An Introduction to Modern Pricing of Interest Rate Derivatives School of Education, Culture and Communication Division of Applied Mathematics Introduction Interest Rates An Introduction to Modern Security Market Pricing of Interest Rate Derivatives Models Term- Master Thesis in Financial Engineering Structure Models Pricing Interest Rate Derivatives Author: Hossein Nohrouzian HJM Framework M¨ alardalen University and LIIBOR Market Model Collateral June 5, 2015 Agreement (CSA) Conclusion 1/30
An School of Education, Culture and Communication Introduction Division of Applied Mathematics Outline to Modern Pricing of Interest Rate Derivatives 1 Introduction Introduction Interest Rates 2 Interest Rates Security Market Models 3 Security Market Models Term- Structure Models 4 Term-Structure Models Pricing Interest Rate 5 Pricing Interest Rate Derivatives Derivatives HJM Framework 6 HJM Framework and LIIBOR Market Model and LIIBOR Market Model 7 Collateral Agreement (CSA) Collateral Agreement (CSA) 8 Conclusion Conclusion 2/30
An School of Education, Culture and Communication Introduction Division of Applied Mathematics Risky Asset vs Risk-Less Asset to Modern Pricing of Interest Rate Derivatives • Does exist two kind of investments? Introduction Interest Rates Security Market Models Term- Structure Models Pricing Interest Rate Derivatives HJM Framework and LIIBOR Market Model Collateral Agreement (CSA) Conclusion 3/30
An School of Education, Culture and Communication Introduction Division of Applied Mathematics Risky Asset vs Risk-Less Asset to Modern Pricing of Interest Rate Derivatives • Does exist two kind of investments? Introduction • An example is pension salary vs inflation. Interest Rates Security Market Models Term- Structure Models Pricing Interest Rate Derivatives HJM Framework and LIIBOR Market Model Collateral Agreement (CSA) Conclusion 3/30
An School of Education, Culture and Communication Introduction Division of Applied Mathematics Risky Asset vs Risk-Less Asset to Modern Pricing of Interest Rate Derivatives • Does exist two kind of investments? Introduction • An example is pension salary vs inflation. Interest Rates • NASDQ value increased by almost 150% in 5 years. Security Market Models Term- Structure Models Pricing Interest Rate Derivatives HJM Framework and LIIBOR Market Model Collateral Agreement (CSA) Conclusion Figure: Price behavior of the NASDAQ from 2010 to 2015 3/30
An School of Education, Culture and Communication Introduction Division of Applied Mathematics Interest Rate and Economics to Modern Pricing of Interest Rate Factors Derivatives Introduction • Interest rate and monetary policy. Interest Rates • Interest rate and international trading. Security • Interest rate and economic growth. Market Models Term- Structure Models Pricing Interest Rate Derivatives HJM Framework and LIIBOR Market Model Collateral Agreement (CSA) Conclusion 4/30
An School of Education, Culture and Communication Introduction Division of Applied Mathematics Interest Rate and Economics to Modern Pricing of Interest Rate Factors Derivatives Introduction • Interest rate and monetary policy. Interest Rates • Interest rate and international trading. Security • Interest rate and economic growth. Market Models • 0.0%, -0.1% and -0.25% Term- Structure Models Pricing Interest Rate Derivatives HJM Framework and LIIBOR Market Model Collateral Agreement (CSA) Conclusion Figure: The exchange rate between USD and SEK 4/30
An School of Education, Culture and Communication Introduction Division of Applied Mathematics Jump Diffusion to Modern Pricing of Interest Rate Derivatives • On 15th of January 2015 SNB unexpectedly scrapped its Introduction cap on the Euro value of the Franc. Interest Rates Security Market Models Term- Structure Models Pricing Interest Rate Derivatives HJM Framework and LIIBOR Market Model Collateral Agreement (CSA) Conclusion 5/30
An School of Education, Culture and Communication Introduction Division of Applied Mathematics Jump Diffusion to Modern Pricing of Interest Rate Derivatives • On 15th of January 2015 SNB unexpectedly scrapped its Introduction cap on the Euro value of the Franc. Interest Rates • The result was 27.5% change in USD vs CHF and shake in Security stock prices. Market Models Term- Structure Models Pricing Interest Rate Derivatives HJM Framework and LIIBOR Market Model Collateral Agreement (CSA) Conclusion Figure: Exchange rate between USD and CHF 5/30
An School of Education, Culture and Communication Introduction Division of Applied Mathematics Banks vs Market Rates to Modern Pricing of Interest Rate Derivatives • Banks offered rates to individuals and companies. Introduction Interest Rates Security • Interest rates in the market. Market Models Term- Structure Models Pricing Interest Rate Derivatives HJM Framework and LIIBOR Market Model Collateral Agreement (CSA) Conclusion 6/30
An School of Education, Culture and Communication Introduction Division of Applied Mathematics Banks vs Market Rates to Modern Pricing of Interest Rate Derivatives • Banks offered rates to individuals and companies. Introduction Interest Rates • Different banks use different rates for loans and savings. Security • Interest rates in the market. Market Models Term- Structure Models Pricing Interest Rate Derivatives HJM Framework and LIIBOR Market Model Collateral Agreement (CSA) Conclusion 6/30
An School of Education, Culture and Communication Introduction Division of Applied Mathematics Banks vs Market Rates to Modern Pricing of Interest Rate Derivatives • Banks offered rates to individuals and companies. Introduction Interest Rates • Different banks use different rates for loans and savings. Security • Interest rates in the market. Market Models • Before the economic crisis in 2007 and 2008: Term- Structure Models Pricing • From and after the economic crisis in 2007 and 2008: Interest Rate Derivatives HJM Framework and LIIBOR Market Model Collateral Agreement (CSA) Conclusion 6/30
An School of Education, Culture and Communication Introduction Division of Applied Mathematics Banks vs Market Rates to Modern Pricing of Interest Rate Derivatives • Banks offered rates to individuals and companies. Introduction Interest Rates • Different banks use different rates for loans and savings. Security • Interest rates in the market. Market Models • Before the economic crisis in 2007 and 2008: Term- • XIBOR was reference of interest rate for loans in the Structure Models international financial market. Pricing • From and after the economic crisis in 2007 and 2008: Interest Rate Derivatives HJM Framework and LIIBOR Market Model Collateral Agreement (CSA) Conclusion 6/30
An School of Education, Culture and Communication Introduction Division of Applied Mathematics Banks vs Market Rates to Modern Pricing of Interest Rate Derivatives • Banks offered rates to individuals and companies. Introduction Interest Rates • Different banks use different rates for loans and savings. Security • Interest rates in the market. Market Models • Before the economic crisis in 2007 and 2008: Term- • XIBOR was reference of interest rate for loans in the Structure Models international financial market. Pricing • From and after the economic crisis in 2007 and 2008: Interest Rate Derivatives • Collateral rate: HJM Framework and LIIBOR Market Model Collateral Agreement (CSA) Conclusion 6/30
An School of Education, Culture and Communication Introduction Division of Applied Mathematics Banks vs Market Rates to Modern Pricing of Interest Rate Derivatives • Banks offered rates to individuals and companies. Introduction Interest Rates • Different banks use different rates for loans and savings. Security • Interest rates in the market. Market Models • Before the economic crisis in 2007 and 2008: Term- • XIBOR was reference of interest rate for loans in the Structure Models international financial market. Pricing • From and after the economic crisis in 2007 and 2008: Interest Rate Derivatives • Collateral rate: • is used in the collateral agreement or CSA, HJM Framework • calculated daily on the overnight index swaps. and LIIBOR Market Model Collateral Agreement (CSA) Conclusion 6/30
An School of Education, Culture and Communication Introduction Division of Applied Mathematics Banks vs Market Rates to Modern Pricing of Interest Rate Derivatives • Banks offered rates to individuals and companies. Introduction Interest Rates • Different banks use different rates for loans and savings. Security • Interest rates in the market. Market Models • Before the economic crisis in 2007 and 2008: Term- • XIBOR was reference of interest rate for loans in the Structure Models international financial market. Pricing • From and after the economic crisis in 2007 and 2008: Interest Rate Derivatives • Collateral rate: • is used in the collateral agreement or CSA, HJM Framework • calculated daily on the overnight index swaps. and LIIBOR Market Model • Swap rates: Collateral Agreement (CSA) Conclusion 6/30
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