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Pricing of the Cheapest Delivery Option of Bond Future Based on CIR Model

Author: RanMao
Tutor: MaRuJing
School: Southwestern University of Finance and Economics
Course: Finance
Keywords: bond future contract delivery option term structure model of interestrate CIR model Kalman filter
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Type: Master's thesis
Year: 2013
Downloads: 78
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Abstract


Interest rate futures are designed to reduce the risk of cash bond or other interest-rate sensitive assets or liabilities. In the future market, what investors concerned with is the movement of the future price. The Holding Cost Pricing Theory states that the future price is equal to the expected price of the future. But most of the interest rate future contract contains Minimum Value Delivery Option, which makes the prices of the two derivate from each other.The Minimum Value Delivery Option gives the short the right to choose the cheapest to delivery amount several bonds, thus the long must be compensated for writing this option. The value of the option is reflected in the real price of the future, thusthe future price is always less than the expected price of that future. Early studies state that the delivery option is greatly influenced by the future price. However, recent researches state that the value of the option is not significant. For a three-month future contract, the value of the option is estimated to be less than2percent of its face value. Owing to the complexity of modeling, many early researches adopted non-stochastic interest rate movements and assumed the equality of futures price and forward price. However, the futures price is greatly influenced by the interest rate movements, and is said to be not equal to the forward price. Neglecting all those mentioned above will lead to the estimating error of futures price and the value of the quality option. To perform a precise estimation, we afford a numerical framework to analyze the futures price and the value of the quality option.The structure of this article is as follows:The first chapter briefly discusses the development of China’s treasury bonds spot market, including the types of bonds, the primary market, and the market that improves liquidity of bonds—the secondary market. Treasury bond future is designed to increase liquidity in, and reduce the risk of, bond market, thus a basic comprehension of the spot market would not be unnecessary. The second chapter reviews the development of treasury bond future market, and made a simple introduction to the treasury bond future contracts which were designed in the early piloting stage. Because of the control of interest rate, the main factor affecting the value of the contract is the inflation subsidy. As a result of the imperfection of the value formation mechanism and the lacking of effective market regulation, the early piloting bond futures market soon fall into chaos.The third chapter of this essay introduces the Treasury bond futures contract that is to be launched. Contract elements include price limits, the settlement price and the margin requirements. We briefly introduced the virtual bond, which is set to be the subject of the treasury bond future contract. The subject of the treasury bond future contract is not a bond in circulation, but a virtual one which has a coupon rate of3%and a life of5years. When the contract expires, the short can make settlement of that contract with any coupon bond with a remaining life of4to7years. The CF (conversion factor) is use to standardize the bond. Method adopted by the exchange for calculating the conversion factor is based on a flat term structure of interest rates. It ignores the stochastic characteristics of interest rate, thus it cannot accurately reflect the relative price of bonds.The fourth chapter introduces delivery options and the theory of term structure of interest rates. Methods used to describe the static term structure of interest rates include parameter method and the spline method, while dynamic term theory adds random variables to describe the stochastic feature of interest rate. Because the observed market interest rates have the characteristics of mean reversion, we adopt CIR model to describe the interest rate movement. Through principal component analysis, we found that three factors can explain more than95%of the variation of interest rates. Thus we use the three factor CIR model, and based on this model we established affine relation between factors and the spot rates.We have31groups of interest rates, but only3factors. Thus it is necessary to add a noise to describe the observed error. To estimate the parameters in the CIR model, we adopted Kalman Filtering method. The process of Kalman Filtering is to construct the state space, then establish the measurement equation and the transferring equation. In each time we compute the state variables, a prediction error will be generated. We adopted the maximum likelihood estimation method to minimize the error, and the parameters of the model can be estimated. Factors in our CIR model include the one that influences the short-term interest rates, and the one that impacts the long-term interest rates. We can then calculate parameters in the affine model and then spot rates of various terms can be got.This paper abandons the holding cost pricing model, suggesting that the essence of the delivery option is a swaption. This swaption gives the short the right to exchange the minimum cost deliverable bond among a group of bonds to the bond of minimum cost in before. Price of the cheapest to deliver bond at the observation point and the one at the expiration of the future contract can be estimate by using the CIR model. Through many times of simulations, we estimated the option value is about1.48per contract with a face value of100.

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