**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*

## No comments:

## Post a Comment