close to maturity increase the magnitude of spread mispricing. © 2002 Wiley Periodicals, Inc. Jrl Fut Mark 22:451–469, 2002     

TIME‐CHANGED ORNSTEIN–UHLENBECK PROCESSES AND THEIR APPLICATIONS IN COMMODITY DERIVATIVE MODELS

This paper studies subordinate Ornstein–Uhlenbeck (OU) processes, i.e., OU diffusions time changed by Lévy subordinators. We construct their sample path decomposition, show that they possess mean‐reverting jumps, study their equivalent measure transformations, and the spectral representation of their transition semigroups in terms of Hermite expansions. As an application, we propose a new class of commodity models with mean‐reverting jumps based on subordinate OU processes. Further time changing by the integral of a Cox–Ingersoll–Ross process plus a deterministic function of time, we induce stochastic volatility and time inhomogeneity, such as seasonality, in the models. We obtain analytical solutions for commodity futures options in terms of Hermite expansions. The models are consistent with the initial futures curve, exhibit Samuelson's maturity effect, and are flexible enough to capture a variety of implied volatility smile patterns observed in commodities futures options.     

A cointegrated commodity pricing model

We propose a commodity pricing model that extends the Gibson–Schwartz two‐factor model to incorporate the effect of linear relations among commodity spot prices, and provide a condition under which such linear relations represent cointegration. We derive futures and call option prices for the proposed model, and indicate that, unlike in Duan and Pliska (2004), the linear relations among commodity prices should affect commodity derivative prices, even when the volatilities of commodity returns are constant. Using crude oil and heating oil market data, we estimate the model and apply the results to the hedging of long‐term futures using short‐term ones.     

A STRUCTURAL RISK‐NEUTRAL MODEL FOR PRICING AND HEDGING POWER DERIVATIVES

We develop a structural risk‐neutral model for energy market modifying along several directions the approach introduced in Aïd et al. In particular, a scarcity function is introduced to allow important deviations of the spot price from the marginal fuel price, producing price spikes. We focus on pricing and hedging electricity derivatives. The hedging instruments are forward contracts on fuels and electricity. The presence of production capacities and electricity demand makes such a market incomplete. We follow a local risk minimization approach to price and hedge energy derivatives. Despite the richness of information included in the spot model, we obtain closed‐form formulae for futures prices and semiexplicit formulae for spread options and European options on electricity forward contracts. An analysis of the electricity price risk premium is provided showing the contribution of demand and capacity to the futures prices. We show that when far from delivery, electricity futures behave like a basket of futures on fuels.     

The Valuation of American Options on Multiple Assets

In this paper we provide valuation formulas for several types of American options on two or more assets. Our contribution is twofold. First, we characterize the optimal exercise regions and provide valuation formulas for a number of American option contracts on multiple underlying assets with convex payoff functions. Examples include options on the maximum of two assets, dual strike options, spread options, exchange options, options on the product and powers of the product, and options on the arithmetic average of two assets. Second, we derive results for American option contracts with nonconvex payoffs, such as American capped exchange options. For this option we explicitly identify the optimal exercise boundary and provide a decomposition of the price in terms of a capped exchange option with automatic exercise at the cap and an early exercise premium involving the benefits of exercising prior to reaching the cap. Besides generalizing the current literature on American option valuation our analysis has implications for the theory of investment under uncertainty. A specialization of one of our models also provides a new representation formula for an American capped option on a single underlying asset.     

Does adverse selection affect bid–ask spreads for options?

This study examines two different option markets to test whether differences in the level of adverse selection faced by market makers affect the size of bid–ask spreads. The data are from bank‐issued options that trade on EuWax, where market makers face little adverse selection and traditional options that trade on EuRex. The results support the hypothesis that the adverse selection component of the bid–ask spread is important, as options on EuWax have lower bid–ask spreads than comparable options on EuRex. The results show that the adverse selection component represents at least half of the overall bid–ask spreads on the traditional EuRex. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:417–437, 2008     

Identifying the Factors that Affect Interest‐Rate Swap Spreads: Some Evidence from the United States and the United Kingdom

We assess the ability of the factors proposed in previous research to account for the stochastic evolution of the term structure of the U.S. and U.K. swap spreads. Using as factor proxies the level, volatility, and slope of the zero‐coupon government yield curve as well as the Treasury‐bill—London Interbank Offer Rate (LIBOR) spread and the corporate bond spread, we identify a procyclical behavior for the short‐maturity U.S. swap spreads and a countercyclical behavior for longer maturity U.S. swap spreads. Liquidity and corporate bond spreads are also significant, but their importance varies with maturity. The liquidity premium is more important for short‐maturity swap spreads, although the corporate bond spread affects long‐maturity swap spreads. For the United Kingdom, swap spreads are countercyclical across maturities. In addition, we find that shocks to the liquidity premium are more significant for long‐maturity swaps and that the links between corporate bond markets and swap markets are much stronger than in the United States. When we look at the links between U.S. and U.K. swap markets, we identify a significant influence of the U.S. factors on the U.K. swap spreads across maturities. © 2001 John Wiley & Sons, Inc. Jrl Fut Mark 21:737–768, 2001     

Bid‐ask spreads,volatility, quote revisions,and trades of thinly traded futures contracts

We investigate intraday bid‐ask spreads (BAS), volatility, and trading activity of thinly traded equity index futures contracts on the Singapore Exchange. Contrary to previous findings, we find a rather flat BAS pattern during the trading day. However, consistent with past findings, an increase in risk widens the spread and a higher trading activity reduces it. When trading occurs in a day, spreads are reduced. No significant difference in volatility between days with and without trades was detected. When trades occur, quote revisions increase, and it is positively related to the number of trades. An increase in the number of quote revisions increases the likelihood of a transaction, and when quotes are current, revisions that are accompanied by trades carry new information. We provide evidence that contracts that are thinly traded may possess liquidity attributes as long as their price quotes remain current. © 2003 Wiley Periodicals, Inc. Jrl Fut Mark 23:455–486, 2003     

Hedging in Futures and Options Markets with Basis Risk

This paper analyzes the hedging decisions for firms facing price and basis risk. Two conditions assumed in most models on optimal hedging are relaxed. Hence, (i) the spot price is not necessarily linear in both the settlement price and the basis risk and (ii) futures contracts and options on futures at different strike prices are available. The design of the first‐best hedging instrument is first derived and then it is used to examine the optimal hedging strategy in futures and options markets. The role of options as useful hedging tools is highlighted from the shape of the first‐best solution. © 2002 John Wiley & Sons, Inc. Jrl Fut Mark 22:59–72, 2002     

Derivative pricing model and time‐series approaches to hedging: A comparison

This research compares derivative pricing model and statistical time‐series approaches to hedging. The finance literature stresses the former approach, while the applied economics literature has focused on the latter. We compare the out‐of‐sample hedging effectiveness of the two approaches when hedging commodity price risk using futures contracts. For various methods of parameter estimation and inference, we find that the derivative pricing models cannot out‐perform a vector error‐correction model with a GARCH error structure. The derivative pricing models' unpalatable assumption of deterministically evolving futures volatility seems to impede their hedging effectiveness, even when potentially foresighted optionimplied volatility term structures are employed. © 2005 Wiley Periodicals, Inc. Jrl Fut Mark 25:613–641, 2005