Topic
Rendleman–Bartter model
About: Rendleman–Bartter model is a research topic. Over the lifetime, 1637 publications have been published within this topic receiving 66993 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, a closed-form solution for the price of a European call option on an asset with stochastic volatility is derived based on characteristi c functions and can be applied to other problems.
Abstract: I use a new technique to derive a closed-form solution for the price of a European call option on an asset with stochastic volatility. The model allows arbitrary correlation between volatility and spotasset returns. I introduce stochastic interest rates and show how to apply the model to bond options and foreign currency options. Simulations show that correlation between volatility and the spot asset’s price is important for explaining return skewness and strike-price biases in the BlackScholes (1973) model. The solution technique is based on characteristi c functions and can be applied to other problems.
7,867 citations
TL;DR: In this article, the authors derived a general form of the term structure of interest rates and showed that the expected rate of return on any bond in excess of the spot rate is proportional to its standard deviation.
6,160 citations
TL;DR: In this article, the authors present a unifying theory for valuing contingent claims under a stochastic term structure of interest rates, based on the equivalent martingale measure technique.
Abstract: This paper presents a unifying theory for valuing contingent claims under a stochastic term structure of interest rates. The methodology, based on the equivalent martingale measure technique, takes as given an initial forward rate curve and a family of potential stochastic processeE for its subsequent movements. A no arbitrage condition restricts this family of processes yielding valuation formulae for interest rate sensitive contingent claims which do not explicitly depend on the market prices of risk. Examples are provided to illustrate the key results. IN RELATION TO the term structure of interest rates, arbitrage pricing theory has two purposes. The first, is to price all zero coupon (default free) bonds of varying maturities from a finite number of economic fundamentals, called state variables. The second, is to price all interest rate sensitive contingent claims, taking as given the prices of the zero coupon bonds. This paper presents a general theory and a unifying framework for understanding arbitrage pricing theory in this context, of which all existing arbitrage pricing models are special cases (in particular, Vasicek (1977), Brennan and Schwartz (1979), Langetieg (1980), Ball and Torous (1983), Ho and Lee (1986), Schaefer and Schwartz (1987), and Artzner and Delbaen (1988)). The primary contribution of this paper, however, is a new methodology for solving the second problem, i.e., the pricing of interest rate sensitive contingent claims given the prices of all zero coupon bonds. The methodology is new because (i) it imposes its stochastic structure directly on the evolution of the forward rate curve, (ii) it does not require an "inversion of the term structure" to eliminate the market prices of risk from contingent claim values, and (iii) it has a stochastic spot rate process with multiple stochastic factors influencing the term structure. The model can be used to consistently price (and hedge) all contingent claims (American or European) on the term structure, and it is derived from necessary and (more importantly) sufficient conditions for the absence of arbitrage. The arbitrage pricing models of Vasicek (1977), Brennan and Schwartz (1979), Langetieg (1980), and Artzner and Delbaen (1988) all require an IFormerly titled "Bond Pricing and the Term Structure of Interest Rates: A New Methodology."
2,574 citations
TL;DR: In this article, the authors present a consistent and arbitrage-free multifactor model of the term structure of interest rates in which yields at selected fixed maturities follow a parametric muitivariate Markov diffusion process with stochastic volatility.
Abstract: This paper presents a consistent and arbitrage-free multifactor model of the term structure of interest rates in which yields at selected fixed maturities follow a parametric muitivariate Markov diffusion process with “stochastic volatility.” the yield of any zero-coupon bond is taken to be a maturity-dependent affine combination of the selected “basis” set of yields. We provide necessary and sufficient conditions on the stochastic model for this affine representation. We include numerical techniques for solving the model, as well as numerical techniques for calculating the prices of term-structure derivative prices. the case of jump diffusions is also considered.
2,288 citations
TL;DR: In this paper, the extended Vasicek model is shown to be very tracta-ble analytically, and option prices are compared with those obtained using a number of other models.
Abstract: This article shows that the one-state-variableinterest-rate models of Vasicek (1977) and Cox,Ingersoll, and Ross (1985b) can be extended sothat they are consistent with both the current termstructure of interest rates and either the currentvolatilities of all spot interest rates or the currentvolatilities of all forward interest rates. Theextended Vasicek model is shown to be very tracta-ble analytically. The article compares option pricesobtained using the extended Vasicek model withthose obtained using a number of other models.
2,132 citations