# Derivative Essay

Preface To The First Edition.

**Section One. Derivatives And Their Markets.**

Essay 1. The Structure Of Derivative Markets.

Essay 2. A Brief History Of Derivatives.

Essay 3. Why Derivatives?

Essay 4. Forward Contracts And Futures Contracts.

Essay 5. Options.

Essay 6. Swaps.

Essay 7. Types Of Risks.

**Section Two. The Basic Instruments.**

Essay 8. Interest Rate Derivatives: FRAs And Options.

Essay 9. Interest Rate Derivatives: Swaps.

Essay 10. Currency Swaps.

Essay 11. Structured Notes.

Essay 12. Securitized Instruments.

Essay 13. Equity Swaps.

Essay 14. Equity-Linked Debt.

Essay 15. Commodity Swaps.

Essay 16. American Versus European Options.

Essay 17. Swaptions.

Essay 18. Credit Derivatives.

Essay 19. Volatility Derivatives.

Essay 20. Weather And Environmental Derivatives.

**Section Three. Derivative Pricing.**

Essay 21. Forward And Futures Pricing.

Essay 22. Put-Call Parity For European Options On Assets.

Essay 23. Put-Call Parity For American Options On Assets.

Essay 24. Call Options As Insurance And Margin.

Essay 25. A Nontechnical Introduction To Brownian Motion.

Essay 26. Building A Model Of Brownian Motion In The Stock Market.

Essay 27. Option Pricing: The Black-Scholes-Merton Model.

Essay 28. Option Pricing: The Binomial Model.

Essay 29. Option Pricing: Numerical Methods.

Essay 30. Dynamic Option Replication.

Essay 31. Risk-Neutral Pricing Of Derivatives: I.

Essay 32. Risk-Neutral Pricing Of Derivatives: II.

Essay 33. It's All Greek To Me.

Essay 34. Implied Volatility.

Essay 35. American Call Option Pricing.

Essay 36. American Put Option Pricing.

Essay 37. Swap Pricing.

**Section Four. Derivative Strategies.**

Essay 38. Asset Allocation With Derivatives.

Essay 39. Protective Puts And Portfolio Insurance.

Essay 40. Misconceptions About Covered Call Writing.

Essay 41. Hedge Funds And Other Privately Managed Accounts.

Essay 42. Spreads, Collars, And Prepaid Forwards.

Essay 43. Box Spreads.

**Section Five. Exotic Instruments.**

Essay 44. Barrier Options.

Essay 45. Straddles And Chooser Options.

Essay 46. Compound And Installment Options.

Essay 47. Digital Options.

Essay 48. Geographic Options.

Essay 49. Multi-Asset Options.

Essay 50. Range Forwards And Break Forwards.

Essay 51. Lookback Options.

Essay 52. Deferred Start And Contingent Premium Options.

**Section Six. Fixed Income Securities And Derivatives.**

Essay 53. Duration.

Essay 54. Limitations Of Duration And The Concept Of Convexity.

Essay 55. The Term Structure Of Interest Rates.

Essay 56. Theories Of The Term Structure: I.

Essay 57. Theories Of The Term Structure: II.

Essay 58. Simple Models Of The Term Structure: Vasicek And Cox-Ingersoll-Ross.

Essay 59. No-Arbitrage Models Of The Term Structure: Ho-Lee And Heath-Jarrow-Morton.

Essay 60. Tree Pricing Of Bond And Interest Rate Derivatives: I.

Essay 61. Tree Pricing Of Bonds And Interest Rate Derivatives: II.

Essay 62. Tree Pricing Of Bonds And Interest Rate Derivatives: III.

Essay 63. Tree Pricing Of Bonds And Interest Rate Derivatives: IV.

Essay 64. Tree Pricing Of Bonds And Interest Rate Derivatives: V.

**Section Seven. Other Topics And Issues.**

Essay 65. Stock Options.

Essay 66.Value At Risk.

Essay 67. Stock As An Option .

Essay 68. The Credit Risk Of Derivatives.

Essay 69. Operational Risk.

Essay 70. Risk Management In An Organization.

Essay 71. Accounting And Disclosure Of Derivatives.

Essay 72. Worst Practices In Derivatives.

Essay 73. Best Practices In Derivatives.

Recommended Reading.

Answers To End-Of-Essay Questions.

I want to talk about the definition of the derivative. Now the definition of the derivative is related to the topics of average rate of change and the instantaneous rate of change. An average rate of change is really fundamental to the idea of derivative, let's start average rate of change, we call it average rate of change of a function is the slope of the secant line drawn between two points on the function. And the slope of secant line like any other slope of a line is going to be rise over run. Now if you notice I got these two points labeled with coordinates the rise is going to be f of a plus h minus f of a. And the run is going to be a+h-a, which is just h. And that's why the slope of the secant line if f of a plus h-f of a over h.

This is the slope of secant line which is the average rate of change of the function. Now instantaneous rate of change is what happens when we take the average rate of change over shorter and shorter increments of time. So we're letting h go to zero and as we do the secant line gets closer and closer to the tangent line, that's what this is. Now the way we do that is the way we get h to go to zero is we take limits. So the limit as h goes to zero of the average rate of change of f of a plus h minus f of a over h and taking the limit of that average rate of change is what gives us the instantaneous rate of change. This quantity is so important to Calculus it's given a much simpler symbol f prime of a this is the derivative of the function f at a and this symbol means the limit is h approaches zero of f of a plus h minus f of a over h. This concept is central to all of differential Calculus which is half of what we're going to do in this course.

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