Pricing Commodity Spread Options with Stochastic Term Structure of Convenience Yields and Interest Rates

The purpose of this research is to provide a valuation formula for commodity spread options. Commodity spread options are options written on the difference of the prices (spread) of two commodities. From the aspect of commodity contingent claims, it is considered that commodity spread options are difficult to evaluate with accuracy because of the existence of the convenience yield. Hence, the model of the convenience yield is the key factor to price commodity spread options. We use the concept of future convenience yields to develop the model that enriches the stochastic behavior of convenience yield. We also introduce Heath-Jarrow-Morton interest rate model to the valuation framework. This general model not only captures the mean reverting feature of the convenience yield, but also allows us to handle a very wide range of shape that the term structure of convenience yield can take. Therefore our model provides various types of models. The numerical analysis presented in this paper provides some unique features of commodity spread options in contrast to normal options. These characteristics have never been addressed in previous studies. Moreover, it suggests that the existing model overprice commodity spread options through neglecting the effect of interest rates.     

Stochastic Interest Rates and the Bond-Stock Mix

The optimal bond-stock mix is examined in light of an apparent inconsistency between the Tobin Separation Theorem and the advice of popular investment advisors which has beenpointed out by Canner et al. (1997). It is shown that the apparent inconsistency is largely explicable in terms of the hedging demands of optimising long-term investors in an environment in which the investment opportunity set is subject to stochastic shocks. The analysis points to the importance of considering investors' time horizons in analyzing optimal portfolio policies.     

Stochastic Interest Rates and the Bond-Stock Mix

The optimal bond-stock mix is examined in light of an apparentinconsistency between the Tobin Separation Theorem and the adviceof popular investment advisors which has been pointed out byCanner et al. (1997).It is shown that the apparent inconsistencyis largely explicable in terms of the hedging demands of optimisinglong-term investors in an environment in which the investmentopportunity set is subject to stochastic shocks. The analysispoints to the importance of considering investors' time horizonsin analyzing optimal portfolio policies.     

Stochastic Convenience Yield and the Pricing of Oil Contingent Claims

This paper develops and empirically tests a two-factor model for pricing financial and real assets contingent on the price of oil. The factors are the spot price of oil and the instantaneous convenience yield. The parameters of the model are estimated using weekly oil futures contract prices from January 1984 to November 1988, and the model's performance is assessed out of sample by valuing futures contracts over the period November 1988 to May 1989. Finally, the model is applied to determine the present values of one barrel of oil deliverable in one to ten years time.     

Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates

This paper specifies a multivariate stochasticvolatility (SV) model for the S & P500 index and spot interest rateprocesses. We first estimate the multivariate SV model via theefficient method of moments (EMM) technique based on observations ofunderlying state variables, and then investigate the respective effects of stochastic interest rates, stochastic volatility, and asymmetric S & P500 index returns on option prices. We compute option prices using both reprojected underlying historical volatilities and the implied risk premiumof stochastic volatility to gauge each model's performance through direct comparison with observed market option prices on the index. Our major empirical findings are summarized as follows. First, while allowing for stochastic volatility can reduce the pricing errors and allowing for asymmetric volatility or leverage effect does help to explain the skewness of the volatility smile, allowing for stochastic interest rates has minimal impact on option prices in our case. Second, similar to Melino and Turnbull (1990), our empirical findings strongly suggest the existence of a non-zero risk premium for stochastic volatility of asset returns. Based on the implied volatility risk premium, the SV models can largely reduce the option pricing errors, suggesting the importance of incorporating the information from the options market in pricing options. Finally, both the model diagnostics and option pricing errors in our study suggest that the Gaussian SV model is not sufficientin modeling short-term kurtosis of asset returns, an SV model withfatter-tailed noise or jump component may have better explanatory power.     

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.     

International Interest Rates,Exchange Rates,and the Stochastic Structure of Supply

In a dual-currency, flexible exchange rate model, both nominal and real foreign exchange premia depend on investor risk attitudes, consumption parameters, and the stochastic structure of currency and commodity supplies. When supplies are random, their joint correlation structure determines the sign of the premia. If the money supplies are identically distributed, then all foreign exchange premia, regardless of the currency of denomination, are zero. A positive correlation between the value of a country's currency and its nominal interest rate need not indicate real interest rate movements. Relative bond prices can be negatively correlated with the terms of trade.     

Option Pricing under Stochastic Interest Rates: An Empirical Investigation

Using daily data of the Nikkei 225 index, call option prices and call money rates of the Japanese financial market,a comparison is made of the pricing performance of stock option pricing modelsunder several stochastic interest rate processes proposedby the existing term structure literature.The results show that (1) one option pricing modelunder a specific stochastic interest ratedoes not significantly outperformanother option pricing model under an alternative stochasticinterest rate, and (2) incorporating stochastic interest ratesinto stock option pricing does not contribute to the performanceimprovement of the original Black–Scholes pricing formula.     

Pricing Options under Stochastic Interest Rates: A New Approach

We will generalize the Black-Scholes option pricing formula by incorporating stochastic interest rates. Although the existing literature has obtained some formulae for stock options under stochastic interest rates, the closed-form solutions have been known only under the Gaussian (Merton type) interest rate processes. We will show that an explicit solution, which is an extended Black-Scholes formula under stochastic interest rates in certain asymptotic sense, can be obtained by extending the asymptotic expansion approach when the interest rate volatility is small. This method, called the small-disturbance asymptotics for Itô processes, has recently been developed by Kunitomo and Takahashi (1995, 1998) and Takahashi (1997). We found that the extended Black-Scholes formula is decomposed into the original Black-Scholes formula under the deterministic interest rates and the adjustment term driven by the volatility of interest rates. We will illustrate the numerical accuracy of our new formula by using the Cox–Ingersoll–Ross model for the interest rates.     

Corporate Bond Valuation and Hedging with Stochastic Interest Rates and Endogenous Bankruptcy

This paper analyzes corporate bond valuation and optimal calland default rules when interest rates and firm value are stochastic.It then uses the results to explain the dynamics of hedging.Bankruptcy rules are important determinants of corporate bondsensitivity to interest rates and firm value. Although endogenousand exogenous bankruptcy models can be calibrated to producethe same prices, they can have very different hedging implications.We show that empirical results on the relation between corporatespreads and Treasury rates provide evidence on duration, andwe find that the endogenous model explains the empirical patternsbetter than do typical exogenous models.     

Futures Commitments and Commodity Price Jumps

We examine the relationship between the commitments of three of the largest groups of futures traders and the abnormal price movements in five agricultural commodities. The general evidence suggests that the commitments of futures traders have been increasing over time, whereas the frequency of price jumps have not. Regression results indicate a negative relationship between price jumps and the commitments of speculators and small traders. There is also evidence of a negative relationship between the number of speculators and cash market volatility, consistent with a host of speculation-based theories.     

基于分数维随机利率的分数跳-扩散外汇期权定价

假设利率为分数维随机利率,外汇汇率服从分数跳一扩散过程,并且波动率为常数,期望收益率为时间的非随机函数,本文利用保险精算方法,得出了看涨、看跌外汇欧武期权的一般定价公式,并建立了平价公式。     

The Stochastic Volatility of Short-Term Interest Rates: Some International Evidence

This paper estimates a stochastic volatility model of short-term riskless interest rate dynamics. Estimated interest rate dynamics are broadly similar across a number of countries and reliable evidence of stochastic volatility is found throughout. In contrast to stock returns, interest rate volatility exhibits faster mean-reverting behavior and innovations in interest rate volatility are negligibly correlated with innovations in interest rates. The less persistent behavior of interest rate volatility reflects the fact that interest rate dynamics are impacted by transient economic shocks such as central bank announcements and other macroeconomic news.     

Interest Rate Futures Options and Interest Rate Options

This paper derives pricing models of interest rate options and interest rate futures options. The models utilize the arbitrage-free interest rate movements model of Ho and Lee. In their model, they take the initial term structure as given, and for the subsequent periods, they only require that the bond prices move relative to each other in an arbitrage-free manner. Viewing the interest rate options as contingent claims to the underlying bonds, we derive the closed-form solutions to the options. Since these models are sufficiently simple, they can be used to investigate empirically the pricing of bond options. We also empirically examine the pricing of Eurodollar futures options. The results show that the model has significant explanatory power and, on average, has smaller estimation errors than Black's model. The results suggest that the model can be used to price options relative to each other, even though they may have different expiration dates and strike prices.     

Empirically Effective Bond Pricing Model and Analysis on Term Structures of Implied Interest Rates in Financial Crisis

In his book (1993) Kariya proposed a government bond (GB) pricing model that simultaneously values individual fixed-coupon (non-defaultable) bonds of different coupon rates and maturities via a discount function approach, and Kariya and Tsuda (Financ Eng Japanese Mark 1:1–20, 1994) verified its empirical effectiveness of the model as a pricing model for Japanese Government bonds (JGBs) though the empirical setting was limited to a simple case. In this paper we first clarify the theoretical relation between our stochastic discount function approach and the spot rate or forward rate approach in mathematical finance. Then we make a comprehensive empirical study on the capacity of the model in view of its pricing capability for individual GBs with different attributes and in view of its capacity of describing the movements of term structures of interest rates that JGBs imply as yield curves. Based on various tests of validity in a GLS (Generalized Least Squares) framework we propose a specific formulation with a polynomial of order 6 for the mean discount function that depends on maturity and coupon as attributes and a specific covariance structure. It is shown that even in the middle of the Financial Crisis, the cross-sectional model we propose is shown to be very effective for simultaneously pricing all the existing JGBs and deriving and describing zero yields.     

Terms Structure of Interest Rates and Implicit Options: The Case of Japanese Bond Futures

The quality option for Japanese Government Bond Futures contracts is analysed using a term structure approach based upon a two-factor Heath, Jarrow and Morton (1990b) model. The option value is found to be 0.12%–0.2% of par three months prior to delivery. Also, analysis of variance confirms that the quality option has a negative theta .