Asian Options: Practice Problems and Solutions

The Actuary's Free Study Guide for Exam 3F / Exam MFE - Section 52

This section of sample problems and solutions is a part of The Actuary's Free Study Guide for Exam 3F / Exam MFE, authored by Mr. Stolyarov.

This is Section 51 of the Study Guide. See Section 1 here. See Section 2 here. See Section 3 here. See Section 4 here. See Section 5 here. See Section 6 here. See Section 7 here. See Section 8 here. See Section 9 here. See Section 10

here. See Section 11 here. See Section 12 here. See Section 13 here. See Section 14 here. See Section 15 here. See Section 16 here. See Section 17 here. See Section 18 here. See Section 19 here. See Section 20 here. See Section 21 here. See Section 22 here. See Section 23 here. See Section 24 here. See Section 25 here. See Section 26 here. See Section 27 here. See Section 28 here. See Section 29 here. See Section 30 here. See Section 31 here. See Section 32 here. See Section 33 here. See Section 34 here. See Section 35 here. See Section 36 here. See Section 37 here. See Section 38 here. See Section 39 here. See Section 40 here. See Section 41 here. See Section 42 here. See Section 43 here. See Section 44 here. See Section 45 here. See Section 46 here. See Section 47 here. See Section 48 here. See Section 49 here. See Section 50 here. See Section 51 here.

An Asian option "has a payoff that is based on the average price over some period of time" (McDonald 2006, p. 444). An Asian option is thus, path-dependent in that the way in which the underlying stock reached its final price matters for determining the price of the option. An Asian tail refers to settling on the basis of the average price.

Asian options can be based on an arithmetic or a geometric average.

The formula for the arithmetic average of N stock prices is A(T) = (1/N)_i=1^NΣS_ih

The formula for the geometric average of N stock prices is G(T) = (S_h*S_2h*....*S_Nh)^(1/N)

It is always the case that G(T) ≤ A(T)

An Asian average price option occurswhen the average used is the asset price.