FX Exotic Options

Day One

Review of the Fundamentals

Fundamentals

• Components of foreign exchange risk: forwards, swaps and vanilla options
• FX options market: who does what and why
• Software solutions: which vendor offers what: Fenics, SuperDerivatives, Bloomberg, Volmaster, Murex, ICY, Reuters

Pricing and Hedging in the Black-Scholes model

• Black-Scholes / Merton model in FX
• Derivation of the value of a call and put option
• Detailed discussion of the formula
• Greeks: delta, gamma, theta, rho, vega, vanna, volga, homogeneity and relationships among Greeks

Vanilla Options

• Put-call parity, put-call symmetry, foreign domestic symmetry
• Quotation conventions in FX, ATM and delta-conventions
• Dates: trade day, premium payment day, exercise/expiration time, settlement day
• Settlement, spreads, deal processing, counterparty risk
• Exotic features: deferred payment, contingent payment, deferred delivery, cash-settlement, American and Bermudan exercise rights, cut-offs and fixings
• Market Data: rates, forward points, swap points, spreads

Workshop: acquaint yourself with pricing software and market quotes

Volatility

• Implied vs. historic
• Quotation in terms of deltas
• Volatility cones
• Volatility smile: term-structure, skew, risk reversals and butterflies
• Volatility sources
• Interpolation and extrapolation across the volatility smile surface: SABR, vanna-volga, Reiswich-Wystup
• Forward volatility

Workshop: Build your own interpolation tool for volatility smile, calculate Greeks in terms of deltas, hedging volatility risk, deriving the strike from the delta with smile

Structuring with Vanilla Options

• Risk reversal and participating forward
• Spreads and seagulls
• Straddles, strangles, butterflies, condors
• Digital options

Workshop: Structure your own seagull. Include sales margin. Solve for zero-cost. Calculate delta and vega hedge. Discuss bid-ask spread. Analyze smile effect.

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Day Two

Structuring and Vanna-Volga-Pricing

First Generation Exotics: Products, Pricing and Hedging

• Digital options: European and American style, single and double barrier
• Barrier options: single and double, knock-in and knock-out, KIKOs, exotic barrier options
• Compound and instalment
• Asian options: options on the geometric, arithmetic and harmonic mean
• Power, lookback, chooser, paylater

Workshop: Hedging a knock-out with a risk reversa. Build your own semi-static hedging tool, discuss forward volatility risk

Applications in Structuring

• Dual currency and other FX-linked deposits
• Structured forwards: shark forward, bonus forward, range-reset forward
• FX-linked interest rate swaps and cross currency swaps
• Exotic spot and forward trades

Workshop: Structuring exercises: build structures, solve for zero cost, smile adjustment, bid-ask spreads

Vanna-Volga Pricing

• How higher order derivatives influence the price
• Vanna-volga pricing approach
• Case study: one-touch, one-touch moustache
• Discussion of model risk and alternatives: stochastic volatility

Workshop: Pricing of barrier options with smile

Overview of Market Models

• Stochastic volatility models
• Heston 93: model properties, calibrations, pricing, pros and cons
• Local Volatility: properties, pros and cons
• Stochastic Local Volatility Hybrid models

Super-Replication of barrier options: using leverage constraints and its first order approximation: the barrier shift. Mixing super-replication and vanna-volga.

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Day Three

Second Generation Exotics, Pricing and Hedging issues

The Pedigree of Barrier and Touch Options

Workshop and Discussion: how to construct the universe of barrier and touch options from key building blocks: vanilla and one-touch. Residual risk and limitations. Static, semi-static and dynamic hedging approaches.

Single Currency Exotics beyond Standard Barrier and Touch Options

• Exotic features in (vanilla) options: deferred payment, contingent payment, deferred delivery, cash-settlement, American and Bermudan exercise rights, cut-offs and fixings
• Exotic barrier and touch options
• Faders, corridors, accumulative forwards, target redemption forwards (TRFs)
• Forward start options, step-ups
• Time options
• Variance and Volatility Swaps

Workshop: Structure and price your own accumulative forward. Smile adjustment. Simulation tool for TRFs. Discussion of TRF hedging

Multi-Currency Exotics

• Product overview with applications: quanto options, baskets, spreads, best-ofs, outside barriers
• Correlation: implied correlations, correlation risk and hedging, currency triangles and tetrahedra
• Pricing in Black-Scholes model: analytic, binomial trees and Monte Carlo

Workshop: Pricing and correlation hedging a two-currency best-of: calculate your own sensitivities and hedge vega and correlation risk.

Long Term FX Options

• Development of Basis Spreads
• Product Range, FX-linked bonds, long-term vanilla and PRDCs
• Modelling approaches
• Discussion of risk features and modelling requirements