Uses of sans arbitrage Models: New Frontiers in Interest Rate, Credit and Energy Risks Third Annual Bloomberg Le .


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Uses of without arbitrage Models: New Boondocks in Loan fee, Credit and Vitality Chances Third Yearly Bloomberg Address in Money. Thomas S. Y. Ho PhD President THC October 26, 2009 Tom.ho@thomasho.com . Sans arbitrage Term Structure Models. Valuation models
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Uses of without arbitrage Models: New Frontiers in Interest Rate, Credit and Energy Risks Third Annual Bloomberg Lecture in Finance Thomas S. Y. Ho PhD President THC October 26, 2009 Tom.ho@thomasho.com

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sans arbitrage Term Structure Models Valuation models Derivative evaluating (relative valuation) under loan cost, credit and other hazard drivers Applications Trading Portfolio administration Enterprise chance administration Impacts on the business sectors Price revelation prepare Regulatory approaches in the monetary markets Introduction

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Questions Addressed What are the model\'s financial rule that make the model prevalent and key? What are the outskirts of uses of the model in going ahead? What are my preventative notes on the utilization of the model? Detail talks are accessible in the references Introduction

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References Amin , Kaushik I., and Andrew J. Morton, 1994, " Implied Volatility Functions in sans arbitrage Term Structure Models, " Journal of Financial Economics, 35 (2), 141-180 Benth , Fred Espen , Lars Ekeland , Ragner Hauger and Bjorn Fredrik Nielsen 2003 "A Note on without arbitrage Pricing of Forward Contracts in Energy Market" Applied Mathematical Finance 10, 325-336 Eydeland , Alexander and Krzysztof Wolyniec 2003 Energy and Power Risk Management, Wiley Finance Harrison, J Michael, and David M. Kreps, 1979 "Martingales and Arbitrage in Multiperiod Securities Markets<" Journey of Economic Theory, 20(3), 381-408 Ho, Thomas S. Y. 1992 "Key rate terms: measures of loan cost dangers" Journal of Fixed-Income, 2(2), 19-44 Ho, Thomas S. Y. what\'s more, Sang-Bin Lee 2003, The Oxford Guide to Financial Modeling, Oxford University Press Ho, Thomas S. Y. what\'s more, Sang-Bin Lee 1986, "Term Structure Movements and the Pricing of Interest Rate Contingent Claims," Journal of Finance, 41 (5), 1011-1029 Ho, Thomas S. Y. furthermore, Sang Bin Lee,2009 " Valuation of Credit Contingent Claims: A sans arbitrage Credit Model" Journal of Investment Management vol 7 No 5 Ho, Thomas S. Y. Ho and Sang Bin Lee, 2009 "A Unified Credit and Interest Rate Arbitrage-Free Contingent Claim Model" Journal of Fixed-Income Ho, Thomas S. Y. furthermore, Blessing Mudavanhu,2007 "Stochastic Movement of the Implied Volatility Function" Journal of Investment Management 4 th quarter Ho, Thomas S. Y. what\'s more, Sang Bin Lee, 2007 ""Generalized Ho-Lee Model: A Multi-calculate State-Time Dependent Implied Volatility Function Approach" Journal of Fixed Income 4 th quarter Ho, Thomas S. Y. 2007 "Overseeing Interest Rate Volatility Risk: Key Rate Vega" Journal of Fixed Income 4 th quarter Ho, Thomas S. Y. what\'s more, Sang-Bin Lee 2009 " A Unified Model: without arbitrage Term Structure Movements of Flow Risks" Ho, Thomas S. Y. what\'s more, Sang Bin Lee " Pricing of Contingent Claims on Natural Gas" working paper Nawalkha , Sanjay K., Natalia A. Beliaeva and Gloria M Soto 2007 Dynamic Term Structure Modeling Wiley Finance References

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Outline Salient elements of the model A point of view of sans arbitrage term structure models A system to investigate new boondocks in applications Apply the system to … Interest rate chance Credit hazard Energy chance Going forward: Managing model dangers Edwards Deming way to deal with hazard administration Introduction

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The Black-Scholes Model Components of a without arbitrage Model Valuation part C( S, t) Specify the unexpected claim dS = r(t) Sdt + σ (t) Sdz Specify the hidden hazard handle Application segment Delta: dynamic replication Calibration to decide the inferred instability sans arbitrage Models

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sans arbitrage Term Structure Model Valuation Component of the Model C = C( r , p(t, T), t) Contingent claims on the markdown work dr = F( p(t, T), t) dt + σ (r, t) dw Short rate display Forward rate show Market demonstrate X(n-1,i) = 0.5 p( n,i )(B( n,i ) + B(n, i+1)) Rolling back balanced by the rebate rate B(n-1, i ) = max ( X(n-1, i ), K) sans arbitrage models

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Key Rate Duration – Dynamic Replication Application Component of the Model Callable security Maturity 2020-10-15 SA settled coupon rate 5.65% Bermudan callable at standard Used for supporting, chance administration, and venture sans arbitrage Models

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Implied Volatility Function Calibration: Application C omponent of the Model sans arbitrage Models

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Term Structure Models and the Black-Scholes Model: a Comparison The term structure display: Time measurement, rate, a "stream idea" From the monetary displaying viewpoint, the Black Scholes model is not a unique instance of a term structure display – subsequently "term structure" Correlations of the securities of the term structure: Principal segment techniques Ho, Thomas S. Y. furthermore, Sang-Bin Lee 2009 " A Unified Model: sans arbitrage Term Structure Movements of Flow Risks" without arbitrage models

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Proposed Perspective of Term Structure Models "Stock" versus "Stream" sans arbitrage models have two parts Valuation segment (a few cases) Multi-consider models Time and state subordinate inferred unpredictability work Unspanned stochastic instability work Application segment Effectiveness of element supporting and ramifications of the suggested volatilities sans arbitrage Models

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Credit Term Structure Valuation of settled salary instruments with credit chance Reduced frame and auxiliary models Credit default swap (CDS) Survival work versus markdown work State and time subordinate survival rate s( n,i ) Ho, Thomas S. Y. what\'s more, Sang Bin Lee,2009 " Valuation of Credit Contingent Claims: A without arbitrage Credit Model" Journal of Investment Management vol 7 No 5 Applications: Credit Risk Modeling

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Valuing Credit Contingent Claims Valuation Component of the Model Make-entire Option X(n-1,i) = 0.5 p(n) s( n,i ) (B( n,i ) + B(n, i+1)) Rolling back balanced by the survival rate B(n-1, i ) = max ( X(n-1, i ), K) Boundary and terminal conditions p(n) one period time esteem rebate figure K strike value (an illustration), exhibit estimation of the yield balanced Treasury securities Applications: Credit Risk Modeling

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Valuation of Embedded Credit Options Applications: Credit Rsk Modeling

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Implications of the Credit Term Structure Application Component of the Model Determine the credit scratch rate spans for credit supporting Specify the exact dollar credit presentation in the term structure Identify the suggested credit volatilities Use of the auxiliary models Interest rate and credit hazard relationship Applications to a callable instruments Applications: Credit Risk Modeling

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Applications of the Term Structure Credit Model Dynamic developments of the term structure of credit Specify the implanted make entire choice in business contracts Impact of the connection to the loan fee level Relating a diminished frame model to the basic model Multi-consider credit show Applications: Credit Risk Modeling

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Natural Gas Futures Term Structure Basic financial matters of characteristic gas: Henry Hub information Well head cost, assembling and handling costs Storage and cost to convey Demand: Weather influences warming; control era Injection season: April - October Withdrawal season: November – March Ho, Thomas S. Y. what\'s more, Sang Bin Lee " Pricing of Contingent Claims on Natural Gas" working paper Applications: Energy Risk Modeling

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Importance of Modeling NG Term Structure Deregulation of force industry Supply: Horizontal apparatuses Power costs D epending on the offer stack and power request Bid stack relies on upon the fuel cost and the blackout Use of subsidiaries to oversee vitality hazard and capital ventures Applications: Energy Risk Modeling

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Modeling of the Natural Gas Price Process Abadic , Luis M and Jose Chamorra (2006) 2 consider demonstrate with the stochastic fuel value mean returning to a stochastic long haul value The stochastic long haul value mean returning to a steady value Eydeland , Alexander and Krzysztof Wolyniec (2003) and Benth et al (2003) Use sans arbitrage models Ho and Lee (2009) Identify the term structure "stream chance" and the "stock hazard" Applications: Energy Risk Modeling

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Data and Methodology Futures and spot every day costs from 1/3/2006 - 12/27/2006 Futures conveyance dates: month to month from 1/1/2007 and 1/1/2010 Implied cost of convey c(t, T) = (1/(T-t)) ln F( t,T )/S(t) Use the key segment way to deal with indicate the developments Data Source: Logical Information Machines (LIM) Applications: Energy Risk Modeling

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Henry Hub $ MMBtu (12/12/05-8/7/09) Applications: Energy Risk Modeling

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Term Structure of Henry Hub Futures Prices 10/16/2009 Applications: Energy Risk Model

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Natural Gas Futures Term Structure Movements Applications: Energy Risk Modeling

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sans arbitrage Natural Gas Model Valuation Component of the Model Contingent claims on the NG spot and prospects costs Implied cost to convey: The term structure Futures contracts deciding the inferred cost of convey The one time frame cost to convey is comparable to the survival rate Dynamics of the term structure: The term structure of cost to convey and the spot rates dS = c(t) S dt + σ (t) S dz dc(t) = F( c(t, T), t) dt + σ * dw Applications: Energy Risk Modeling

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Preliminary Results on Dynamic Hedging Application Component of the Model The fates term structure developments have two elements: "Cost" (85%), "Cost to Carry" (14%), 3 rd vector (0.3%) The cost of convey developments has one element: level development (99.5%) and 2 nd calculate (0.4%) Correlation of the spot cost and cost to convey: low The utilization of key rate spans on the cost to convey and the spot cost for supporting Applications: Energy Risk Modeling

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1 st Principal Movement of the Cost to Carry Applications: Energy Risk Modeling .:tslidesep.

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