Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis

We empirically compare Libor and Swap Market Models for the pricing of interest rate derivatives, using panel data on prices of US caplets and swaptions. A Libor Market Model can directly be calibrated to observed prices of caplets, whereas a Swap Market Model is calibrated to a certain set of swaption prices. For both models we analyze how well they price caplets and swaptions that were not used for calibration. We show that the Libor Market Model in general leads to better prediction of derivative prices that were not used for calibration than the Swap Market Model. Also, we find that Market Models with a declining volatility function give much better pricing results than a specification with a constant volatility function. Finally, we find that models that are chosen to exactly match certain derivative prices are overfitted; more parsimonious models lead to better predictions for derivative prices that were not used for calibration.     

Asset pricing theory for two price economies

We show that nonlinearly discounted nonlinear martingales are related to no arbitrage in two price economies as linearly discounted martingales were related to no arbitrage in economies satisfying the law of one price. Furthermore, assuming risk acceptability requires a positive physical expectation, we demonstrate that expected rates of return on ask prices should be dominated by expected rates of return on bid prices. A preliminary investigation conducted here, supports this hypothesis. In general we observe that asset pricing theory in two price economies leads to asset pricing inequalities. A model incorporating both nonlinear discounting and nonlinear martingales is developed for the valuation of contingent claims in two price economies. Examples illustrate the interactions present between the severity of measure changes and their associated discount rates. As a consequence arbitrage free two price economies can involve unique discount curves and measure changes that are however specific to both the product being priced and the trade direction. Furthermore the developed valuation operators call into question the current practice of Debt Valuation Adjustments.     

Libor Market Models versus Swap Market Models for Pricing Interest Rate Derivatives: An Empirical Analysis

We empirically compare Libor and Swap Market Models for thepricing of interest rate derivatives, using panel data on pricesof US caplets and swaptions. A Libor Market Model can directlybe calibrated to observed prices of caplets, whereas a SwapMarket Model is calibrated to a certain set of swaption prices.For both models we analyze how well they price caplets and swaptionsthat were not used for calibration. We show that the Libor MarketModel in general leads to better prediction of derivative pricesthat were not used for calibration than the Swap Market Model.Also, we find that Market Models with a declining volatilityfunction give much better pricing results than a specificationwith a constant volatility function. Finally, we find that modelsthat arechosen to exactly match certain derivative prices areoverfitted; more parsimonious models lead to better predictionsfor derivative prices that were not used for calibration. JELClassification: G12, G13, E43.     

Exploring the transmission mechanism of speculative and inventory arbitrage activity to commodity price volatility. Novel evidence for the US economy

In the realm of monetary policy, we explore the transmission mechanism that relates speculative activity, inventory arbitrage activity, and commodity price volatility. In this direction, an ARMA-GARCH model is adopted to test this transmission effect on seven commodities using weekly U.S. data for the period 2008:12 to 2018:6. The results suggest that inventory arbitrage activities transmit monetary policy's effect onto commodities by strengthening the effect of the real interest rate on commodities' prices; in the case of palladium and crude oil's price conditional variances however the opposite effect is established. Speculative activities transmit monetary policy's effect mainly on commodities by increasing the positive effect of the real interest rate on metals and crude oil's prices, and on palladium and crude oil's price conditional variances. Our results show that inventory arbitrage activities are negatively related with commodities' prices, whilst speculative activities are positively related with commodities' prices. The two activities appear to exert mixed effects on commodities' price conditional volatilities. Additional evidence indicates that the relationship between the real interest rate and commodities' prices is positive and significant when unconventional monetary policy is considered, whilst we find that the real interest rate does not have any significant impact on most commodities' price conditional volatilities.     

LIBOR and swap market models and measures

A self-contained theory is presented for pricing and hedging LIBOR and swap derivatives by arbitrage. Appropriate payoff homogeneity and measurability conditions are identified which guarantee that a given payoff can be attained by a self-financing trading strategy. LIBOR and swap derivatives satisfy this condition, implying they can be priced and hedged with a finite number of zero-coupon bonds, even when there is no instantaneous saving bond. Notion of locally arbitrage-free price system is introduced and equivalent criteria established. Stochastic differential equations are derived for term structures of forward libor and swap rates, and shown to have a unique positive solution when the percentage volatility function is bounded, implying existence of an arbitrage-free model with such volatility specification. The construction is explicit for the lognormal LIBOR and swap “market models”, the former following Musiela and Rutkowski (1995). Primary examples of LIBOR and swap derivatives are discussed and appropriate practical models suggested for each.     

Forward-neutral valuation relationships for options on zero coupon bonds

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.     

Arbitrage-free market models for option prices: the multi-strike case

This paper studies modeling and existence issues for market models of option prices in a continuous-time framework with one stock, one bond and a family of European call options for one fixed maturity and all strikes. After arguing that (classical) implied volatilities are ill-suited for constructing such models, we introduce the new concepts of local implied volatilities and price level. We show that these new quantities provide a natural and simple parametrization of all option price models satisfying the natural static arbitrage bounds across strikes. We next characterize absence of dynamic arbitrage for such models in terms of drift restrictions on the model coefficients. For the resulting infinite system of SDEs for the price level and all local implied volatilities, we then study the question of solvability and provide sufficient conditions for existence and uniqueness of a solution. We give explicit examples of volatility coefficients satisfying the required assumptions, and hence of arbitrage-free multi-strike market models of option prices.      

On the Information in the Interest Rate Term Structure and Option Prices

We examine whether the information in cap and swaption prices is consistent with realized movements of the interest rate term structure. To extract an option-implied interest rate covariance matrix from cap and swaption prices, we use Libor market models as a modelling framework. We propose a flexible parameterization of the interest rate covariance matrix, which cannot be generated by standard low-factor term structure models. The empirical analysis, based on US data from 1995 to 1999, shows that option prices imply an interest rate covariance matrix that is significantly different from the covariance matrix estimated from interest rate data. If one uses the latter covariance matrix to price caps and swaptions, one significantly underprices these options. We discuss and analyze several explanations for our findings.     

Price discovery on traded inflation expectations: does the financial crisis matter?

We analyze contributions of different markets, related by an approximate arbitrage relationship, to price discovery on traded inflation expectations and how it changed during the financial crisis. We use a new high-frequency data-set on inflation-indexed and nominal government bonds as well as inflation swaps to calculate information shares of break-even inflation rates in the euro area and the USA. In the euro area, for maturities up to 5 years new information comes from both the swap and the bond markets. For longer maturities, the swap market provides less and less information in the euro area. In the USA, the bond market dominates the price discovery process for all maturities. The severe financial crisis that spread out in Autumn 2008 drove a wedge between bond and swap break-even inflation rates in both currencies. Price discovery ceased to take place on the swap market. Disruptions coming from the short-end of the market even separated price formation on both segments for maturities of up to 6 years in the USA. Against the backdrop of the most severe financial crisis in decades, contributions to price formation concentrated a lot more on the presumably safest financial instrument: government bonds.     

Hedging in the Possible Presence of Unspanned Stochastic Volatility: Evidence from Swaption Markets

This paper examines whether higher order multifactor models, with state variables linked solely to underlying LIBOR‐swap rates, are by themselves capable of explaining and hedging interest rate derivatives, or whether models explicitly exhibiting features such as unspanned stochastic volatility are necessary. Our research shows that swaptions and even swaption straddles can be well hedged with LIBOR bonds alone. We examine the potential benefits of looking outside the LIBOR market for factors that might impact swaption prices without impacting swap rates, and find them to be minor, indicating that the swaption market is well integrated with the LIBOR‐swap market.     

Consistent Variance Curve Models

We introduce a general approach to model a joint market of stock price and a term structure of variance swaps in an HJM-type framework. In such a model, strongly volatility-dependent contracts can be priced and risk-managed in terms of the observed stock and variance swap prices. To this end, we introduce equity forward variance term structure models and derive the respective HJM-type arbitrage conditions. We then discuss finite-dimensional Markovian representations of the fixed time-to-maturity forward variance swap curve and derive consistency results for both the standard case and for variance curves with values in a Hilbert space. For the latter, our representation also ensures non-negativity of the process. We then give a few examples of such variance curve functionals and briefly discuss completeness and hedging in such models. As a further application, we show that the speed of mean reversion in some standard stochastic volatility models should be kept constant when the model is recalibrated.     

Implied Foreign Exchange Risk Premia

This paper uses implied volatilities from foreign exchange option prices and the results of no‐arbitrage theory to estimate foreign exchange risk premia. In particular, under the assumption of no‐arbitrage, the foreign exchange risk premium is driven by the difference between investors’ market prices of risk in the two currencies. In an international economy with three currencies, sterling, US dollar and Deutschemark, we can use the information on implied volatilities of the three cross rates to derive estimates of implied or ex ante market prices of risk and of foreign exchange risk premia. The foreign exchange risk premia estimates are then compared to survey‐based risk premia.     

PRICING CURRENCY OPTIONS UNDER STOCHASTIC INTEREST RATES AND JUMP‐DIFFUSION PROCESSES

We investigate the effects of stochastic interest rates and jumps in the spot exchange rate on the pricing of currency futures, forwards, and futures options. The proposed model extends Bates's model by allowing both the domestic and foreign interest rates to move around randomly, in a generalized Vasicek term‐structure framework. Numerical examples show that the model prices of European currency futures options are similar to those given by Bates's and Black's models in the absence of jumps and when the volatilities of the domestic and foreign interest rates and futures price are negligible. Changes in these volatilities affect the futures options prices. Bates's and Black's models underprice the European currency futures options in both the presence and the absence of jumps. The mispricing increases with the volatilities of interest rates and futures prices. JEL classification: G13     

Relative asset price bubbles

In models of financial bubbles, the price of a stock is typically unbounded, and this plays a fundamental role in the analysis of finite horizon local martingale bubbles. It would seem that price bubbles do not apply to a priori bounded risky asset prices, such as bond prices. To avoid this limitation, to characterize, and to identify bond price mispricings consistent with an absence of arbitrage, we develop the concept of a relative asset price bubble. This notion uses a risky asset’s price as the numéraire instead of the money market account’s value. This change of numéraire generates some interesting mathematical complexities because many important numéraires, including risky bonds, can vanish with positive probability over the model’s horizon.     

The Black Market for Dollars in Venezuela

In February 2003, the Venezuelan government imposed a strict capital controls policy to stem the outflow of dollars. We describe the mechanics and structure of the resulting black market and analyze the comparative performance of alternative models in explaining and forecasting the black market premium. Robustly significant determinants of the premium include the lagged premium, the official real exchange rate, the implied returns from arbitrage, and the oil price. Our preferred model exhibits outstanding out-of-sample forecasting performance, with an average prediction error of -0.9 percent, and an error standard deviation of 7.8 percent, during the ten-month period until July 2009. We provide evidence that the exogenous change of the black market swap vehicle to government bonds in 2007 induced a significant shift in the relative importance of the determinants of the premium, causing shocks to become significantly more persistent, the coefficient on the implied returns from arbitrage to double, and rendering the beneficial effect of oil price increases insignificant.     

Index arbitrage and the pricing relationship between Australian stock index futures and their underlying shares

This paper examines the mispricing of Australian stock index futures. Exogenous and endogenous price volatility is confirmed to have a positive impact on the mispricing spread, after filtering out predictable time series components. More accurate pricing associated with surprise trading volume in the underlying stocks is consistent with arbitrageurs acting to narrow price disparities relative to the futures market. Ex‐ante interest rate volatility is the primary source of risk faced by arbitrageurs and fluctuations in the transaction cost of opening index arbitrage positions influence the extent to which they drive prices towards theoretical fair values.     

Pricing default swaps: Empirical evidence

In this paper we compare market prices of credit default swaps with model prices. We show that a simple reduced form model outperforms directly comparing bonds' credit spreads to default swap premiums. We find that the model yields unbiased premium estimates for default swaps on investment grade issuers, but only if we use swap or repo rates as proxy for default-free interest rates. This indicates that the government curve is no longer seen as the reference default-free curve. We also show that the model is relatively insensitive to the value of the assumed recovery rate.     

A simple robust model for Cat bond valuation

This note provides a simple closed form solution for valuing Cat bonds. The formula is consistent with any arbitrage-free model for the evolution of the Libor term structure of interest rates. The crucial inputs to the valuation formula are the likelihood of the catastrophe event, per unit time, and the percentage loss rate realized if an event occurs. The pricing methodology is based on the reduced form models used to price credit derivatives.     

The mispricing of U.S. Treasury bonds: a case study

This article documents an apparent pricing anomaly involving9? percent, 30-year Treasury bonds during the months of Mayand June 1986. During this period, the price of the 9?s rosesharply relative to the prices of other long-term Treasury bondsand created a potential arbitrage opportunity. In addition,owners of the 9? bonds were able to borrow at a zero interestrate by pledging their bonds. Detailed examination reveals thatthis relative pricing anomaly cannot be attributed to changesin the level or term structure of interest rates or to differencesbetween the bonds with respect to liquidity, taxation, or duration.     

A model for interest rates with clustering effects

We propose a model for short-term rates driven by a self-exciting jump process to reproduce the clustering of shocks on the Euro overnight index average (EONIA). The key element of the model is the feedback effect between the absolute value of jumps and the intensity of their arrival process. In this setting, we obtain a closed-form solution for the characteristic function for interest rates and their integral. We introduce a class of equivalent measures under which the features of the process are preserved. We infer the prices of bonds and their dynamics under a risk-neutral measure. The question of derivatives pricing is developed under a forward measure, and a numerical algorithm is proposed to evaluate caplets and floorlets. The model is fitted to EONIA rates from 2004 to 2014 using a peaks-over-threshold procedure. From observation of swap curves over the same period, we filter the evolution of risk premiums for Brownian and jump components. Finally, we analyse the sensitivity of implied caplet volatility to parameters defining the level of self-excitation.