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研究生： 蔡孟軒
Meng-Hsuan Tsai
論文名稱： Pricing Credit Linked Notes with a modifi ed LIBOR MARKET MODEL
指導教授： 張焯然
Jow-Ran Chang
口試委員:
學位類別： 碩士
Master
系所名稱： 科技管理學院 - 科技管理研究所
Institute of Technology Management
論文出版年： 2008
畢業學年度： 96
語文別： 英文
論文頁數： 49
中文關鍵詞： Credit linked notes 、LIBOR market model 、default intensity
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    • Due to the global depression economy with the low interest rate accompanied,
    the credit derivatives and interest rate derivatives have been blossoming. Structure
    notes are tailor-made products which are created by nancial engineering.
    In Lotz and Schlogl (2000), they supposed a model for nite-interval interest
    rates, for example, LIBOR (London InterBank O ered Rate) rate, which explicitly
    takes into account the possibility of default through the in
    uence of a point process
    with deterministic intensity. They relate the defaultable interest rate to the
    non-defaultable interest rate and to the credit risk characteristics default intensity
    and recovery rate in comparison with the forward LIBOR model that can derive the
    appropriate model assumption by using the observable market rate to calibrate the
    parameter of the model.
    Before having modi ed market model process, we should construct the termstructure
    of default intensity in advance that can transform non-defaultable into
    defaultable interest rate.
    Therefore, the rst aim of this study is to utilize the modi ed market model to
    construct the defaultable LIBOR rate, and to use defaultable cap to calibrate the
    instantaneous volatility of defaultable LIBOR used in modi ed market model as a
    parameter. After simulating defaultable LIBOR rate has been developed, the cash

    ows of credit linked notes will be identi ed.
    The second aim of this study is following Sch�onbucher (2000), he models effective
    default-free forward rates and forward credit spreads as lognormal di usion
    processes. Therefore, we also consider that default intensity is stochastic, and analyze
    what e ects will be produced in di erent correlation coefficient
    Keyword : Credit linked notes, LIBOR market model, default intensity

    1 Introduction 2 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.3 Credit default linked notes . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Literature review 7 2.1 Two approach of model credit derivatives . . . . . . . . . . . . . . . . 7 2.2 Market Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3 Methodology 9 3.1 Lognormal forward LIBOR Model . . . . . . . . . . . . . . . . . . . . 9 3.2 Merge the default risk into market model . . . . . . . . . . . . . . . . 11 3.3 Stochastic default intensity . . . . . . . . . . . . . . . . . . . . . . . . 13 3.4 Model Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.4.1 Set up of Instantaneous Volatility . . . . . . . . . . . . . . . . 14 3.4.2 Calibration of the LFM to the prices of Caps . . . . . . . . . . 15 3.5 Construct the Credit Curve . . . . . . . . . . . . . . . . . . . . . . . 16 4 Case Study 18 4.1 Notes description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4.2 Valuation in default intensity is deterministic . . . . . . . . . . . . . . 19 4.2.1 Construction of Yield curve . . . . . . . . . . . . . . . . . . . 19 4.2.2 Generate initial forward LIBOR . . . . . . . . . . . . . . . . 21 4.2.3 Construct the Credit Curve . . . . . . . . . . . . . . . . . . . 22 4.2.4 Change initial LIBOR into defaultable LIBOR . . . . . . . . . 23 4.2.5 Calibration Instantaneous Volatility of defaultable LIBOR 24 4.2.6 Calibration Instantaneous Volatility of non-defaultable LIBOR 27 4.2.7 Simulation non-defaultable and defaultable LIBOR . . . . 29 4.2.8 Calculation discount cash ows and pricing product . . . . .30 4.2.9 Sensitive analysis . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.2.9.1 Delta analysis . . . . . . . . . . . . . . . . . . . . . . 32 4.2.9.2 Gamma analysis . . . . . . . . . . . . . . . . . . . . 33 4.2.9.3 Vega analysis . . . . . . . . . . . . . . . . . . . . . . 33 4.2.10 Analysis of issuer strategy . . . . . . . . . . . . . . . . . . . . 34 4.2.10.1 Pro_t of issuer . . . . . . . . . . . . . . . . . . . . . 34 4.2.10.2 Risk of issuer . . . . . . . . . . . . . . . . . . . . . . 34 4.2.10.3 Hedging strategy of issuer . . . . . . . . . . . . . . . 34 4.2.11 Analysis of investor strategy . . . . . . . . . . . . . . . . . . 34 4.2.11.1 Pro_t of investors . . . . . . . . . . . . . . . . . . . . 34 4.2.11.2 Risk of investors . . . . . . . . . . . . . . . . . . . . 35 4.3 Valuation in default intensity is stochastic . . . . . . . . . . . . . . . 35 4.3.1 Find standard deviation . . . . . . . . . . . . . . . . . . . . . 35 4.3.2 Simulate default intensity to construct credit curve . . . 36 4.3.3 Plus non-defaultable LIBOR with default intensity . . . .37 4.3.4 Calculation discount cash ows and pricing product . . . .38 4.3.5 Sensitive analysis . . . . . . . . . . . . . . . . . . . . . . . . . 39 4.3.5.1 Delta analysis . . . . . . . . . . . . . . . . . . . . . . 39 4.3.5.2 Gamma analysis . . . . . . . . . . . . . . . . . . . . 39 4.3.5.3 Vega analysis . . . . . . . . . . . . . . . . . . . . . . 40 4.3.5.4 Default intensity analysis . . . . . . . . . . . . . . . 40 4.3.6 Analysis of issuer strategy . . . . . . . . . . . . . . . . . . . . 40 4.3.6.1 Pro_t of issuer . . . . . . . . . . . . . . . . . . . . . 40 4.4 Contrast between di_erent default intensity . . . . . . . . . . . . . . 41 4.5 Dependence relationships with two stochastic process . . . . . . .42 5 Conclusion and future work 45 Reference . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 A Term sheet 49

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