Spot and forward volatility in foreign exchange

This paper investigates the empirical relation between spot and forward implied volatility in foreign exchange. We formulate and test the forward volatility unbiasedness hypothesis, which may be viewed as the volatility analogue to the extensively researched hypothesis of unbiasedness in forward exchange rates. Using a new dataset of spot implied volatility quoted on over-the-counter currency options, we compute the forward implied volatility that corresponds to the delivery price of a forward contract on future spot implied volatility. This contract is known as a forward volatility agreement. We find strong evidence that forward implied volatility is a systematically biased predictor that overestimates movements in future spot implied volatility. This bias in forward volatility generates high economic value to an investor exploiting predictability in the returns to volatility speculation and indicates the presence of predictable volatility term premiums in foreign exchange.     

Commodity price modelling that matches current observables: a new approach

We develop a stochastic model of the spot commodity price and the spot convenience yield such that the model matches the current term structure of forward and futures prices, the current term structure of forward and futures volatilities, and the inter-temporal pattern of the volatility of the forward and futures prices. We let the underlying commodity price be a geometric Brownian motion and we let the spot convenience yield have a mean-reverting structure. The flexibility of the model, which makes it possible to simultaneously achieve all these goals, comes from allowing the volatility of the spot commodity price, the speed of mean-reversion parameter, the mean-reversion parameter, and the diffusion parameter of the spot convenience yield all to be time-varying deterministic functions.     

Spot price modeling and the valuation of electricity forward contracts: The role of demand and capacity

We propose a model where wholesale electricity prices are explained by two state variables: demand and capacity. We derive analytical expressions to price forward contracts and to calculate the forward premium. We apply our model to the PJM, England and Wales, and Nord Pool markets. Our empirical findings indicate that volatility of demand is seasonal and that the market price of demand risk is also seasonal and positive, both of which exert an upward (seasonal) pressure on the price of forward contracts. We assume that both volatility of capacity and the market price of capacity risk are constant and find that, depending on the market and period under study, it could either exert an upward or downward pressure on forward prices. In all markets we find that the forward premium exhibits a seasonal pattern. During the months of high volatility of demand, forward contracts trade at a premium. During months of low volatility of demand, forwards can either trade at a relatively small premium or, even in some cases, at a discount, i.e. they exhibit a negative forward premium.     

Identifying volatility risk premia from fixed income Asian options

Fixed income options are frequently adopted by companies to hedge interest rate risk. Their payoff dependence on the cumulative short-term rate makes them particularly informative about interest rate volatility risk. Based on a joint dataset of bonds and Asian interest rate options, we study the interrelations between bond and volatility risk premia in a major emerging fixed income market. We propose a dynamic term structure model that generates an incomplete market compatible with a preliminary empirical analysis of the dataset. Approximation formulas for at-the-money Asian option prices avoid the use of computationally intensive Fourier transform methods, allowing for an efficient implementation of the model. The model generates a bond risk premium strongly correlated with a widely accepted emerging market benchmark index (EMBI-Global), and a negative volatility risk premium, consistent with the use of Asian options as insurance in this market.     

Pricing of discount bonds with a Markov switching regime

We consider a Markov switching regime and price a discount bond using a CIR-type short rate model. An explicit formula is obtained for the bond price which includes the solution of a matrix ODE. Our model is easy to calculate and captures the effect of regime uncertainty in the price and term structure.     

Term premium dynamics in an emerging market: Risk,liquidity, and behavioral factors

This paper contributes to the fixed income research by identifying determinants of term premium in an emerging market’s treasury bond yields with particular attention on ambiguity. We use Nelson–Siegel yield curves generated from daily bond price quotes as input to construct a three-factor affine term structure model which decomposes observed yields into risk-neutral and term premium components. We also construct an ambiguity index using intraday FX return data following Brenner and Izhakian (2018). Our analyses suggest that a combination of factors representing market risk, credit risk, liquidity, ambiguity, and investor sentiments can explain majority of the variation in term premia. Explanatory power of credit risk measures are found to increase while those of volatility, ambiguity, and sentiment measures diminish with the maturity horizon. The results imply that ambiguity aversion of bond investors is a major determinant of the shape of the yield curve as it drives the premia for short end of the yield curve lower in line with the expectation of flight-to-safety behavior.     

Volatility spillovers and dynamic correlation in European bond markets

This paper examines the dynamic linkages among the European bond markets. We model the price and volatility spillovers from the US bond market and the aggregate Euro area bond market to twelve individual European bond markets using an EGARCH model that allows for a dynamic correlation structure. Our results suggest that significant volatility spillovers exist from both the aggregate Euro area bond market and the US bond market to the individual European markets. Moreover, the introduction of the Euro has strengthened the volatility spillover effects and the cross-correlations for most European bond markets.     

Macroeconomic announcements and asymmetric volatility in bond returns

This study analyses the impact of macroeconomic news announcements on the conditional volatility of bond returns. Using daily returns on the 1, 3, 5 and 10 year US Treasury bonds, we find that announcement shocks have a strong impact on the dynamics of bond market volatility. Our results provide empirical evidence that the bond market incorporates the implications of macroeconomic announcement news faster than other information. Moreover, after distinguishing between types of macroeconomic announcements, releases of the employment situation and producer price index are especially influential at the intermediate and long end of the yield curve, while monetary policy seem to affect short-term bond volatility.     

An extention of Samuelson's warrant valuation model and its application to Japanese data

It is well known among warrant traders that the Black & Scholes model cannot be directly used for warrant and convertible bond valuation. In this paper, a new warrant valuation model based on both the Samuelson and the Barone-Adesi & Whaley model is proposed, and the model is applied to convertible bond valuation. Our model is an extension of Samuelson's perpertual warrant model, whose parameters depend on stock price, volatility, term to maturity and interest rate.     

Term Structure Movements and Pricing Interest Rate Contingent Claims

This paper derives an arbitrage-free interest rate movements model (AR model). This model takes the complete term structure as given and derives the subsequent stochastic movement of the term structure such that the movement is arbitrage free. We then show that the AR model can be used to price interest rate contingent claims relative to the observed complete term structure of interest rates. This paper also studies the behavior and the economics of the model. Our approach can be used to price a broad range of interest rate contingent claims, including bond options and callable bonds.     

Executive stock options: volatility,managerial decisions and agency costs

This paper proposes a new rationale for understanding managerial contracts which set-out to induce stock price volatility in the form of granting of executive stock options. First, we suggest that previous research focuses too much on short term volatility effects and offering neither a theoretical or empirical perspective on incentives which might influence long-term behaviour. To address this, we offer a theoretical structure of why managerial incentives might be important in determining the evolution of volatility over the life of an option contract and provide empirical support for our views. Second, we examine the impact of option moneyness on managerial behaviour over time and provide an analysis, with supporting empirical work, of the unintended incentives thereby created. Our approach suggests that volatility-inducing contracts do not work in the intended manner and supports a growing body of work which indicates that option-based remuneration does not incentivise managers to enhance corporate performance. Our evidence is within a UK context, based on a near-population sample size.     

Linear‐Rational Term Structure Models

We introduce the class of linear‐rational term structure models in which the state price density is modeled such that bond prices become linear‐rational functions of the factors. This class is highly tractable with several distinct advantages: (i) ensures nonnegative interest rates, (ii) easily accommodates unspanned factors affecting volatility and risk premiums, and (iii) admits semi‐analytical solutions to swaptions. A parsimonious model specification within the linear‐rational class has a very good fit to both interest rate swaps and swaptions since 1997 and captures many features of term structure, volatility, and risk premium dynamics—including when interest rates are close to the zero lower bound.     

Interest Rate Caps “Smile” Too! But Can the LIBOR Market Models Capture the Smile?

Using 3 years of interest rate caps price data, we provide a comprehensive documentation of volatility smiles in the caps market. To capture the volatility smiles, we develop a multifactor term structure model with stochastic volatility and jumps that yields a closed‐form formula for cap prices. We show that although a three‐factor stochastic volatility model can price at‐the‐money caps well, significant negative jumps in interest rates are needed to capture the smile. The volatility smile contains information that is not available using only at‐the‐money caps, and this information is important for understanding term structure models.     

Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model

We develop a two-factor general equilibrium model of the term structure. The factors are the short-term interest rate and the volatility of the short-term interest rate. We derive closed-form expressions for discount bonds and study the properties of the term structure implied by the model. The dependence of yields on volatility allows the model to capture many observed properties of the term structure. We also derive closed-form expressions for discount bond options. We use Hansen's generalized method of moments framework to test the cross-sectional restrictions imposed by the model. The tests support the two-factor model.     

Pricing Contingent Claims on a Risky Asset and Stochastic Interest Rates: A New Discrete Time Approach

This paper presents a new discrete time approach to pricing contingent claims on a risky asset and stochastic interest rates. The term structure of interest rates is modeled so that arbitrage-free bond prices depend on an observable initial forward rate curve rather than an exogenously specified market price of risk. A restricted binomial process is employed to model both interest rates and an asset price. As a result, a complete market valuation formula obtains. By choosing the parameters of the discrete joint distribution such that, in the limit, the discrete model converges to the continuous one, a model is obtained that requires the estimation of only three parameters. The approach is parsimonious with respect to alternative models in the literature and can be used to price contingent claims on any two state variables. The procedure is used to numerically analyze the effects of the volatility of interest rates on the determination of mortgage contract rates.     

Volatility transmission between stock and bond markets

A two-factor no-arbitrage model is used to provide a theoretical link between stock and bond market volatility. While this model suggests that short-term interest rate volatility may, at least in part, drive both stock and bond market volatility, the empirical evidence suggests that past bond market volatility affects both markets and feeds back into short-term yield volatility. The empirical modelling goes on to examine the (time-varying) correlation structure between volatility in the stock and bond markets and finds that the sign of this correlation has reversed over the last 20 years. This has important implications far portfolio selection in financial markets.     

The Effect of Interest Rates on the Value of Corporate Assets and the Risk Premia of Corporate Debt

A growing number of papers have applied option pricing techniques to the valuation of risky debt. This paper deals directly with how a firm's relationship to interest rates affects its debt. A sequential binomial model is used to price the zero-coupon bonds of a firm whose value is related to interest rate changes.The results show that the strength of the relationship between firm value and interest rates (interest-rate risk) can have a significant impact on the value of a firm's debt. The model produces its most powerful results when the volatility of firm value is high and the term structure has a steep (negative or positive) slope; there is no impact when the term structure is flat. Our results indicate that empirical studies of yield spreads may have severe shortcomings if the relationship of firm value to interest rate changes is ignored.     

An interest rate model with a Markovian mean reverting level

Abstract

A two‐factor Vasicek model, where the mean reversion level changes according to a continuous time finite state Markov chain, is considered. This model could capture the behaviour of monetary authorities who normally set a reference rate which changes from time to time. We derive the term structure via the analytic expression of the bond price that involves a fundamental matrix. The validity of the bond price closed form solution is verified via the forward rate dynamics.     

Option Prices, Implied Price Processes, and Stochastic Volatility

This paper characterizes all continuous price processes that are consistent with current option prices. This extends Derman and Kani (1994), Dupire (1994, 1997), and Rubinstein (1994), who only consider processes with deterministic volatility. Our characterization implies a volatility forecast that does not require a specific model, only current option prices. We show how arbitrary volatility processes can be adjusted to fit current option prices exactly, just as interest rate processes can be adjusted to fit bond prices exactly. The procedure works with many volatility models, is fast to calibrate, and can price exotic options efficiently using familiar lattice techniques.