FRM Part I · FRM Exam Part I · Exotic Options
A basket option is written on an equally weighted portfolio of two stocks, each with a 25% volatility. A risk manager compares the option value when the correlation between the stocks is 0.9 versus 0.1, all other parameters unchanged. Which statement is correct for a basket call?
The basket call is worth more at correlation 0.9. Higher correlation means less diversification, so the basket's volatility is higher, about 24% versus about 17%, and a higher volatility increases the value of the call option.
- AThe call is worth more at correlation 0.9 because basket volatility is higherCorrect
- BThe call is worth more at correlation 0.1 because diversification raises the expected basket price
- CThe call has the same value because the stocks have equal volatilities
- DThe call is worth less at correlation 0.9 because the payoff becomes more predictable
Explanation
Basket variance = 0.25^2(0.25+0.25+2*0.25*rho)... rises with correlation. At rho 0.9 basket vol is about 24.4%, at rho 0.1 about 17.5%. Higher basket volatility raises option value. Diversification lowers volatility, not the expected price, which is unchanged.
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