Assumption Of Constant Interest Rate Research Articles

Martingale Measures & Change of Measure Explained

An option is a financial instrument that allows the holder to buy or sell an underlying security in the future at an agreed strike or price set today. European options are often priced under the assumption of constant interest rates as seen in the Black-Scholes (1973) model. In interest rate markets however the underlying security is an interest rate, which cannot be assumed constant. Likewise bond markets have a similar requirement. To relax such an assumption option payoffs and prices can be evaluated as the expectation of a stochastic martingale process. In this paper we illustrate how to use the change of measure technique to evaluate the dynamics of a stochastic process. Firstly we discuss the preliminaries, namely Martingale measures and numeraires. Secondly we model interest rates as a Vasicek short rate process. Finally we outline how to apply a change of measure technique, where it can be seen that a change of measure to the terminal-forward measure allows us to evaluate model dynamics and simplify the calculation.

UJI HIPOTESIS “JALAN-ACAK” DALAM FUNGSI KONSUMSI DI INDONESIA

This study is aimed at testing the random-walk hypothesis in the Indonesian economy consumption function. If the random-walk exists then the consumption can not be predicted sistematicaly. The study found that there was no random-walk in the Indonesian consumption function either under the assumption of constant interest rate or that of variable interest rate. Other finding is that both nominal interest rate and the rate of inflation had significant effect on the consumption. Keywords: consumption, random-walk, rational expectation, life cycle-permanent income

Bond Option Pricing using the Vasicek Short Rate Model

An option is a financial instrument that allows the holder to buy or sell an underlying security in the future at an agreed strike or price set today. Many options are priced under the assumption of constant interest rates as seen in the Black-Scholes (1973) model. In interest rate markets however the underlying security is an interest rate, which cannot be assumed constant. Likewise bond markets have a similar requirement.In what follows the assumption of a constant interest rate is relaxed. Bond option pricing using the Vasicek short rate model is examined in such a way that the methodology could be applied to any short rate model such as the classical Hull-White model (1990a).Firstly we discuss the preliminaries, namely numeraires and measures, where it can be seen that a careful choice of numeraire can simplify option calculations. Secondly we summarize the Vasicek short rate process and a change of numeraire to the terminal-forward measure is outlined, which simplifies bond option pricing calculations. Thirdly we review both pure discount and coupon bond pricing. Fourthly bond option pricing formulae are derived and Jamshidian's Trick outlined.Finally in conclusion practical implementation considerations and model extensions are discussed. The aim of this paper is to provide a general overview of option pricing using short rate models, using the Vasicek model as an important case study.

The Value of Embedded Real Options: Evidence from Consumer Automobile Lease Contracts

Under the common assumption of constant interest rates, we show that penalties for early termination of a lease are often structured in such a way that the cancellation option embedded in consumer automotive leases has little value. Furthermore, our estimates drawn from a sample of three popular car models over 1990 to 2000 indicate that the stand-alone value of the lease-end purchase option is, on average, about 16% of the market value of underlying used vehicles, or about $1,462 per contract. Finally, we examine the sensitivity of our option value estimates to model parameters and default risk.

Valuation of Equity-Indexed Annuities Under Stochastic Interest Rates

This paper considers the pricing of equity-indexed annuities (EIAs). Traditionally, the values of the guarantees embedded in these contracts are priced by modeling the underlying index fund while keeping the interest rates constant. The assumption of constant interest rates becomes unrealistic in pricing and hedging the EIAs since the embedded guarantees are often of much longer maturity. To solve this problem, the authors propose an economic model that has the flexibility of modeling the underlying index fund as well as the interest rates. Some popular EIAs are illustrated to assess the implication of the proposed model.

On the Tree-Cutting Problem Under Interest Rate and Forest Value Uncertainty

The current literature on optimal forest rotation makes the unrealistic assumption of constant interest rate though harvesting decisions of forest stands are typically subject to long time horizons. We apply the Wicksellian single rotation framework to cover the unexplored case of variable and stochastic interest rate. By modelling the stochastic interest rate according to the Cox-Ingersoll-Ross model and the forest value as a geometric Brownian motion we provide an explicit solution for the Wicksellian single rotation problem and show that increased interest rate volatility increases the optimal exercise threshold of the irreversible harvesting opportunity and thereby prolongs the optimal rotation period. Numerical illustration indicates that the optimal threshold becomes higher at an increasing rate.

Wicksellian Theory of Forest Rotation Under Interest Rate Variability

The current literature on optimal forest rotation makes the assumption of constant interest rate. However, the irreversible harvesting decisions of forest stands are typically subject to relatively long time horizons over which interest rates do fluctuate considerably. In this paper we apply the Wicksellian single rotation framework to extend the existing studies to cover the unexplored case of variable interest rate. Given the technical generality of the considered valuation problem, we provide a thorough mathematical characterization of the optimal timing problem and develop new results. We show that even in the deterministic case if the current interest rate deviates from its long-run steady state, interest rate variability changes the rotation age significantly when compared with the constant discounting case. Further, and importantly, allowing for interest rate uncertainty is shown to increase the optimal rotation period when the value of the optimal policy is a convex function of the current interest rate. In line with this finding, we also establish that increased interest rate volatility has a positive impact on the optimal rotation period.

The Relative Valuation of American Currency Spot and Futures Options: Theory and Empirical Tests

This study empirically tests contingent claims pricing models for American currency spot and futures options. Numerical analysis indicates that the difference in the model prices of spot and futures put (call) options (with the same exercise price and maturity) is, for a premium (discount) currency, positive and an increasing function of (a) the absolute dif? ference in the prices of the underlying spot and futures contracts and (b) the maturity of the options. Tests on British pound, Deutsche mark, and Swiss franc options indicate many violations ofthe ordinal pricing relationships noted above. Additional tests indicate that option prices are inconsistent with functional relationship (b) above. Most of the ob? served violations are sufficiently large to provide arbitrage profits net of transaction costs, assuming interest rates are constant and the Interest Rate Parity theorem holds continu? ously. Alternatively, both the violations and the inconsistent functional relationship may be due to violation of the assumption of constant interest rates.