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Chapter 9. Dynamic Hedging

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Trading and Pricing Financial Derivatives
This chapter is in the book Trading and Pricing Financial Derivatives
Chapter 9 Dynamic HedgingDynamic hedging is an approach used by options traders to hedge their options positions. Because this approach involves adjusting the hedge as the underly-ing asset moves, it is referred to as dynamic hedging. While dynamic hedging is important to understand as a hedging technique, it is more important to under-stand it because of the link between this hedging technique and options pricing theory. Once you understand how dynamic hedging works, you can understand how the various options pricing techniques work and understand why options traders think about options as volatility bets rather than bets on the future price of an underlying security.A replicating portfolio for a given asset or series of cash flows is a portfolio of assets designed to replicate the cash flows or market values of another asset in all market scenarios. The idea is that if you can find a replicating portfolio for a given asset, this portfolio must then be priced the same as the asset it replicates, otherwise an arbitrage opportunity would exist. If there is a replicating portfolio for an option made up of the underlying stock and a bond for example, we can then use the prices of those instruments to work out the fair value of our option. If the replicating portfolio requires constant adjustment (dynamic hedging) then the price of the option should relate to the cost of creating this dynamic portfolio.Replicating portfolios can occur in two ways: static replication, where the portfolio has the same cash flows as the asset in question and no changes to the portfolio need to be made to maintain this; and dynamic replication, where the stand alone portfolio does not necessarily have the same cash flows as the asset It seeks to replicate, but once the trading strategy underlying the replication is followed the cashflows of the portfolio match the cashflows of the underlying asset perfectly. Dynamic replication requires continual adjustment, as the asset and portfolio are only assumed to behave similarly for small market movements. The notion of a replicating portfolio is fundamental to options pricing, which assumes that market prices are arbitrage-free as arbitrage opportunities are exploited by constructing replicating portfolios and trading one against the other to profit from price discrepancies.One of the most important things to understand about call and put options and their pricing is that their payoffs can be replicated by following a trading strategy in the underlying—without entering into an options position at all. This trading strategy, which we touched on earlier is known as dynamic replication. The fact that this can be done validates our methods of option pricing, and allows a trader or arbitrageur to generate an offsetting (hedging) set of cash flows pre-DOI 10.1515/9781547401161-009
© 2018 Walter de Gruyter GmbH, Berlin/Munich/Boston

Chapter 9 Dynamic HedgingDynamic hedging is an approach used by options traders to hedge their options positions. Because this approach involves adjusting the hedge as the underly-ing asset moves, it is referred to as dynamic hedging. While dynamic hedging is important to understand as a hedging technique, it is more important to under-stand it because of the link between this hedging technique and options pricing theory. Once you understand how dynamic hedging works, you can understand how the various options pricing techniques work and understand why options traders think about options as volatility bets rather than bets on the future price of an underlying security.A replicating portfolio for a given asset or series of cash flows is a portfolio of assets designed to replicate the cash flows or market values of another asset in all market scenarios. The idea is that if you can find a replicating portfolio for a given asset, this portfolio must then be priced the same as the asset it replicates, otherwise an arbitrage opportunity would exist. If there is a replicating portfolio for an option made up of the underlying stock and a bond for example, we can then use the prices of those instruments to work out the fair value of our option. If the replicating portfolio requires constant adjustment (dynamic hedging) then the price of the option should relate to the cost of creating this dynamic portfolio.Replicating portfolios can occur in two ways: static replication, where the portfolio has the same cash flows as the asset in question and no changes to the portfolio need to be made to maintain this; and dynamic replication, where the stand alone portfolio does not necessarily have the same cash flows as the asset It seeks to replicate, but once the trading strategy underlying the replication is followed the cashflows of the portfolio match the cashflows of the underlying asset perfectly. Dynamic replication requires continual adjustment, as the asset and portfolio are only assumed to behave similarly for small market movements. The notion of a replicating portfolio is fundamental to options pricing, which assumes that market prices are arbitrage-free as arbitrage opportunities are exploited by constructing replicating portfolios and trading one against the other to profit from price discrepancies.One of the most important things to understand about call and put options and their pricing is that their payoffs can be replicated by following a trading strategy in the underlying—without entering into an options position at all. This trading strategy, which we touched on earlier is known as dynamic replication. The fact that this can be done validates our methods of option pricing, and allows a trader or arbitrageur to generate an offsetting (hedging) set of cash flows pre-DOI 10.1515/9781547401161-009
© 2018 Walter de Gruyter GmbH, Berlin/Munich/Boston

Chapters in this book

  1. Frontmatter I
  2. About De/G PRESS V
  3. Contents VII
  4. Chapter 1. Introduction to Derivatives 1
  5. Chapter 2. Futures & Forwards 11
  6. Chapter 3. Introduction to Options 27
  7. Chapter 4. Simple Options Trading Strategies 45
  8. Chapter 5. Options Pricing History 63
  9. Chapter 6. Binomial Tree Valuation 69
  10. Chapter 7. The Black-Scholes Model 85
  11. Chapter 8. Option Sensitivities—The Greeks 97
  12. Chapter 9. Dynamic Hedging 111
  13. Chapter 10. Options on Indices, Futures, and Foreign Exchanges 121
  14. Chapter 11. Volatility Smiles 127
  15. Chapter 12. Volatility & Variance Swaps 137
  16. Chapter 13. The Monte Carlo Method 145
  17. Chapter 14. Exotics 149
  18. Chapter 15. Interest Rate Swaps 157
  19. Chapter 16. Risk Management and Value at Risk 177
  20. Chapter 17. Credit Derivatives 191
  21. Chapter 18. Structured Products 207
  22. Chapter 19. Optionality in Corporate Structures 215
  23. Chapter 20. Real Options 225
  24. Index 231
Readers are also interested in:
https://doi.org/10.1515/9781547401161-009

Chapters in this book

  1. Frontmatter I
  2. About De/G PRESS V
  3. Contents VII
  4. Chapter 1. Introduction to Derivatives 1
  5. Chapter 2. Futures & Forwards 11
  6. Chapter 3. Introduction to Options 27
  7. Chapter 4. Simple Options Trading Strategies 45
  8. Chapter 5. Options Pricing History 63
  9. Chapter 6. Binomial Tree Valuation 69
  10. Chapter 7. The Black-Scholes Model 85
  11. Chapter 8. Option Sensitivities—The Greeks 97
  12. Chapter 9. Dynamic Hedging 111
  13. Chapter 10. Options on Indices, Futures, and Foreign Exchanges 121
  14. Chapter 11. Volatility Smiles 127
  15. Chapter 12. Volatility & Variance Swaps 137
  16. Chapter 13. The Monte Carlo Method 145
  17. Chapter 14. Exotics 149
  18. Chapter 15. Interest Rate Swaps 157
  19. Chapter 16. Risk Management and Value at Risk 177
  20. Chapter 17. Credit Derivatives 191
  21. Chapter 18. Structured Products 207
  22. Chapter 19. Optionality in Corporate Structures 215
  23. Chapter 20. Real Options 225
  24. Index 231
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