24. Investigate the moments of lnStDt=St under the risk-neutral probability. (a) Derive (9.95) using the expansion of

24. Investigate the moments of ln½StþDt=St under the risk-neutral probability.

(a) Derive (9.95) using the expansion of qðDtÞ in (9.88). (Hint: Only keep track of the terms in qðDtÞ and 1  qðDtÞ up to Oð

ffiffiffiffiffi Dt p Þ, since the higher order terms will be part of the error, O½Dt3=2, as will be confirmed next.)

(b) Demonstrate that this shift in the mean is caused only by the coe‰cient of ffiffiffiffiffi Dt p in the expansion of qðDtÞ, and that the higher order terms have no e¤ect on these moments larger than O½Dt3=2.

Assignment Exercises