5.10.2005

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

this call option is selling for $3?

A: the call option is overpriced, so sell the option and buy the underlying. Suppose an investor sells 300 calls and buys 100 shares

  • The number of units of the underlying purchased for each option sold would be the hedge ratio: n = (c+ - c-) / (S+ - S-) = 0.3333.
  • The initial outlay would be 100 * $80 - 300 * $3 = $7100.
  • 6 months later, the portfolio value will be
    • S- - c- * n = 100 x $75 - 0 = $7500 * S+ - c+ * n = 100 x $90 - 300 * $5 = $7500
  • the six-month return is 7500/7100 - 1 = 5.63%, and the annualized return is (1.0563)^2 - 1 = 11.58% > the actual risk-free return of 6%

Bonus Points

  • If the call option is underpriced (selling for < $2.38), an investor would buy the option and sell short the underlying, which would generate cash up front. At expiration, the investor would have to pay back an amount less than 7%

Category: C++ Quant > Derivatives > Valuation

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