The IFF School of Derivatives

This intensive course is designed primarily to provide detailed insights into the principles, methods and mathematical tools for understanding the analytics of derivatives structuring, use, valuation, control, and risk management. The emphasis is on better understanding of the intuition behind the analytics employed, and not the complex mathematics per se.

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MODULE 1: Yield Curves, Swaps & Interest Rate Derivatives

Yield Curve Derivatives: Hedging/Arbitraging Taxonomy, Markets Linkage & Overview

• Risk measures, concept of volatility & model-specific valuations
• Decomposition into simpler (fixed, floating, contingent) cash flows

Forward Rate Agreements (FRAs)

• FRAs, swaps & futures: convexity bias adjustment
• Computer Workshop: FRAs cash flows

Fundamentals of Yield Curve Construction, Interest Rate Swaps & Micro-Structure

• Computer Workshop: Swap fixed leg cash flows

Stochastic Floating Cash Flow Valuation (Some Key Results)

• Valuing unknown LIBOR cash flows
• Key strategic (static) replicating portfolio & exit strategies
• Forward rate method & spot-forward parity
• Principal (FRN, Synthetic Bond) Method

Swap Yield Curves & Zero-Coupon Valuation

• Par money market (spot LIBOR) and swaps (forward LIBOR) rates
• “Stripping” par-rates curve
• “Bootstrapping” zero-coupon bond price curve
• Audit checks: profit & loss: principal & forward rate methods
• Effective yield-to-maturity, zero-coupon bond yield curve
• Computer Workshop: Constructing annual swap
• Stripping “special” one-year semi-annual equivalent par rate
• Computer Workshop: Constructing semi-annual swap

Off-Market Swap Points

• Linear, geometric (log-linear), exponential & spline interpolations
• Computer Workshop: Exponential interpolation

Interest Rate Futures

• Forward rate, futures price/rate, convexity adjustment
• First futures stub rate, futures strip zero-coupon bond prices
• Computer Workshop: Bootstrapping futures strip zeros
• Integrating money, swap & futures curves
• Computer Workshop: Incorporating futures strip prices

Principal Component Analysis (PCA) & Swap Pricing

• Yield curves dynamics: Shifts, tilts & turns
• Correlation, factor components & volatility (cone) surface

FX Currency Swaps

• Equivalent bond positions
• Equivalent forward exchange positions
• Computer Workshop: Valuing FX currency swaps

Non-Standard & Off-Market Swaps

• Amortising swaps, accreting swaps & rollercoaster swaps
• Computer Workshop: Valuing existing off-market swaps
• Pricing LIBOR-in-arrears (DRS) interest rate swaps
• Limitations of forward rate method & volatility model

MODULE 2: Optionalities: Equity, FX & Interest Rate Options

Derivatives Contracts: Fundamental Building Blocks, Arbitrage Boundaries, Synthetics & Strategies

• Arbitrage boundaries & properties of option pricing
• Determinants of an option’s value
• Option strategies & payoffs
• Covered call writing – PERCS, DECS
  – M-KMV structural model of credit risk
  – Mertonian structural model of credit risk
• Protective puts: Portfolio insurance
• Put-call parity
  – Accounting, tax and regulatory arbitrage
  – Locking in unrealised speculative profits
  – Zero-cost collars
  – Capital structure arbitrage
  – Securitisation & CDOs

Computational Workshop Exercises: Structured Product Solutions, Embedding & Embedded Options

• Bank loan decisions (embedding options)
• Real estate and credit risk analysis (embedded options)
• Zero-cost collar
• Creative Security design embedded options
  – Explore creation of hybrid securities and contingent forms of payment & embedded optionalities
  – Tax, accounting & regulatory arbitrage

Derivatives Valuation: Concepts & Insights

• Overview of valuation model
• Intuitive concepts: Binomial option pricing model
  – Portfolio duplication (replication) approach
  – Self-financing strategy approach
  – Risk-neutral (martingale) probability approach
• Computer Workshop: Binomial option pricing model
• Black–Scholes option pricing mode
• Options insights of valuation and risk management
• Computer Workshop: Black–Scholes option pricing model

Understanding Options Risk: Stock Exposure (Delta)

• Delta hedging/replication as cost of option
• Monte-Carlo simulation: Delta-neutral hedging strategy
• Computer Workshop: Delta-neutral exit strategy cost

Volatility (Convexity) Risk Mechanics

• Delta-neutral long volatility trade and hedged portfolio
• Mechanics and essence of buying volatilities (long gamma)
• Time-decay (Theta) effects of delta and gamma
• Computer Workshop: Long volatility (Gamma) trading

FX Currency Options

• Arbitrage bounds, zero-cost collars, risk reversals, butterflies
• Structured products and implications for corporate treasurers
• Binomial and Black–Scholes (Garman-Kolhagen) valuation
• Exotic currency options
• Computer Workshop: Pricing FX options

Interest Rate, Yield Curve Volatilities & Options: Portfolio of Options on FRAs

• Interest rate options: Caps/floors
  – Valuation of caps: Black’s (1976) market model
  – Valuation of interest rate floors: Cap/floor-swap parity
  – Computer Workshop: Pricing interest rate caps and floors
         * Using flat brokers’ (market’s) volatilities
         * Using term-structure of volatilities (volatility surface)

Option on Portfolio of FRAs (Swaps)

• Options on interest rate swaps: Swaptions
  – Black (1976) market model valuation of payers/receiver swaptions
  – Computer Workshop: Pricing swaptions
         *Hedging cap with swaptions

Volatility Surface Asymptotics

• Volatility skews, volatility smile effects
• Stochastic Alpha Beta Rho (SABR) Black (1976) model

Yield Curve Models: Motivation

• Inconsistencies in applying Black–Scholes/Black (1976) models
• Black (1976) cap/floor pricing bias & convexity adjustment
• Effects of interest rate volatility on bond prices
• Computer Workshop: Yield curve model & convexity adjustment

Derivatives Pricing Tools: Fundamental Theorem

• Applied to interest rates & fixed-income options
• Arrow–debreu state primitive prices (stochastic discount function)
• State prices, risk-neutral & martingale probabilities

Yield Curves Models

• Equilibrium and fitting no-arbitrage models
  – Vasicek, Cox–Ingersoll–Ross (CIR), Ho–Lee, Hull–White, Black–Derman–Toy (BDT) & HJM/BGM LIBOR Market Model (LMM)

Implementing & Calibrating Yield Curve Models: One-Factor Models

Black-Derman-Toy (BDT) Model: Implementation

• Main features of BDT model
• Term structures of interest rates and volatilities

Black-Derman-Toy (BDT) Model: Applications

• Valuing interest rate options: Caps/floors
• Valuing European coupon bond options
• Valuing Bermudan coupon bond options
• Valuing payer/receiver swaptions
• Valuing swaps and bonds with BDT model

Computer Workshops:

• Constructing Black-Derman–Toy (BDT) yield curve model
• Valuing interest rate caps, bond options, swaptions, futures
• Valuing Bermudan options, interest rate swaps
• Comparison of BDT & Black (market) models – onvexity adjustment

MODULE 3: Credit Risk Derivatives Models

Credit Default Swaps (CDS): Structure, Pricing & Hedging

• Decomposing defaultable risky bond
• Isolating underlying default (credit) risk using swap/CDS
• Adding swap floating LIBOR-based payments
• Pricing the CDS premium leg & protection leg

Computer Workshop: Pricing Single-Named CDSs

Main Uses of Credit Derivatives

Mertonian/KMV Structural Model (Firm Assets) Approach

• Embedded complexities of interim cash flows
  – Effects of dividends on default risk
  – Effects of capital structure on default risk
  – Effects of investments on default risk
• Recapitalisation effects

Computer Workshop: Mertonian/KMV Binomial Models

Credit (default) risk measurement spreadsheet based on the mertonian option pricing methodology, and study the effects of dividend, capital structure and investment policies on default risk

Jarrow–Turnbull (JT) Reduced-Form (Intensity- Based) Model: Applying Term Structure Models

• Stochastic term structure of default–free interest rates
• The Markov process for credit ratings
• Stochastic maturity specific credit-risk spread
• Implementing a discrete-time Markov model
  – Pricing credit risky bonds
  – Pricing options on credit risky bonds
  – Pricing vulnerable derivatives
  – Credit Default Swaps (CDS)

Computer Workshop: Jarrow–Turnbull Reduced-Form Model

This unique residential course:

• Provides a unifying framework for understanding the two most influential analytical tools underpinning derivatives market valuation and products
  - model-free swaps (forwards)
  - model-dependent option
• Will be taught in a series of connected modules that focus on applicable techniques, whilst remaining analytically and mathematically rigorous and in an accessible manner
• Emphasises the economic intuition behind the key theoretical concepts, apparatus and vocabulary of derivatives
• Distils the subtleties and essence of derivatives use and valuation tools, bridging the gap between theory and practice
• Uses numerous worked examples set in a real-life context using actual historical market prices
• Demystifies difficult concepts illustrated throughout with concrete examples and worked through by extensive modelling using Excel spreadsheet applications