The Valuation of CBOT Mortgage-Backed Options

CBOT不動產抵押擔保選擇之評價

10.6545/JoFS.1996.4(1).4

許溪南(His-Nan Hsu)

選擇權 ； 不動產抵抽擔保證券 ； 蒙地卡羅法 ； options ； mortgage-backed securities ； Monte Carlo simulation

中國財務學刊

4卷1期（1996 / 07 / 31）

83 - 114

英文

CBOT不動產犯押擔保遺擇權之棒的詮券為CBOT不動產抵押擔保期貨，而後者之樺的證券又為GNMA濃濃授券。CBOT不動產抵押擔保選擇權與商品期貨選擇權或無違約風險債券選擇權之間，有許多重大的差異存在。本文的第一個目的是利用標準套利理論對CBOT不動產犯押擔保選擇權提供一均衡的評價架構。此一評價架構包含由三個偏微分方程式及其邊界條件所組成。此一評價架構非常有用，可應用於其他與利率有關的複雜證券上。本文的第二個目的是在應用蒙地卡羅方法求解這被雜的偏微分方程。在模擬過程，看見們利用對偽變異法來降低模擬結果的變異數。結果顯示，CBOT不動產抵押擔保選擇權之價格行為與商品期貨選擇權之價格行為有不同。

CBOT Mortgage-Backed options are options on CBOT Mortgage-Backed futures which, in turn, are futures on GNMA pass-through securities. Many significant differences exist between CBOT Mortgage-Backed options and commodity futures options or default-free bond options. The first purpose of this paper is to use standard arbitrage argument to provide an equilibrium valuation framework for the CBOT Mortgage-Backed options. This framework consists of a system of three partial differential equations with initial and boundary conditions. This valuation framework is very useful in that it is applicable to other complicated interest-dependent securities. The second purpose of this paper is to use Monte Carlo simulation to solve these complicated partial differential equations. In the simulation process, we use antithetic variate method to reduce the variance of simulation results. Results indicate that the price behavior of CBOT Mortgage-Backed options is different from that of commodity futures options.