5.10.2005

Q&A: How would investors exploit the arbitrage opportunity if...

this put option is selling for $4?

A: the put option is underpriced, so buy the option and the underlying. Suppose an investor buys 150 puts and 100 shares.

  • The number of units of the underlying purchased for each option sold would be the hedge ratio: n = (p+ - p-) / (S+ - S-) = 0.66.
  • The initial outlay would be 100 * $80 + 150 * $4 = $8600.
  • 6 months later, the portfolio value will be
    • S- + p- * n = 100 * $75 + 10 * 150 = $9000 * S+ + p+ * n = 100 x $90 + 0 * 150 = $9000
  • the six-month return is 9000/8600 - 1 = 4.6%, and the annualized return is (1.046)^2 - 1 = 9.4% > the actual risk-free return of 6%

Bonus Points

  • Unlike a call option, the arbitrage strategy for a under-priced put is to long positions in BOTH instruments.

Category: C++ Quant > Derivatives > Valuation

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