Interest Rate Derivatives
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Day 1 Brief revision of swaps Pricing off a Futures Strip Building a discount curve Adjusting for the convexity bias Fair pricing of a short-term swap Demonstrating hedge effectiveness Computer-based exercise Pricing a swap Derivation of Zero Coupon Discount Factors and Forward Rates Brief reminder: bootstrapping and estimation of forward rates When does bootstrapping breakdown? Practical issues: interpolation, blending and smoothing What represents a “good” curve: an alternative approach Building a curve from a sparse market Demonstrating blending and smoothing algorithms Computer-based exercise: Imply the discount factors from a swap curve Pricing a Range of Non-generic Interest Rate Swaps Yield curve swaps such as constant maturity swaps - Risk management characteristics Computer-based exercise: Price a CMS Mismatch Swaps What are the assumptions underlying the normal floating conventions Violating the conventions - In-arrears, average-rate and compound swaps - Overnight indexed swaps (OISs) such as EONIAs and RODS - Turbo swaps Convexity adjustment of normal swaps - Convexity adjustment of mismatch swaps - Convexity adjustment of CMS Day 2 Asset Packaging & a brief revision of IR options Asset Packaging Creating different packages: premium, par, discount Creating a par maturity package What’s really going on? Arbitrage between bond and swap valuation methods: the credit implications - Subsidisation effects - Forward valuing: how to include your cost of funding Practical details Computer-based exercise: Price an asset package Simple Caps and Floors A fundamental knowledge of Black’s model for pricing European-style interest rate options is assumed Generic, digital and spread caps Floors, collars, forward swaps and put-call parity Volatility surfaces and smiles Swaps with embedded caps and floors Computer-based exercise: Price a swap with embedded options Taking advantage of the multi-period structure: barriers, choosers and periodic caps Swaptions Pricing swaptions - Swaption smile spaces - Compatibility with cap pricing Swaps and embedded swaptions: pricing extendible and retractable swaps Computer-based exercise: Price an extendible step-up swap Structured Securities A very brief overview of the structured securities market - Description of some of the more common structures Day 3 Modelling structured products with embedded options Advanced Modelling Methodologies Analytic modelling - Example: swapping a range accrual note Computer-based exercise: Swapping a different range accrual note Numerical modelling - Outline: building an arbitrage-free forward interest rate tree - Brief discussion on the inclusion of a smile effect - Using the tree to model a complex security such as a Bermudan swap - How to model a callable range accrual Computer-based exercise: Modelling a callable swap Simulation - Building a BGM simulator - Using the simulation to model a range of complex securities, such as: - Path-dependent floating notes - TARNs - Index amortising swap - Callable snowball - Brief discussion on calibration and other techniques Computer-based exercise: Modelling a structured security Day 4 Risk Management of Swap and Option Portfolios Risk Management A fundamental knowledge of IR risk management is assumed How do interest rate curves behave? - Some empirical results Risk management reporting: - Construction of a delta and gamma reports for different curve movements - The concept of an equivalence Construction of a volatility report Hedging swap and option portfolios - The use of Taylor’s theorem - Delta hedging - Delta-gamma hedging - Delta-gamma-volatility hedging - Assessing hedge effectiveness using shocks and simulation - Construction of a theta report - Running a portfolio: funding and other issues - Control frameworks Computer-based exercise: Creating an effective hedge for a portfolio An outline of Value-at-Risk - Measuring VaR for a single risk factor - Extending this to two, and multiple, risk factors - Measuring VaR for a mixed swap/option portfolio Computer-based exercise: Building a minimum-VaR hedge for a portfolio Course summary and close
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