The Pricing, Risk Measure, Hedging and Arbitrage of Bonds with Embedded Options

• Main Authors: CHOU,PO-YEN, 周伯彥
• Other Authors: Lee, Shyan-Yuan
• Format: Others
• Language: zh-TW
• Published: 2003
• Online Access: http://ndltd.ncl.edu.tw/handle/59443477946643949050

碩士 === 國立臺灣大學 === 財務金融學研究所 === 91 === Fixed-Income market is the largest financial market in the world. With the progress of financial engineering technologies, the interest rate options become the fastest growing products in the derivative market. Bonds with embedded call or put options combine the characters of fixed-income security and interest rate options and can be viewed as the most basic form of the recently popular structured products .The embedded option provisions can not only meet the special financing needs of enterprises, but also provide investors with more investment choices. In spite of all the advantages, embedded option provisions will make the pricing and interest rate risk measurements more difficult. Therefore, it may cause considerable inaccuracy in both investment and hedging performance. Thus, this thesis focuses on the pricing, risk measures, hedging and arbitrage issues of bond with embedded options. The volatility of underlying asset is the most important factor of pricing an option. Empirical studies show that implied volatility extracted from the market price of an option can forecast the future volatility of the underlying asset. In the case of interest rate option market, besides the term structure of interest rates, there exits a term structure of volatilities, which can be extracted from the market prices of interest rate options with different maturities. Therefore, the pricing of interest rate options is more difficult due to the above-mentioned complex scheme. This thesis chooses the Ritchken and Chuang(1999) interest rate model as the pricing model and the analytic tool because the model is of HJM paradigm, which means it can take the most general form of volatility structure into consideration, and the numerical procedure has been developed well in order to pricing the path-dependent style options. By implementing the interest rate model, we can examine the influence of the volatility structure on the price and the risk measures (ED & EC) of bond with embedded options. This thesis follows the research scheme of Buetow, Hanke and Fabozzi(2001) to analyze the reasonability of the risk measures (ED & EC)for callable and putable bonds by using the RC model. Further, this thesis compares ED and EC of the three styles of embedded options (American, Burmudan, and European) to see whether the corresponding relationships are reasonable or not. By those two kinds of examinations, we conclude that the risk measures of bond with embedded options derived from RC model are credible. Moreover, from the hedging relationship between bullet bond and interest rate swap, we find the comparable hedging relationship between bond with embedded options and putable swap, and therefore, between bond option and swaption. Because of the inconsistency in the standard market models, there might exist arbitrage opportunities between bond option and swaption. By implementing the RC model, it provides a consistent analytic surrounding to detect the arbitrage opportunities between bond option and swaption. In summery, this thesis researches risk measures, hedging and arbitrage issues of bond with embedded options with RC model and obtains practical conclusions. These results can provide good reference to further researches on bonds with more complicated embedded options as well as the MBS products.