Question

The value of an Asian put option is computed using the geometric average strike. What is the expected payoff if the observed prices to date are 72,71, 72, 70, 68, 69, 68, and 70, respectively?

Answer 1

In case of Asian options the strike price can be calculated using arthimetic average or using geometric average.

Example of Arithmetic average is we have 3 numbers say 2, 4 and 8 so sithmetic avergae or simple average is 2+4+8/3= 14/3= 4.667

In geometic average it is (2*4*8)^1/3​ = cube root of 64 is 4 so formula for geometric average is ( 1*2*3*4*......n)^1/n ​we have 8 numbers above so we multiply all of them and take their 8th root either using MS excel or log tables.

In MS excel it is very easy just multiply all numbers and then result say 64 then press Shift+6 we get carrot sign(^) then take power 1/3 or 1/8 whatever root is needed example 64^1/3 for cube root.

Here Geometric Average is (72*71*72*70*68*69*68*70)^0.125 = (575421835161600)^0.125= 69.98 Here we take 1/8= 0.125 for calculation purpose.

So strike price is 69.98 and expected market price as on expiry are given as 72,71,72,70,68,69,68,70 respectively and Remeber here we are assuming to buy asian put means we have bought a right and not obligation to sell the underlying assest shares or other assets at strike price and strike price here is 69.98 so if Market price as on expiry is lower than this 69.98 then we would exercise the put option and sell at 69.98 otherwise we would not exercise the option and sell them at market prices which are higher than 69.98. Always remember Put option means we have bought a right to sell at strike price and we will exercise our right to sell at strike price if strike price at expiry or cut-off date is more than market price otherwise if market price is more we will not exercise and simply sell at market price which is higher than strike price. In this question Option premium is not given so pay off is given ignoring any option premium.

Strike price	Market Price	Exercise put option when Strike price > Market price	Pay off = Strike price - Market price
69.98	72	Not exercise	0
69.98	71	Not exercise	0
69.98	72	Not exercise	0
69.98	70	Not exercise	0
69.98	68	Exercise	1.98
69.98	69	Exercise	0.98
69.98	68	Exercise	1.98
69.98	70	Not exercise	0