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Testing a Market-Linked CD for Arbitrage with Put-Call Parity

Article Quant Q&A · Author: Matthew Farant
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Summary

The document asks whether a two-year market-linked certificate of deposit offers an arbitrage opportunity. Its payoff combines a guaranteed principal with a stated interest rate and a fraction of the gain in a non-dividend-paying stock. The question supplies the stock price, risk-free rate, and premium of an at-the-money put, then invokes put-call parity to estimate the corresponding call value and asks how to compare that option with the certificate.

The setup points toward decomposing the structured payoff into a zero-coupon bond and an equity call, then comparing the cost of that replicating portfolio with the certificate's price. However, the document contains no answer or explicit arbitrage trades, and the certificate's issue price is not stated. Thus it raises the valuation question but does not establish mispricing or provide evidence that an arbitrage can be executed. The parity calculation and replication comparison would need to be checked using the full payoff and relevant prices.

Key ideas

  • A principal-protected equity-linked certificate can be analyzed by decomposing its payoff into fixed-income and option components.
  • Put-call parity can help infer a call value from a put price under matching contract assumptions.
  • An arbitrage claim requires comparing the certificate's price with the cost of a replicating portfolio.
  • The document gives a valuation question but no solution or demonstrated arbitrage trade.

Tags

OptionsFixed incomeArbitrageDerivatives pricing
Full text
# How to Show an Arbitrage Opportunity Exist From a Market-Linked CD?


# How to Show an Arbitrage Opportunity Exist From a Market-Linked CD?












A bank issues a market-linked CD that guarantees the original principal with an interest at an effective annual rate of 2%, plus 70% of the percentage gain on the ABC Inc. non-dividend-paying stock price over a two-year period. At the time the CD is issued, a share of ABC Inc. is worth USD 118.60, and the risk-free annual interest rate is 5%. Currently, the premium of an at-the-money put option on a share of ABC Inc. is USD 3. Show that an arbitrage opportunity exists from the CD offered by the bank, and explain your strategy to exploit the arbitrage opportunity!

My argument: According to the put-call parity, the fair price of an ATM 118.6-strike call option is USD 14.28. And we all know that a CD has the same payoff as combining a bond and call option. But how do I compare the price of the CD and the fair price of the ATM call option? I'm kind of lost here, please help...

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.