Interest Rate Options Research Articles

Investor sentiment and interest rate volatility smile: evidence from Eurodollar options markets

This paper studies the extent to which investor sentiment affects the Eurodollar option smile and finds that there is the dynamic interplay between sentiment-driven investors and arbitrageurs. The results reveal a significant relation between investor sentiment and interest rate volatility smile. The significant relations are stronger for put options, for short-maturity options, and for periods with higher uncertainty. The results are robust when considering controlling variables, net buying pressure, different interest rate option models, model-free method, or excluding rational components from the sentiment measures. Our findings favor the limits to arbitrage hypothesis against the positive feedback hypothesis, suggesting that the sentiment effect is transitory. Change in investor sentiment explains the time-varying smile that can be explained neither by rational interest rate models nor by net buying pressure.

Risk Management in Enterprise Value Creation in the Example of Agricultural Sector

This report shows how to protect themselves against interest rate risk in the example of a company in the agricultural sector. This paper contains strategies for managing interest rate risk, consisting of a cash flow hedge in using of derivative instruments such as futures contacts FRA, interest rate option.

Fast Swaption Pricing in Gaussian Term Structure Model

We propose a fast and accurate numerical method to price European swaptions in a multi-factor Gaussian term structure model that can speed up the calibration to the volatility surface. Pricing an interest rate option in such a multi-factor term structure model involves evaluating a multi-dimensional integration of the underlying claim's payoff on a domain where the payoff is positive. In our method, we approximate the exercise boundary of the state variables as a hyperplane tangent to the maximum probability point on the boundary and simplify the multi-dimensional integration into an analytic form. The maximum probability point can be found using the gradient descent method. We show that the quality of our method is superior to the result of previous studies by directly comparing them to the exact price obtained from the numerical integration.

Forward‐Looking Monetary Policy Rules and Option‐Implied Interest Rate Expectations

AbstractThis paper examines the association between option‐implied interest rate distributions and macroeconomic expectations in the context of a forward‐looking monetary policy rule. We presume that market participants view the policy rule as a guide to the path of future policy rates and price interest rate options in accordance with the policy rule fundamentals. Using data from the UK, we confirm that Libor expectations implied by option prices are consistent with the policy rule variables. The results demonstrate that changes in the distributional form of Libor expectations are strongly associated with changes in the expected inflation and output gaps and financial uncertainty. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:346–373, 2014

The Effects of the Federal Reserve's Date-Based Forward Guidance

Between August 2011 and December 2012 the Federal Open Market Committee (FOMC) used date-based forward guidance to help stimulate the U.S. economy and promote its objectives of maximum employment and price stability. Some have argued that the formulation of the guidance that the FOMC used may have reduced interest rates primarily by signaling a weak economic outlook rather than by signaling a more accommodative stance of monetary policy. I examine the impact of the date-based guidance, with the principal goal of discerning the extent to which it altered investors' views of the FOMC's policy reaction function. I show that one seemingly straightforward way to address this question--using estimates of the sensitivity of money market futures rates to macroeconomic data surprises--is confounded by the zero lower bound on nominal interest rates, a point that has more general implications for the analysis of the effects of monetary policy at the zero bound. I demonstrate that the problem can be overcome using distributions of investors' short-term interest rate expectations constructed from interest rate options. Using PDFs constructed from these options, along with survey measures of macroeconomic surprises, I find the date-based guidance led to a statistically significant and economically meaningful change in investors' perceptions of the FOMC's reaction function. This finding is robust to various regression specifications and the use of alternative options contracts and PDF fitting methodologies.

Pricing Interest Rate Derivatives Under Monetary Policy Changes

Traders worldwide use interest rate options and futures to speculate on future monetary decisions, in particular in countries where the monetary regime is Inflation Targeting (IT). Central Banks under an IT regime tend to define the target rate on scheduled meetings. We propose in this paper a simple and consistent way to explicitly incorporate the potential changes in the target rate during Central Bank's meetings into interest rate futures and option pricing. We calibrate the model to data from Brazil. Brazil came up with the right place to applying our model because it has adopted an inflation targeting regime to monetary policy since 1999 with scheduled meeting to define the target rate and there is a very liquid overnight interest rate derivative market which is used by market participants to bet on future monetary decisions.

Negative Probabilities in Financial Modeling

We first define and derive general properties of negative probabilities. We then show how negative probabilities can be applied to modeling financial options such as Caps and Floors. In trading practice, these options are typically valued in a Black-Scholes-Merton framework, assuming a lognormal distribution for the underlying interest rate. However, in some cases, such as the 2008/2009 financial crisis, interest rates can get negative. Then the lognormal distribution is inapplicable. We show how negative probabilities associated with negative interest rates can be applied to value interest rate options. A model in VBA, which prices Caps and Floors with negative probabilities, is available upon request. A follow up paper will address bigger than unity probabilities in financial modeling. Copyright © 2012 Wilmott Magazine Ltd.

Valuation of american interest rate options by the least-squares Monte Carlo method

The purpose of this study is to verify the efficiency and the applicability of the Least-Squares Monte Carlo method for pricing American interest rate options. Results suggest that this technique is apromising alternative to evaluate American-style interest rate options. It provides accurate option price estimates which are very close to results provided by a binomial model. Besides, actual implementation can be easily adapted to accept different interest rate models.

Evolving fuzzy systems for pricing fixed income options

During the recent decades, option pricing became an important topic in computational finance. The main issue is to obtain a model of option prices that reflects price movements observed in the real world. In this paper we address option pricing using an evolving fuzzy system model and Brazilian interest rate options data. Evolving models are particularly appropriate because they gradually develops the model structure and parameters from a stream of data. Therefore, evolving fuzzy models provide a higher level of system adaptation and learns the system dynamics continuously, an essential attribute in pricing options estimation. In particular, we emphasize the use of the evolving participatory learning methods. The participatory evolving models considered in this paper are compared against the traditional Black’s closed-form formula, artificial neural networks structures, and alternative evolving fuzzy system approaches reported in the literature. Actual daily data used in the experiments cover the period from January 2003 to June 2008. We measure forecast performance of all models and report the statistical tests done for the competing forecast models. The results show that the participatory evolving fuzzy system modeling approach is effective to estimate prices of fixed income options.

Pricing American interest rate options under the jump-extended constant-elasticity-of-variance short rate models

This paper demonstrates how to value American interest rate options under the jump-extended constant-elasticity-of-variance (CEV) models. We consider both exponential jumps (see Duffie et al., 2000) and lognormal jumps (see Johannes, 2004) in the short rate process. We show how to superimpose recombining multinomial jump trees on the diffusion trees, creating mixed jump-diffusion trees for the CEV models of short rate extended with exponential and lognormal jumps. Our simulations for the special case of jump-extended Cox, Ingersoll, and Ross (CIR) square root model show a significant computational advantage over the Longstaff and Schwartz’s (2001) least-squares regression method (LSM) for pricing American options on zero-coupon bonds.

Linearity-Generating Processes, Unspanned Stochastic Volatility, and Interest-Rate Option Pricing

We propose to use the linearity-generating framework to accommodate the evidence of unspanned stochastic volatility: Variations in implied volatilities on interest-rate options such as caps and swaptions are independent of the variations on the interest rate term structure. Under this framework, bond valuation depends only on the transition dynamics of interest-rate factors, but not on their volatilities. Thus, interest-rate volatility is truly unspanned. Furthermore, this framework allows tractable pricing of options on any bond portfolios, including both caps and swaptions. This feat is not possible under existing exponential-affine or quadratic frameworks. Finally, the framework allows sequential estimation of the interest-rate term structure and the interest-rate option implied volatility surface, thus facilitating joint empirical analysis. Within this framework, we perform specification analysis on interest-rate factor transition dynamics and its relation to the interest-rate term structure; we also analyze the interest-rate volatility dynamics and its impact on interest-rate option pricing. We estimate several specifications for the transition dynamics to ten years worth of U.S. dollar LIBOR and swap rates across 15 maturities. We also estimate several interest-rate volatility dynamics specifications using ten years of swaption implied volatilities across a matrix of ten option maturities and seven swap tenors. The estimation results show that the volatility dynamics dictate the option implied volatility variation along the option maturity dimension, whereas the interest-rate transition dynamics dictate the implied volatility variation along the underlying swap maturity dimension.

Negative Probabilities in Financial Modeling

We first define and derive general properties of negative probabilities. We then show how negative probabilities can be applied to modeling financial options such as Caps and Floors. In trading practice, these options are typically valued in a Black-Scholes-Merton framework assuming a lognormal distribution for the underlying interest rate. However, in some cases, such as the 2008/2009 financial crisis, interest rates can get negative. Then the lognormal distribution is inapplicable. We show how negative probabilities associated with negative interest rates can be applied to value interest rate options. A model in VBA, which prices Caps and Floors with negative probabilities, is available upon request. A follow up paper will address bigger than unity probabilities in financial modeling.

Do interest rate options contain information about excess returns?

There is strong empirical evidence that long-term interest rates contain a time-varying risk premium. Options may contain valuable information about this risk premium because their prices are sensitive to the underlying interest rates. We use the joint time series of swap rates and interest rate option prices to estimate dynamic term structure models. The risk premiums that we estimate using option prices are better able to predict excess returns for long-term swaps over short-term swaps. Moreover, in contrast to the previous literature, the most successful models for predicting excess returns have risk factors with stochastic volatility. We also show that the stochastic volatility models we estimate using option prices match the failure of the expectations hypothesis.

Pricing American Interest Rate Options Under the Jump-Extended Constant-Elasticity-of-Variance Short Rate Models

This paper demonstrates how to value American interest rate options under the jump extended constant-elasticity-of-variance (CEV) models. We consider both exponential jumps (see Duffie, Pan, and Singleton (2000)) and lognormal jumps (see Johannes (2004)) in the short rate process. We show how to superimpose recombining multinomial jump trees on the diffusion trees, creating mixed jump-diffusion trees for the CEV models of short rate extended with exponential and lognormal jumps. Our simulations for the special case of jump-extended Cox, Ingersoll, and Ross (CIR) square root model show a significant computational advantage over the Longstaff and Schwartz’s (2001) least-squares regression method (LSM) for pricing American options on zero-coupon bonds.

Interest rate derivatives in developing countries in Europe

Financial derivatives (interest rate futures, options and swaps) are a very simple way to minimize interest rate risk and therefore are extremely popular. The value of interest rate derivatives transactions in the world is increasing dramatically. Unfortunately, this is not the case with developing countries in Europe. Although significantly increased in the last decade, interest rate derivatives markets in developing countries are still in nascent stage. In most developing countries still the main problem for the interest rate derivatives development is the lack of basic conditions, including inadequate measurement of interest rate risk exposure, underdevelopment of financial markets in general and especially of market instruments that underlying derivatives, weak and/or inadequate infrastructure and legal framework, misunderstanding and lack of experience in operations with financial derivatives and the complexity of the derivatives accounting

Valuation of Asian Interest Rate Options within the BGM Model

Within the BGM (Brace, Gatarek and Musiela, 1997) interest rate model, this article prices Asian interest rate options via the Vorst (1992) approximation approach. To consist with market practice, we modify the setting of the average rate in Longstaff (1995) by employing the arithmetic average of (market-observable) LIBOR rates. The LIBOR rates are specified directly rather than transformed from the unobservable short rates. Moreover, the parameters in our pricing formula can be easily calibrated from market data. The pricing formula is shown to be sufficiently accurate as compared with Monte Carlo simulation. The calibration procedure and the practical examples are also presented.

Forward-Looking Monetary Policy Rules and Option-Implied Interest Rate Expectations

This paper examines the association between option-implied interest rate distributions and macroeconomic expectations in the context of a forward-looking monetary policy rule. We presume that market participants view the policy rule as a guide to the path of future policy rates and price interest rate options in accordance with the policy rule fundamentals. Using data from the UK, we confirm that Libor expectations implied by option prices are consistent with the policy rule variables. The results demonstrate that changes in the distributional form of Libor expectations are strongly associated with changes in the expected inflation and output gaps and financial uncertainty.

Pricing and hedging volatility smile under multifactor interest rate models

The paper extends Amin and Morton (1994), Zeto (2002), and Kuo and Paxson (2006) by considering jump-diffusion model of Das (1999) with various volatility functions in pricing and hedging Euribor options across strikes and maturities. Adding the jump element into a diffusion model helps capturing volatility smiles in the interest rate options markets, but specifying the mean-reversion volatility function improves the most. A humped volatility function with the additional jump component yields better in-sample and out-of-sample valuation, but level-dependent volatility becomes more crucial for hedging. The specification of volatility function is more crucial than merely adding jumps into any model and the effect of jumps declines as the maturity of options is longer.

Valuing Early Exercise Interest Rate Options with Multi-Factor Affine Models

Multi-factor interest-rate models are widely used. Contingent claims with early-exercise features are often valued by resorting to trees, finite-difference schemes and Monte Carlo simulations. When jumps are present, however, these methods are less effective. In this work we develop an algorithm based on a sequence of measure changes coupled with Fourier transform solutions of the pricing partial integro-differential equation to solve the pricing problem. The new algorithm, which we call the irFST method, also neatly computes option sensitivities. Furthermore, we develop are able to obtain closed-form formulae for accrual swaps and accrual range notes. We demonstrate the versatility and precision of the method through numerical experiments on European, Bermudan and callable bond options, accrual swaps and accrual range notes.

Interest Rate Models for Pricing Derivatives: The Case of Cap Contracts

This paper deals with issues related to the choice of the interest rate model to price interest rate derivatives. After the development of the market models, choosing the interest rate model is become almost a trivial task. However their use not always is possible, so that the problem of choosing the right methodology still attains.The aim of this paper is to compare some of the most used interest rate derivatives pricing models to understand what are the issues and the drawbacks connected to each one. It is shown why and in which cases the use of each model does not give appreciable results and when, on the other hand, the opposite occurs. More exactly, it will be shown that the lack of data on the implied volatilities or the inefficiencies in the financial market can prevent the use of the market models, because a satisfying calibration of the interest rate trajectories cannot be guaranteed. Moreover it is shown how the smile effect in the interest rate options market can affect the price provided by each model and, more exactly, that the difference between the price provided by the models and the observed market prices gets larger, as the strike price increases.