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Article

Pricing an Accumulator with Continuous or Discrete Barrier

Ling Xin, Philip L.H. Yu and Kin Lam
The Journal of Derivatives Summer 2017, 24 (4) 93-107; DOI: https://doi.org/10.3905/jod.2017.24.4.093
Ling Xin
is an assistant professor in the Division of Business and Management at BNU–HKBU United International College in Zhuhai, China
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Philip L.H. Yu
is an associate professor in the Department of Statistics and Actuarial Science at the University of Hong Kong in Pokfulam, Hong Kong
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Kin Lam
is a professor emeritus in the Department of Finance and Decision Science at Hong Kong Baptist University in Kowloon, Hong Kong
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Abstract

The low interest rate environment of recent years has sent many investors looking for ways to enhance returns. This has stimulated the creation of investment products with what were once known as “exotic” payoff patterns. These products tend to involve exposure to a risky security like a stock index, overlaid with a combination of guarantees and barriers designed to appeal to the target investor audience. Small investors, and many fiduciaries such as small pension funds, are rarely in a position to evaluate the highly path-dependent payoffs on such securities. In this article, the authors analyze a somewhat different product, the “accumulator” contract. This product is actually a formalized plan to build up a holding in some specific asset, typically a stock, through a series of purchases over time. In a typical example, the buyer commits to buy some number X of shares per day at a fixed price that is initially set below the current market price. If the market price subsequently falls below the contract price, the required purchase amount is doubled. But if the market price goes too far above the strike price, the contract terminates. The article presents valuation formulas for some standard variants and shows empirically that accumulator contracts are priced in the market at levels that tend to be quite favorable to the issuer.

  • © 2017 Institutional Investor, Inc.
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The Journal of Derivatives: 24 (4)
The Journal of Derivatives
Vol. 24, Issue 4
Summer 2017
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Pricing an Accumulator with Continuous or Discrete Barrier
Ling Xin, Philip L.H. Yu, Kin Lam
The Journal of Derivatives May 2017, 24 (4) 93-107; DOI: 10.3905/jod.2017.24.4.093

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Pricing an Accumulator with Continuous or Discrete Barrier
Ling Xin, Philip L.H. Yu, Kin Lam
The Journal of Derivatives May 2017, 24 (4) 93-107; DOI: 10.3905/jod.2017.24.4.093
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  • Article
    • Abstract
    • ACCUMULATOR’S SETTLEMENT, BARRIER, AND LEVERAGE
    • ACCUMULATOR WITH CONTINUOUS BARRIER AND IMMEDIATE SETTLEMENTS
    • ACCUMULATOR WITH CONTINUOUS BARRIER AND PERIODIC SETTLEMENTS
    • ACCUMULATOR WITH DISCRETE BARRIER
    • ANALYZING A SAMPLE ACCUMULATOR: HOW GOOD IS THE APPROXIMATION TO A DISCRETE BARRIER?
    • FAIR VALUE AND FAIR STRIKE PRICE
    • IMPLIED VOLATILITY
    • DURATION, PROFIT DISTRIBUTION, AND THE GREEK LETTERS
    • CONCLUSION AND NEW DEVELOPMENTS
    • APPENDIX A
    • APPENDIX B
    • APPENDIX C
    • REFERENCES
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