FX Options and Smile Risk 1st Edition by Antonio Castagna ISBN 978-0470754191 0470754192
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ISBN 10: 0470754192
ISBN 13: 978-0470754191
Author: Antonio Castagna
The FX options market represents one of the most liquid and strongly competitive markets in the world, and features many technical subtleties that can seriously harm the uninformed and unaware trader.
This book is a unique guide to running an FX options book from the market maker perspective. Striking a balance between mathematical rigour and market practice and written by experienced practitioner Antonio Castagna, the book shows readers how to correctly build an entire volatility surface from the market prices of the main structures.
Starting with the basic conventions related to the main FX deals and the basic traded structures of FX options, the book gradually introduces the main tools to cope with the FX volatility risk. It then goes on to review the main concepts of option pricing theory and their application within a Black-Scholes economy and a stochastic volatility environment. The book also introduces models that can be implemented to price and manage FX options before examining the effects of volatility on the profits and losses arising from the hedging activity.
Coverage includes:
how the Black-Scholes model is used in professional trading activity
the most suitable stochastic volatility models
sources of profit and loss from the Delta and volatility hedging activity
fundamental concepts of smile hedging
major market approaches and variations of the Vanna-Volga method
volatility-related Greeks in the Black-Scholes model
pricing of plain vanilla options, digital options, barrier options and the less well known exotic options
tools for monitoring the main risks of an FX options’ book
Table of contents:
1 The FX Market
1.1 FX rates and spot contracts
1.2 Outright and FX swap contracts
1.3 FX option contracts
1.3.1 Exercise
1.3.2 Expiry date and settlement date
1.3.3 Premium
1.3.4 Market standard practices for quoting options
1.4 Main traded FX option structures
2 Pricing Models for FX Options
2.1 Principles of option pricing theory
2.1.1 The Black–Scholes economy
2.1.2 Stochastic volatility economy
2.1.3 Change of numeraire
2.2 The Black–Scholes model
2.2.1 The forward price to use in the formula
2.2.2 BS greeks
2.2.3 Retrieving implied volatility and strike
2.2.4 Some relationships of the BS formula
2.3 The Heston Model
2.3.1 Time-dependent parameters in the Heston model
2.4 The SABR model
2.5 The mixture approach
2.5.1 The LMLV model
2.5.2 The LMUV model
2.5.3 Features of the LMLV and LMUV models and a comparison between them
2.5.4 Extension of the LMUV model
2.6 Some considerations about the choice of model
3 Dynamic Hedging and Volatility Trading
3.1 Preliminary considerations
3.2 A general framework
3.3 Hedging with a constant implied volatility
3.4 Hedging with an updating implied volatility
3.4.1 A market model for the implied volatility
3.5 Hedging Vega
3.6 Hedging Delta, Vega, Vanna and Volga
3.6.1 Vanna–Volga hedging with one implied volatility
3.6.2 Vanna–Volga hedging with different implied volatilities
3.7 The volatility smile and its phenomenology
3.8 Local exposures to the volatility smile
3.8.1 Retrieving the strikes of the main structures
3.8.2 ATM straddle exposures
3.8.3 Risk reversal exposures
3.8.4 Vega-weighted butterfly exposures
3.9 Scenario hedging and its relationship with Vanna–Volga hedging
3.9.1 Scenario hedging with constant Delta options
4 The Volatility Surface
4.1 General definitions
4.1.1 Arbitrage opportunities under the three different rules
4.2 Criteria for an efficient and convenient representation of the volatility surface
4.3 Commonly adopted approaches to building a volatility surface
4.4 Smile interpolation among strikes: the Vanna–Volga approach
4.4.1 The Vanna–Volga approach: general setting
4.4.2 Computing the Vanna–Volga weights and option prices
4.4.3 Limit and no-arbitrage conditions
4.4.4 Approximating implied volatilities
4.5 Some features of the Vanna–Volga approach
4.5.1 Hedging error for longer expiries
4.5.2 The implied risk-neutral density and smile asymptotics
4.5.3 Two consistency results
4.6 An alternative characterization of the Vanna–Volga approach
4.7 Smile interpolation among expiries: implied volatility term structure
4.8 Admissible volatility surfaces
4.9 Taking into account the market butterfly
4.10 Building the volatility matrix in practice
5 Plain Vanilla Options
5.1 Pricing of plain vanilla options
5.1.1 Delayed settlement date
5.1.2 Cash settlement
5.2 Market-making tools
5.2.1 Inferring the implied volatility for a given strike
5.2.2 Inferring the implied volatility for a given Delta
5.2.3 Quoting the Vega-weighted butterfly and the risk reversal
5.3 Bid/ask spreads for plain vanilla options
5.4 Cutoff times and spreads
5.5 Digital options
5.5.1 Digital options pricing: the static replica approach
5.5.2 Digital options pricing in specific model settings
5.5.3 Delayed cash settlement date
5.5.4 Bid/ask spreads
5.5.5 Quotation conventions
5.6 American plain vanilla options
5.6.1 Valuation of American plain vanilla options in a BS setting
5.6.2 Pricing of American plain vanilla options with the volatility smile
6 Barrier Options
6.1 A taxonomy of barrier options
6.2 Some relationships of barrier option prices
6.3 Pricing for barrier options in a BS economy
6.3.1 The diffusion equation under single absorbing boundaries
6.3.2 Dealing with a constant barrier
6.4 Pricing formulae for barrier options
6.5 One-touch (rebate) and no-touch options
6.6 Double-barrier options
6.6.1 Two absorbing states
6.6.2 Pricing formula for double-barrier options
6.7 Double-no-touch and double-touch options
6.8 Probability of hitting a barrier
6.9 Greek calculation
6.10 Pricing barrier options in other model settings
6.11 Pricing barriers with non-standard delivery
6.11.1 Delayed settlement date
6.11.2 Cash settlement
6.12 Market approach to pricing barrier options
6.12.1 Inclusion of the smile: the Vanna–Volga approach for barrier options
6.12.2 The Vanna–Volga approach for barrier options: variations on the theme
6.12.3 Slippage at the barrier level
6.12.4 Delta-hedging near the barrier level
6.12.5 Implicit one-touch and gearing
6.12.6 Vega-hedge rebalancing
6.13 Bid/ask spreads
6.14 Monitoring frequency
7 Other Exotic Options
7.1 Introduction
7.2 At-expiry barrier options
7.3 Window barrier options
7.4 First–then and knock-in–knock-out barrier options
7.5 Auto-quanto options
7.6 Forward start options
7.6.1 Including the volatility smile in the pricing
7.6.2 Forward implied volatility smiles
7.6.3 Forward start barrier and bet options
7.6.4 Dealing with notional amounts expressed in numeraire currency
7.7 Variance swaps
7.8 Compound, Asian and lookback options
8 Risk Management Tools and Analysis
8.1 Introduction
8.2 Implementation of the LMUV model
8.2.1 The forward volatility surfaces
8.2.2 Calculating the sensitivity to the movements of the volatility surface
8.3 Risk monitoring tools
8.3.1 FX spot rate-related Greeks
8.3.2 Cash-settled options
8.3.3 Volatility-related Greeks and sensitivities
8.3.4 Barrier implicit one-touch, bets and digitals
8.3.5 Interest rate-related Greeks
8.4 Risk analysis of plain vanilla options
8.4.1 ATM straddle
8.4.2 Risk reversal
8.4.3 Vega-weighted butterfly
8.5 Risk analysis of digital options
8.6 Risk analysis of exotic options
8.6.1 Barrier options
8.6.2 Double barrier options
8.6.3 Bet options
9 Correlation and FX Options
9.1 Preliminary considerations
9.2 Correlation in the BS setting
9.3 Contracts depending on several FX spot rates
9.4 Dealing with correlation and volatility smile
9.4.1 Vanna–Volga extension
9.5 Linking volatility smiles
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Tags: Antonio Castagna, FX Options, Smile Risk