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.     

The information content of credit ratings: evidence from European convertible bond markets

Prior research has investigated the information content of credit ratings for standard financing instruments such as stocks and corporate bonds, while this question has been neglected for convertible bonds (CBs) so far. CBs are simultaneously determined by the bond floor and the conversion value, which makes it more difficult to assess price effects following rating announcements. In this context, we compare price effects of CBs with those of stocks and corporate bonds of the same issuer using robust event study methods. Our findings indicate that rating changes convey new information for investors in European CBs. In terms of the direction of the expected price reaction, we find CBs to react in a more debt-like manner to the announcement of a rating change. Moreover, our results provide evidence that the magnitude of price reactions differs among different types of securities.     

Optimal policies of call with notice period requirement

When an American warrant or a convertible bond is called by its issuer, the holder is usually given a notice period to decide whether to sell the derivative back to the issuer at the call price or to exercise the conversion right. Several earlier papers have shown that such notice period requirement may substantially affect the optimal call policy adopted by the issuer. In this paper, we perform theoretical studies on the impact of the notice period requirement on issuer’s optimal call policy for American warrants and convertible bonds. We also examine how the optimal call policy of the issuer interacts with holder’s optimal conversion policy.     

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.     

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     

Consumption and Equilibrium Interest Rates in Stochastic Production Economies

In this paper, we analyze the behavior of equilibrium real interest rates in an identical consumer economy in which the preferences are represented by time additive logarithmic utility functions and production technologies are Cobb-Douglas with stochastic constant returns to scale. The following main results are established.

• (i) When there is no relative price uncertainty, it is shown that the equilibrium interest rate exhibits a mean reverting tendency. A nontrivial steady state distribution is found to exist for the equilibrium interest rate. The properties of the equilibrium interest rate are also derived and discussed.
• (ii) In a multigood economy, even with additive preferences across goods, the equilibrium interest rates depend explicitly on relative prices. The substitution possibilities in production technologies induce this result. This is in contrast to the findings of Richard and Sundaresan 11 who show that the analytical general equilibrium term structure of interest rates formula of Cox, Ingersoll, and Ross 5 is unaffected by the introduction of relative price uncertainty when the technologies are linear and hence involve no substitution.

Furthermore, we relate our results to those of Cox, Ingersoll, and Ross 5 , Breeden 3 , and Richard and Sundaresan 11 with special emphasis on stochastic production and realtive price uncertainty.     

Trading strategies based on term structure model residuals

The term structure of interest rates is an important input for basically every pricing model and is mostly calibrated on coupon bond prices. Therefore, the estimated interest rates should accurately explain the market prices of these bonds. However, nearly all empirical papers on interest rate estimation, e.g. Svensson, L.E.O. 1994. Estimating and interpreting forward interest rates: Sweden 1992–1994, IMF Working Paper, International Monetary Fund, report significant pricing errors in their sample. So an important question is what drives these pricing errors of the bonds. One simple explanation would be different tax treatment or different liquidity, but most papers on this research topic, e.g. Elton, E., and T.C. Green. 1998. Tax and liquidity effects in pricing government bonds. Journal of Finance 53: 1533–62, cannot fully explain the observed pricing errors. Therefore, these errors must be at least partially caused by either model misspecification or by the deviation of particular bond prices from general market conditions, i.e. mispricing revealing insufficient market efficiency. We provide empirical evidence for the German government bond market that risk-adjusted trading strategies based on bond pricing errors can yield about 15 basis points p.a. abnormal return compared to benchmark portfolios. Furthermore, the abnormal returns are continuously achieved over the whole time period and not randomly on a few days and show a relation to changes in the level and the curvature of the term structure of interest rates. Therefore, pricing errors contain economic information about deviations of bond prices from general market conditions and are not exclusively caused by model misspecification and/or differences in liquidity and tax treatment of individual bonds.     

Do banks price their informational monopoly?

Theory suggests that banks’ private information lets them hold up borrowers for higher interest rates. Since new information about a firm is revealed at the time of its bond IPO, it follows that banks will be forced to adjust their loan interest rates downwards after firms undertake their bond IPO. We test this hypothesis and find that firms are able to borrow at lower interest rates after their bond IPO. Importantly, firms that get their first credit rating at the time of their bond IPO benefit from larger interest rate savings than those that already had a credit rating. These findings provide support for the hypothesis that banks price their informational monopoly. We also find that it is costly for firms to enter the public bond market.     

A Comparison of Option Prices Under Different Pricing Measures in a Stochastic Volatility Model with Correlation

This paper investigates option prices in an incomplete stochastic volatility model with correlation. In a general setting, we prove an ordering result which says that prices for European options with convex payoffs are decreasing in the market price of volatility risk.As an example, and as our main motivation, we investigate option pricing under the class of q-optimal pricing measures. The q-optimal pricing measure is related to the marginal utility indifference price of an agent with constant relative risk aversion. Using the ordering result, we prove comparison theorems between option prices under the minimal martingale, minimal entropy and variance-optimal pricing measures. If the Sharpe ratio is deterministic, the comparison collapses to the well known result that option prices computed under these three pricing measures are the same.As a concrete example, we specialize to a variant of the Hull-White or Heston model for which the Sharpe ratio is increasing in volatility. For this example we are able to deduce option prices are decreasing in the parameter q. Numerical solution of the pricing pde corroborates the theory and shows the magnitude of the differences in option price due to varying q.JEL Classification: D52, G13     

An Empirical Comparison of Convertible Bond Valuation Models

This paper empirically compares three convertible bond valuation models. We use an innovative approach where all model parameters are estimated by the Marquardt algorithm using a subsample of convertible bond prices. The model parameters are then used for out-of-sample forecasts of convertible bond prices. The mean absolute deviation is 1.86% for the Ayache-Forsyth-Vetzal model, 1.94% for the Tsiveriotis-Fernandes model, and 3.73% for the Brennan-Schwartz model. For this and other measures of fit, the Ayache-Forsyth-Vetzal and Tsiveriotis-Fernandes models outperform the Brennan-Schwartz model.     

A Note on Forward Price and Forward Measure

The forward measure is convenient in calculating various contingent claim prices under stochastic interest rates. We demonstrate that caution needs to be drawn when the forward measure is used to price contingent claims that involve multiple cash flows. We also derive partial different equations for the forward price to demonstrate how forward contracts can be used for dynamic hedging and how hedges can be conducted if the payoff of a contingent claim depends on the forward price.     

Reduced-form Models with Regime Switching: An Empirical Analysis for Corporate Bonds

Empirical evidence shows that there is a close link between regime shifts and business cycle fluctuations. A standard term structure of interest rates, such as the Cox et al. (1985 Econometrica, 53, 385–407; CIR) model, is sharply rejected in the Treasury bond data. Only Markov regime-switching models on the entire yield curve of the Treasury bond data can account for the observed behavior of the yield curve. In this paper, we examine the impact of regime shifts on AAA-rated and BBB-rated corporate bonds through the use of a reduced-form model. The model is estimated by the Efficient Method of Moments (EMM). Our empirical results suggest that regime-switching risk has significant implications for corporate bond prices and hence has a material impact on the entire corporate bond yield curve, providing evidence for the approach of rating through the cycle employed by rating agencies.     

An Empirical Investigation of the Market for Comex Gold Futures Options

Option-pricing models that assume a constant interest rate may misprice futures options if the interest rate fluctuates significantly or if the price of the underlying asset is correlated with the interest rate. The futures option-pricing model of Ramaswamy and Sundaresan allows for a stochastic interest rate and correlation of the underlying asset's price with the interest rate. Using a data set of daily closing prices for Comex gold futures options, this paper tests the Ramaswamy and Sundaresan model against a constant interest rate model. Results indicate that the stochastic interest rate model is a superior predictor of market prices.     

On the valuation of reverse mortgage insurance

This article presents a closed-form formula for calculating the loan-to-value (LTV) ratio in an adjusted-rate reverse mortgage (RM) with a lump sum payment. Previous literatures consider the pricing of RM in a constant interest rate assumption and price it on fixed-rate loans. This paper successfully considers the dynamic of interest rate and the adjustable-rate RM simultaneously. This paper also considers the housing price shock into the valuation model. Assuming that house prices follow a jump diffusion process with a stochastic interest rate and that the loan interest rate is adjusted instantaneously according to the short rate, we demonstrate that the LTV ratio is independent of the term structure of interest rates. This argument holds even when housing prices follow a general process: an exponential Lévy process. In addition, the HECM (Home Equity Conversion Mortgage) program may be not sustainable, especially for a higher level of housing price volatility. Finally, when the loan interest rate is adjusted periodically according to the LIBOR rate, our finding reveals that the LTV ratio is insensitive to the parameters characterizing the CIR model.     

OPTIONS ON U.S. TREASURY COUPON ISSUES

Pricing models for options on default-free coupon bonds are developed and tested under the assumption that the bond prices, rather than interest rates, are the underlying stochastic factors. Under the assumption that coupon bond prices, excluding accrued interest, follow a generalized Brownian bridge process, preference-free, continuous-time pricing models are developed for European put and call options, and a discrete-time model is developed for American puts and calls. The empirical validity of the models is assessed using a six-moth sample of daily closing prices.     

Can negative interest rates really affect option pricing? Empirical evidence from an explicitly solvable stochastic volatility model

The profound financial crisis generated by the collapse of Lehman Brothers and the European sovereign debt crisis in 2011 have caused negative values of government bond yields both in the USA and in the EURO area. This paper investigates whether the use of models which allow for negative interest rates can improve option pricing and implied volatility forecasting. This is done with special attention to foreign exchange and index options. To this end, we carried out an empirical analysis on the prices of call and put options on the US S&P 500 index and Eurodollar futures using a generalization of the Heston model in the stochastic interest rate framework. Specifically, the dynamics of the option’s underlying asset is described by two factors: a stochastic variance and a stochastic interest rate. The volatility is not allowed to be negative, but the interest rate is. Explicit formulas for the transition probability density function and moments are derived. These formulas are used to estimate the model parameters efficiently. Three empirical analyses are illustrated. The first two show that the use of models which allow for negative interest rates can efficiently reproduce implied volatility and forecast option prices (i.e. S&P index and foreign exchange options). The last studies how the US three-month government bond yield affects the US S&P 500 index.     

A positive interest rate model with sticky barrier

This paper proposes an efficient model for the term structure of interest rates when the interest rate takes very small values. We make the following choices: (i) we model the short-term interest rate, (ii) we assume that once the interest rate reaches zero, it stays there and we have to wait for a random time until the rate is reinitialized to a (possibly random) strictly positive value. This setting ensures that all term rates are strictly positive.

Our objective is to provide a simple method to price zero-coupon bonds. A basic statistical study of the data at hand indeed suggests a switch to a different mode of behaviour when we get to a low level of interest rates. We introduce a variable for the time already spent at 0 (during the last stay) and derive the pricing equation for the bond. We then solve this partial integro-differential equation (PIDE) on its entire domain using a finite difference method (Cranck–Nicholson scheme), a method of characteristics and a fixed point algorithm. Resulting yield curves can exhibit many different shapes, including the S shape observed on the recent Japanese market.     

Pricing Contingent Claims under Interest Rate and Asset Price Risk

This paper presents a general framework for pricing contingent claims under interest rate and asset price uncertainty. The framework extends Ho and Lee's (1986) valuation framework by allowing not only future interest rates but also future asset prices to depend on the current term structure of interest rates. The approach is shown to provide risk-neutral valuation relationships that are consistent with the initial term structure of interest rates and can be applied to valuation of a broad class of assets including stock options, convertible bonds, and junk bonds.     

Exchange Rates and the Conversion of Currency‐Specific Risk Premia

How do the risk factors that drive asset prices influence exchange rates? Are the parameters of asset price processes relevant for specifying exchange rate processes? Most international asset pricing models focus on the analysis of asset returns given exchange rate processes. Little work has been done on the analysis of exchange rates dependent on asset returns. This paper uses an international stochastic discount factor (SDF) framework to analyse the interplay between asset prices and exchange rates. So far, this approach has only been implemented in international term structure models. We find that exchange rates serve to convert currency‐specific discount factors and currency‐specific prices of risk – a result linked to the international arbitrage pricing theory (IAPT). Our empirical investigation of exchange rates and stock markets of four countries presents evidence for the conversion of currency‐specific risk premia by exchange rates.