Iain Clark is a foreign exchange option pricing expert. A guide for practitioners.

Foreign exchange options are covered in this book. It contains everything a quant or trader working in a bank or hedge fund would need to know about the mathematics of foreign exchange, not just the theoretical mathematics covered in other books but also comprehensive coverage of implementation, pricing and calibration.

With input from traders and examples using real-world data, this book introduces many of the more commonly requested products from FX options trading desks, together with the models that capture the risk characteristics necessary to price these products accurately. The numerical methods required for calibration of these models are described in this book, an area that is often neglected in the literature. Thorough treatment is given in one unified text.

• Correct market conventions for FX volatility surface construction
• Adjustment for settlement and delayed delivery of options
• Pricing of vanillas and barrier options under the volatility smile
• Barrier bending for limiting barrier discontinuity risk near expiry
• Industry strength partial differential equations in one and several spatial variables using finite differences on nonuniform grids
• Fourier transform methods for pricing European options using characteristic functions
• Stochastic and local volatility models, and a mixed stochastic/local volatility model
• Three-factor long-dated FX model
• Numerical calibration techniques for all the models in this work
• The augmented state variable approach for pricing strongly path-dependent options using either partial differential equations or Monte Carlo simulation

This is the essential guide to foreign exchange options in the real financial marketplace.

TABLE OF CONTENTS

Acknowledgements

There is a list of tables.

There is a list of figures.

The introduction is 1

A gentle introduction to the markets.

There are 2 Quotation Styles.

There are 5 risk considerations.

Spot settlement rules

Expiry and delivery rules

Expiry and delivery rules can be days or weeks.

Expiry and delivery rules can be months or years.

Cutoff times 10

There are 2 mathematical preliminaries.

The Black–Scholes Model 13 is a model.

The Black–Scholes model 13 has some assumptions.

Risk Neutrality 13

The Black– Scholes equation wasDerived.

The SDE for ST 17 has been integrated.

There are 2.5 black–cholesterol PDEs in Logspot 18.

Risk-neutral Expectation 18 is about Feynman–Kac.

Risk Neutrality and the Presumption of Drift 20

There is a valuation of European options.

There are 26 forwards.

The law of one price.

The Black– Scholes Term Structure is a model.

Breeden–Litzenberger analysis 30

European Digitals 31

Settlement Adjustments 32.

There were 33 delayed delivery adjustments.

Pricing using Fourier Methods 35

One numerical integral 37 is involved in European option pricing.

More than Fat Tails 38 is the name of the disease.

There are 3 Deltas and Market Conventions.

Quote style conversions are 41.

The law of many Deltas.

There are 47 Delta Conventions.

Market Volatility Surfaces 49.

At-the-Money 50

Market Strangle 53.

The example is EURUSD 1Y 55.

Risk Reversal and Smile Strangle are included.

There is a visualisation of strangles.

Polynomial in Delta 59 is referred to as smile Interpolation.

SABR 60 is 3.10 smile Interpolation.

Remarks 62 were concluded by 3.11

There are 4 Volatility Surface Constructions.

The Flat Forward Interpolation 65 is based on the Volatility Backbone.

There is a surface temporal correlation.

The Holidays and Weekends are 70.

There are temporal effects on the volatility surface.

Implied and local volatility are included.

The introduction 77

The Fokker–Planck Equation is 78.

The construction of local volatility was done by Dupire.

There is a relationship between implied volcker and local volcker.

There is local volatility as a condition of expecting.

Local volatility for the markets.

The PDE for Local Volatility 89 is 5.7.

The Model 90 of the CEV.

There is asymptotic expansion.

The Stochastic Volatility is 95.

The introduction 95

Uncertain volatility 95.

There are 96 Stochastic Volatility Models.

Uncorrelated Stochastic Volatility is more than 100.

Spot108 is related to the Stochastic Volatility Correlated.

The Fokker–Planck PDE Approach is referred to as the Fokker–Planck PDE Approach.

The approach to the PDE is called the Feynman–Kac approach.

The LSV models have a number of variables.

There are 7 numerical methods for pricing and Calibration.

Implied Volatility Calculation 129 is a one-dimensional root finding.

Least squares minimisation 130

Simulation 131 of Monte Carlo.

There are 7.4 Convection–Diffusion PDEs in Finance.

There are 7.5 numerical methods for PDEs.

There is an explicit difference scheme.

There is an explicit difference on nonuniform meshes.

There is an implicit difference finite scheme.

The Crank–Nicolson scheme was used.

There are numerical schemes for multidimensional PDEs.

There are 173 schemes for practical nonuniform grid generation.

Further reading 176.

There are 8 first generation exotics.

There is a reflection principle.

European Barriers and Binaries 180

Binaries and Barriers are continuously monitored.

Double Barrier Products is a product.

There is a sensitivity to local and Stochastic Volatility.

Barrier bending 199.

Value Monitoring 202

There are 9 Second Generation Exotics.

Chooser options 206

Range options 206

There are 207 forward start options.

There are 204 lookback options.

There are Asian options.

Target redemption notes

There are Volatility and Variance swaps.

There are 10 multi currency options.

There are Correlations, Triangulation and Absence of Arbitrage.

Exchange options 229

Quantos 229

There are best-ofs and worst-ofs.

There are a number of basket options.

There are 241 numerical methods.

A note on Greeks.

There are 243 untradeable factors.

Further reading 244.

There are 11 longdated foreign exchange rates.

Currency swaps are 245.

There is a risk of Basis Risk.

The forward measure is 249.

The rate is in Arrears 250.

There are a lot of longdated products in the market.

There is a three-factor model.

The three-factor model has an interest rate Calibration.

The Three-Factor Model 259 has Spot FX Calibration.

The conclusion of 11.9

There are references to 265.

Further reading 271.

Index 273

AUTHOR INFORMATION

Dr. Iain J. Clark. The Head of Foreign Exchange Quantitative Analysis at Dresdner Kleinwort in London is responsible for developing pricing libraries for the front office. He was the Director of the Quantitative Research Group at Lehman Brothers and also worked at JP Morgan. He received his masters degree in mathematics from the University of Edinburgh, and his PhD in applied mathematics from the University ofQueensland, Australia. Dr Clark is a regular speaker at key finance events, and has presented at London Imperial College, The Bachelier Society Annual Conference, London Imperial College, world business Strategies annual Conference, Risk events, Marcus Evans events and many more.